Abstract

BabyIAXO is the intermediate stage of the International Axion Observatory program and will operate as a solar axion helioscope with low-background X-ray detectors installed on a moving, surface-level apparatus. For the Micromegas detector line, this operating scenario makes the control of cosmic-ray-induced backgrounds a central requirement. The expected axion signal consists of a small excess of keV X-rays focused onto the detector plane, so the detector response, event reconstruction, background normalization, and veto strategy must be understood at the level of the same observables used in data analysis.

This thesis develops simulation infrastructure and background-modeling tools for IAXO-D0 and BabyIAXO Micromegas detectors, with emphasis on detector-response-level Monte Carlo workflows, cosmic-ray and cosmic-neutron-induced backgrounds, and active-veto validation. The software work is based on REST-for-Physics and its Geant4 interface restG4, including workflow organization, source generation, detector-response chains, and large-scale production strategies. These tools are used to construct a background-model methodology in which source-specific simulations are propagated through common reconstruction and selection observables.

A major part of the work addresses the shielding and veto system required for surface operation. The studies show that passive shielding alone cannot fully suppress the high-energy neutron component, because cosmic neutrons can generate secondary cascades inside the lead shield. The resulting active-veto strategy combines prompt scintillator signals, delayed neutron-capture-related activity, and veto multiplicity in a multilayer plastic-scintillator and cadmium design. Waveform-level simulations predict strong rejection of muon-induced backgrounds and partial rejection of neutron- and proton-induced residuals after Micromegas cuts. Prototype data taken with the IAXO-D0 detector and veto system validate the prompt/delayed/multiplicity discrimination strategy, while also showing that an absolute neutron-veto efficiency measurement still requires a prototype-matched simulation and a more complete treatment of thresholds, timing, calibration, and source normalization.

The thesis therefore contributes to the transition from idealized energy-deposition simulations to reconstructed observables that can be compared with experimental data. It provides the software and analysis basis for a quantitative BabyIAXO detector-background model and identifies the main remaining uncertainties: cosmic-neutron normalization, DESY site dependence, hadronic modeling, detector-response calibration, veto thresholds, timing alignment, geometry details, and finite Monte Carlo statistics.

Resumen

BabyIAXO es la etapa intermedia del programa del International Axion Observatory y funcionará como un helioscopio solar de axiones con detectores de rayos X de bajo fondo instalados en una infraestructura móvil a nivel de superficie. Para la línea de detectores Micromegas, estas condiciones hacen que el control del fondo inducido por rayos cósmicos sea un requisito central. La señal esperada consiste en un pequeño exceso de rayos X de energía keV focalizados sobre el plano del detector, por lo que la respuesta del detector, la reconstrucción de sucesos, la normalización del fondo y la estrategia de veto deben entenderse al nivel de los mismos observables utilizados en el análisis de datos.

Esta tesis desarrolla infraestructura de simulación y herramientas de modelado de fondo para los detectores Micromegas de IAXO-D0 y BabyIAXO, con énfasis en flujos de trabajo Monte Carlo a nivel de respuesta del detector, fondos inducidos por rayos cósmicos y neutrones cósmicos, y validación del veto activo. El trabajo de software se basa en REST-for-Physics y en su interfaz restG4 con Geant4, incluyendo la organización de flujos de trabajo, la generación de fuentes, las cadenas de respuesta del detector y las estrategias de producción a gran escala. Estas herramientas se utilizan para construir una metodología de modelo de fondo en la que simulaciones específicas de cada fuente se procesan mediante observables comunes de reconstrucción y selección.

Una parte importante del trabajo se centra en el sistema de blindaje y veto necesario para la operación en superficie. Los estudios muestran que el blindaje pasivo por sí solo no puede suprimir completamente la componente de neutrones de alta energía, ya que los neutrones cósmicos pueden generar cascadas secundarias dentro del blindaje de plomo. La estrategia de veto activo resultante combina señales rápidas en centelleadores, actividad retardada asociada a capturas neutrónicas y multiplicidad de canales en un diseño multicapa de centelleador plástico y cadmio. Las simulaciones a nivel de forma de onda predicen un fuerte rechazo del fondo inducido por muones y un rechazo parcial de los residuos inducidos por neutrones y protones tras los cortes Micromegas. Los datos del prototipo IAXO-D0 con sistema de veto validan la estrategia de discriminación basada en señales rápidas, retardadas y de multiplicidad, aunque una medida absoluta de la eficiencia del veto de neutrones requiere todavía una simulación ajustada al prototipo y un tratamiento más completo de umbrales, tiempos, calibración y normalización de fuentes.

La tesis contribuye así a la transición desde simulaciones idealizadas de depósito de energía hacia observables reconstruidos comparables con datos experimentales. Proporciona la base de software y análisis para un modelo cuantitativo de fondo de los detectores BabyIAXO e identifica las principales incertidumbres restantes: normalización de neutrones cósmicos, dependencia del emplazamiento en DESY, modelado hadrónico, calibración de la respuesta del detector, umbrales del veto, alineamiento temporal, detalles geométricos y estadística finita de Monte Carlo.

Agradecimientos

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna. Donec vehicula augue eu neque. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Mauris ut leo. Cras viverra metus rhoncus sem. Nulla et lectus vestibulum urna fringilla ultrices. Phasellus eu tellus sit amet tortor gravida placerat. Integer sapien est, iaculis in, pretium quis, viverra ac, nunc. Praesent eget sem vel leo ultrices bibendum. Aenean faucibus. Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla. Curabitur auctor semper nulla. Donec varius orci eget risus. Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam. Duis eget orci sit amet orci dignissim rutrum.

Contents

Introduction

The Standard Model of particle physics provides an exceptionally successful description of the known elementary particles and their interactions. Nevertheless, several observations and theoretical questions point to physics beyond this framework. Among them, the nature of dark matter and the absence of observed \(\mathrm {CP}\) violation in the strong interaction remain two of the most compelling open problems. The axion was originally proposed as a dynamical solution to the strong \(\mathrm {CP}\) problem, but it also emerged as a well-motivated dark-matter candidate. More generally, axion-like particles appear naturally in many extensions of the Standard Model and can be searched for through their weak couplings to photons, electrons, and nucleons.

Solar axion helioscopes exploit one of the most direct experimental signatures of these particles. If axions are produced in the solar interior, they can traverse the Sun and the interplanetary medium essentially unattenuated. Inside a strong laboratory magnetic field, a small fraction of them can convert into X-ray photons through the inverse Primakoff effect. The experimental task is therefore conceptually simple but technically demanding: point a powerful magnet toward the Sun, focus any converted photons onto a small detector area, and identify a possible excess of keV X-rays above an extremely low background.

The International Axion Observatory (IAXO) is designed as the next major step in this technique, building on the experience of previous helioscopes and especially on the CERN Axion Solar Telescope (CAST). BabyIAXO is the intermediate stage of this program. It will validate the main technologies required for IAXO while also operating as a competitive helioscope in its own right. For the detector line studied in this thesis, BabyIAXO is not only a scaled-down version of a future experiment. It is a realistic environment in which low-background X-ray detection, solar tracking, mechanical integration, and surface-level operation must be made compatible.

This thesis focuses on the Micromegas detector line developed for IAXO-D0 and BabyIAXO. Microbulk Micromegas detectors are well suited to helioscope searches because they combine low intrinsic radioactivity, good energy response in the keV range, topological discrimination, and compatibility with compact shielding and focusing optics. However, the expected signal rate is extremely small. The physics reach of the experiment therefore depends not only on detector performance, but also on the reliability of the background model, the realism of the detector-response simulation, and the effectiveness of the shielding and active veto strategy.

The work presented here addresses these requirements from three connected directions. First, it describes contributions to the software and simulation infrastructure used by the collaboration, with particular emphasis on REST-for-Physics, its Geant4 interface restG4, and the production workflows needed for large Monte Carlo campaigns. Second, it develops a background-model methodology for IAXO-D0 and BabyIAXO, combining radiopurity information, environmental measurements, cosmic-ray source terms, detector-response emulation, and common reconstruction observables. Third, it studies the surface-level cosmic-ray-induced background and the corresponding active veto system, including the optimization of a multilayer plastic-scintillator and cadmium design, waveform-level veto observables, construction and commissioning aspects, and comparison with experimental data.

This thesis develops the software and detector-response simulation infrastructure required to build a quantitative background model for BabyIAXO Micromegas detectors, with emphasis on surface cosmic-ray backgrounds, cosmic-neutron-induced residuals, and active-veto observables comparable to experimental data.

A central theme of the thesis is the transition from idealized background estimates to analysis objects that can be compared with real detector data. The relevant question is not only whether a simulated particle deposits energy in the detector volume, but whether the resulting event would pass the same energy, topology, timing, and veto selections applied to the experimental data. For this reason, the simulations are propagated through a detector-response chain whenever possible, and the veto studies are expressed in terms of prompt signals, delayed activity, channel multiplicity, and reconstructed observables. This approach is especially important for surface operation, where muons, high-energy neutrons, and secondary particles produced in the shielding can generate backgrounds that are not adequately described by passive shielding arguments alone.

The structure of the thesis follows this logic. Chapter 1 introduces the axion and axion-like-particle motivation, the strong \(\mathrm {CP}\) problem, and the main experimental approaches used in axion searches. Chapter 2 describes the IAXO program, the helioscope figure of merit, the role of BabyIAXO, and the experimental context in which the detector work is carried out. Chapter 3 presents the Micromegas detector technology, the IAXO-D0 and BabyIAXO detector prototypes, and the associated gas, high-voltage, slow-control, data-acquisition, and calibration systems. Chapter 4 describes the computational framework used in the thesis, including ROOT, REST-for-Physics, restG4, data production, visualization, and related software developments. Chapter 5 studies the shielding and veto system, with emphasis on cosmic-ray-induced backgrounds, passive-shielding limitations, the active scintillator–cadmium veto concept, and the comparison between simulations and prototype data. Chapter 6 presents the broader background model for IAXO-D0 and BabyIAXO, including external and intrinsic background contributions and the simulation methodology used to estimate their impact in the signal region. The final chapter summarizes the results and outlines the next steps toward a complete BabyIAXO detector-background model.

The common objective of these chapters is to show how the detector, software, simulation, and shielding developments fit together into a single experimental program. In a helioscope, sensitivity is ultimately limited by the ability to convert a rare solar-axion signal into a small, well-characterized X-ray excess. This thesis contributes to that goal by developing the tools and background-rejection strategy needed to make the BabyIAXO Micromegas detector line a quantitatively understood low-background instrument.

Chapter 1
Axions and Axion-Like Particles

1.1 Why Axions?

The axion is a rare example of a hypothetical particle motivated simultaneously by particle theory, cosmology, and astrophysics. It was introduced as a consequence of the most widely studied dynamical solution to the strong \(\mathrm {CP}\) problem of quantum chromodynamics (QCD), but it also provides a natural cold-dark-matter candidate and appears generically in many extensions of the Standard Model. This combination of theoretical economy and experimental accessibility has made axion searches one of the most active frontiers in astroparticle physics [1–3].

The Standard Model describes the strong, weak, and electromagnetic interactions with remarkable precision, yet it leaves several fundamental questions unresolved. It does not include gravity, it does not identify the particle nature of dark matter, and it contains parameters whose values appear unnaturally small or specially arranged. The strong \(\mathrm {CP}\) problem is one of the clearest examples: QCD permits a \(\mathrm {CP}\)-violating term, but experiments show that the coefficient of this term must be extremely close to zero. The Peccei–Quinn (PQ) mechanism promotes this apparently fixed parameter to a dynamical field. The relaxation of that field removes strong \(\mathrm {CP}\) violation, and the associated pseudo-Nambu–Goldstone boson is the axion [4–7].

From an experimental point of view, axions and axion-like particles (ALPs) are compelling because they are light, weakly coupled, and detectable through several complementary portals. The axion-photon interaction is especially important: it allows axions to convert into photons in external electromagnetic fields and therefore underlies helioscopes, haloscopes, and light-shining-through-wall experiments. Other possible interactions, particularly with electrons and nucleons, broaden the search program and connect laboratory experiments to stellar evolution, supernovae, spin-precession searches, and precision measurements. The present thesis is situated in this landscape through the helioscope program, where a small flux of solar axions would be converted into keV X-rays and detected above an extremely low background.

1.2 The Strong CP Problem

The strong \(\mathrm {CP}\) problem arises because the most general QCD Lagrangian contains a term

where \(G_{\mu \nu }^a\) is the gluon field-strength tensor, \(\tilde {G}^{a,\mu \nu } = \varepsilon ^{\mu \nu \lambda \rho }G^a_{\lambda \rho }/2\) is its dual, and \(\alpha _{\mathrm {s}}\) is the strong coupling. The physical parameter is not only the bare QCD angle \(\theta \), but

where \(M_q\) is the quark mass matrix. The term proportional to \(\bar {\theta }\) violates parity and \(\mathrm {CP}\) in the strong interactions. This should be distinguished from the observed \(\mathrm {CP}\) violation in the weak sector, which is described by the Cabibbo–Kobayashi–Maskawa phase and does not remove the need to explain why strong \(\mathrm {CP}\) violation has not been observed.

The most stringent direct constraint on \(\bar {\theta }\) comes from the neutron electric dipole moment (nEDM). If QCD contained sizable strong \(\mathrm {CP}\) violation, the neutron would acquire an electric dipole moment of order [8, 9]

The current experimental result [10] is

which implies

For a dimensionless angular parameter that could naturally have been of order unity, this bound represents a severe fine-tuning. The strong \(\mathrm {CP}\) problem is therefore the question of why the strong interactions conserve \(\mathrm {CP}\) to such high accuracy.

1.3 The Peccei–Quinn Mechanism and the QCD Axion

Several solutions to the strong \(\mathrm {CP}\) problem have been proposed, including the massless up-quark hypothesis, which is excluded by low-energy QCD data, and models in which \(\mathrm {CP}\) is imposed as an exact or approximate symmetry at high energies [11–15]. The Peccei–Quinn mechanism remains the most widely studied dynamical solution. It postulates a new global \(U(1)_{\mathrm {PQ}}\) symmetry that is spontaneously broken at an energy scale \(f_a\). Because the symmetry is anomalous under QCD, the associated pseudo-Nambu–Goldstone field \(a(x)\) couples to gluons as

Non-perturbative QCD generates a potential for \(a(x)\). Its minimum occurs at \(\langle a \rangle /f_a = \bar {\theta }\), so the effective strong \(\mathrm {CP}\) angle relaxes dynamically to zero. The same mechanism predicts a new pseudoscalar particle, the QCD axion [6, 7].

The axion mass is determined by the QCD topological susceptibility \(\chi \), because the axion potential originates in the QCD anomaly. At leading order one expects \(m_a f_a \simeq \sqrt {\chi } \sim m_\pi f_\pi \), and modern chiral and lattice calculations give [16–19]

The original Peccei–Quinn–Weinberg–Wilczek axion had \(f_a\) near the electroweak scale and therefore sizable couplings. Such “visible” axions were rapidly excluded, for example by rare meson decays such as \(K^+ \rightarrow \pi ^+ + a\) [4, 6, 7, 20]. Viable QCD axions require \(f_a \gg v_{\textrm {EW}}\), which makes them light and weakly interacting. These are the invisible axion models explored by modern laboratory, astrophysical, and cosmological searches.

1.4 Couplings and Benchmark Models

The model-independent interaction in Eq. 1.6 fixes the solution to the strong \(\mathrm {CP}\) problem, but the axion couplings to photons, electrons, and nucleons depend on the ultraviolet realization of the PQ symmetry. For the photon coupling, the relevant interaction is

where \(F_{\mu \nu }\) is the electromagnetic field tensor and \(\tilde {F}^{\mu \nu }\) its dual. For a QCD axion,

where \(\alpha \) is the electromagnetic fine-structure constant. The ratio \(E/N\) is the electromagnetic-to-color anomaly ratio of the PQ current, while the numerical term \(1.92(4)\) is the model-independent contribution from axion mixing with neutral mesons [3, 18]. The appearance of the electromagnetic coupling \(\alpha \), rather than the strong coupling \(\alpha _{\mathrm {s}}\), reflects the fact that this is the axion-photon interaction. Equivalently, for a QCD axion one may write

which makes explicit the approximately linear relation between \(g_{a\gamma }\) and \(m_a\) inside a fixed QCD-axion model.

The two standard invisible-axion benchmarks are KSVZ and DFSZ models [21–24]. In the simplest KSVZ construction, Standard Model fermions do not carry PQ charge and the anomaly is generated by a new heavy quark; an electrically neutral heavy quark gives \(E/N=0\), although KSVZ-like models with other heavy-quark charges can produce different photon couplings. In DFSZ models, the PQ charge is assigned to Standard Model quarks and leptons through an extended Higgs sector, with the commonly quoted benchmark value \(E/N=8/3\). These models are useful reference lines in parameter-space plots, but they do not exhaust the QCD axion landscape. Modern constructions include photophobic, electrophilic, nucleophobic, and other non-minimal variants whose couplings can populate regions outside the traditional benchmark band [1, 3].

Equation 1.8 has two experimentally important consequences that should be kept distinct. The same interaction permits the decay \(a\rightarrow \gamma \gamma \), when kinematically and cosmologically relevant, and coherent axion-photon conversion in an external electromagnetic field. The latter process is the Primakoff or inverse Primakoff conversion, depending on direction, and is the mechanism used by helioscopes, haloscopes, and light-shining-through-wall experiments [25, 26]. This coherent conversion should therefore be distinguished from a spontaneous two-photon decay.

1.5 Axion-Like Particles

The term axion-like particle refers to light pseudoscalar bosons with interactions similar to the axion but without the strict QCD relation between mass and couplings. A QCD axion solves the strong \(\mathrm {CP}\) problem and has \(m_a\) and its leading couplings tied to \(f_a\). An ALP may arise from the breaking of an approximate global symmetry, from string compactifications, or from other hidden-sector dynamics, but its mass and couplings are usually treated as independent parameters [27–30]. ALPs therefore need not solve the strong \(\mathrm {CP}\) problem, although their phenomenology can closely resemble that of the axion in a detector.

For this reason, experiments often present results in the same mass-coupling planes for QCD axions and ALPs. The diagonal QCD axion band reflects Eq. 1.9, while ALPs can occupy the wider surrounding parameter space. Figure 1.2 later in the chapter shows how this wider parameter space is divided among laboratory searches, astrophysical bounds, dark-matter searches, and future projections.

1.6 Axions as Dark Matter

Axions are natural cold-dark-matter candidates because a coherently oscillating light scalar field redshifts like non-relativistic matter. The most important production mechanism is misalignment: after the PQ symmetry is broken, the axion field is generally displaced from the minimum of its potential. When the Hubble expansion rate drops below the axion mass, the field begins to oscillate and stores energy in a cold population of axions [2, 31].

The predicted relic abundance depends on the cosmological history. If PQ symmetry breaking occurs before inflation and is not restored afterward, the observable Universe samples one initial misalignment angle. In that scenario the abundance depends on this angle and on \(f_a\), while isocurvature constraints link the model to the inflationary scale. If PQ symmetry breaking occurs after inflation, different regions begin with different initial angles, and topological defects such as axion strings and domain walls contribute to the final abundance. The post-inflationary case can also produce small-scale structures such as axion miniclusters. Consequently, cosmology does not select a single axion mass; it identifies broad target regions whose interpretation depends on assumptions about inflation, topological defects, and the fraction of dark matter made of axions [2, 32].

This point is essential when comparing experimental strategies. Haloscopes search for dark-matter axions in the local Galactic halo and therefore quote limits under an assumed local density and velocity distribution. Helioscopes search for axions produced in the Sun and are insensitive to whether axions compose the dark matter. Both approaches are central, but they test different physical hypotheses.

1.7 Astrophysical Constraints, Hints, and Target Regions

Astrophysical systems provide some of the strongest constraints on axion and ALP couplings because weakly interacting particles can carry energy out of stars, supernovae, or compact objects. For the axion-photon coupling, horizontal-branch stars in globular clusters provide a classic bound through Primakoff energy losses. The Sun, red giants, white dwarfs, neutron stars, and supernova SN1987A constrain different combinations of axion couplings to photons, electrons, and nucleons [33, 34]. At very low masses, black-hole superradiance constrains bosons whose Compton wavelength is comparable to the gravitational radius of astrophysical black holes, while high-energy gamma-ray observations can probe ALP-photon oscillations in cosmic magnetic fields.

Some stellar observations have historically been discussed as possible cooling anomalies, especially in white dwarfs and red giants. The current interpretation is cautious: these effects are useful as motivation for improved searches, but they are not compelling evidence for axions. A robust thesis-level summary is therefore that astrophysics both constrains axion models and identifies well-motivated regions for laboratory tests. BabyIAXO and IAXO are particularly important in this context because they can test solar axion emission directly, under controlled detector conditions, in part of the parameter space suggested by stellar energy-loss arguments [34–36].

Cosmology provides a complementary set of constraints. Thermally produced eV-scale axions would behave as hot dark matter and are limited by cosmic microwave background and large-scale-structure observations [37, 38]. Non-thermal cold axions remain viable over a much wider mass range and motivate the broad experimental program shown in Figure 1.2.

1.8 Experimental Strategies

A large and historically central class of axion searches exploits the axion-photon interaction, using electromagnetic fields to convert axions into detectable photons. This class includes helioscopes, haloscopes, and light-shining-through-wall experiments. Complementary searches target other possible axion couplings, especially to electrons and nucleons, and are essential for mapping the broader axion and ALP parameter space [3, 39, 40].

1.8.1 Haloscopes and Dark-Matter Axion Searches

The haloscope technique uses a strong magnetic field and a resonant electromagnetic structure to convert non-relativistic halo axions into photons [41]. For a conventional microwave cavity, the signal frequency is set by the axion rest mass, \(h\nu \simeq m_ac^2\), with a small broadening from the Galactic velocity distribution. The experiment therefore scans frequency to cover axion mass. The power is extremely small, so sensitivity depends on magnetic volume, cavity quality factor, noise temperature, integration time, and quantum-limited or quantum-enhanced readout.

Haloscopes have reached QCD-axion sensitivity in selected \(\mu \mathrm {eV}\) mass intervals, but only under assumptions about the local dark-matter density and axion fraction. ADMX has excluded benchmark couplings in several ranges and reported a 2025 search over \(1.10\)–\(1.31\,\si {GHz}\), corresponding to \(4.54\)–\(5.41\,\mu \mathrm {eV}\), with extended KSVZ sensitivity [42–44]. CAPP has published high-sensitivity results in the \(4.24\)–\(4.91\,\mu \mathrm {eV}\) range using a large-volume cavity in a 12 T magnet [45]. HAYSTAC has demonstrated squeezed-state receiver technology and reported exclusions across parts of the \(16.96\)–\(19.46\,\mu \mathrm {eV}\) range [46]. Beyond microwave cavities, the field includes dielectric haloscopes such as MADMAX, lumped-element searches at low mass, plasma and dish-antenna concepts, radio-frequency cavities at higher masses, and quantum sensors [47, 48].

1.8.2 Light Shining Through Walls

Light-shining-through-wall (LSW) experiments produce axions or ALPs in the laboratory and regenerate photons after an optical barrier. A laser beam traverses a magnetic conversion region, unconverted photons are blocked, and axions pass into a second magnetic region where they can reconvert into photons. The technique is highly model independent because it does not rely on astrophysical sources, cosmological abundance, or stellar modeling. Its limitation is the small probability, which scales as \(g_{a\gamma }^4\) for production and regeneration.

ALPS II at DESY is the current state-of-the-art LSW experiment. Its first science campaign, using data taken from February to May 2024, found no signal and reported a 95% confidence-level pseudoscalar limit of approximately \(g_{a\gamma }=1.5\times 10^{-9}\,\si {GeV^{-1}}\) for masses below about \(0.1\,\si {meV}\), improving previous comparable LSW results by more than a factor of 20 [49]. Further optical upgrades are intended to increase the sensitivity substantially. LSW searches are therefore conceptually clean and complementary, even though their present reach in \(g_{a\gamma }\) is weaker than helioscope and stellar bounds in the low-mass region.

1.8.3 Other Direct and Precision Approaches

The axion program is broader than photon conversion in magnets. Axion-electron couplings can be probed through absorption in atoms, semiconductors, and superconductors, as well as through solar axion searches in low-threshold detectors. Axion-nucleon and axion-gluon couplings motivate nuclear magnetic resonance, spin-precession, oscillating electric-dipole-moment, and fifth-force experiments such as CASPEr and ARIADNE [39, 50]. These methods are especially important because a QCD axion or ALP may have suppressed photon coupling while remaining visible through matter couplings.

1.9 Connection to Solar Helioscopes

The preceding sections explain why axions and ALPs motivate a broad search program: the QCD axion solves the strong \(\mathrm {CP}\) problem, axions can be viable dark matter, and weak couplings to photons, electrons, and nucleons open several experimental portals. Within this landscape, solar helioscopes occupy a distinctive role. They do not assume that axions constitute the Galactic dark matter, and they test particle interactions through a controlled laboratory conversion of axions produced in a well-modeled astrophysical source.

For the present thesis, the essential bridge is the axion-photon coupling. The Sun can produce keV-scale axions through Primakoff conversion and, in models with electron couplings, through atomic and plasma processes. A helioscope then attempts to reconvert those axions into focused X-rays in a strong transverse magnetic field. This links the particle-physics parameters introduced in this chapter to a concrete detector problem: search for a small, time-correlated X-ray excess during solar tracking, while suppressing environmental and cosmic-ray backgrounds.

The central detector challenge follows directly from this physics. The relevant energy scale is the \(1\)–\(10\,\si {keV}\) region, where optics, detector efficiency, threshold, radiopurity, stability, topology, and background rejection all matter. The next chapter, The Helioscope Technique and the IAXO Program, develops these experimental ingredients in detail: solar axion spectra, axion-photon conversion probability, coherence and buffer-gas operation, the helioscope figure of merit, and the transition from CAST to BabyIAXO and IAXO. The rest of the thesis then follows this experimental logic into Micromegas operation, simulation, veto design, and background modeling.

Chapter 2
The Helioscope Technique and the IAXO Program

Introduction

The previous chapter established the particle-physics, cosmological, and astrophysical motivation for axions and axion-like particles, and identified solar helioscopes as the experimental route most directly connected to this thesis. This chapter turns that motivation into an instrument. It first develops the helioscope technique, including solar production, axion-photon conversion, coherence, and the experimental figure of merit. It then follows the realization of that technique from CAST to the IAXO program, with particular attention to BabyIAXO and to the detector-background problem addressed in this thesis.

The International Axion Observatory (IAXO) is the next major step in the development of the helioscope technique for the search for solar axions and axion-like particles [52–54]. It builds on the experience accumulated in CAST and replaces the logic of a repurposed installation with a fully purpose-built experiment in which the magnet, the X-ray optics, the detectors, and the solar-tracking system are optimized as parts of a single instrument.

BabyIAXO is the intermediate stage toward that final observatory [55, 56]. It is designed both as a competitive helioscope in its own right and as a technological demonstrator in which the key IAXO subsystems can be validated at a relevant scale. This dual role is especially important for the detector line studied in this thesis, where background reduction, realistic simulation, and system integration must all be demonstrated under surface-level operating conditions.

Together, these elements define the experimental context for the Micromegas, simulation, veto, and background-modeling work developed in the following chapters.

2.1 The Helioscope Technique

2.1.1 Solar Axions

Solar axions are produced in the hot and dense plasma of the Sun through several processes. The best known is Primakoff conversion, in which thermal photons convert into axions in the electromagnetic fields of the plasma constituents. Additional contributions arise from processes involving the axion-electron coupling, notably axio-recombination, axio-deexcitation, bremsstrahlung, and Compton-like scattering, often grouped together as the ABC channels [57].

The coupling dependence follows immediately from this chain. For Primakoff solar axions, both production in the Sun and conversion in the laboratory depend on \(g_{a\gamma }\), so the expected signal rate scales as \(g_{a\gamma }^{4}\). For ABC solar axions, production depends on \(g_{ae}\), while detection still requires axion-photon conversion, so the signal scales as \(g_{ae}^{2}g_{a\gamma }^{2}\). This distinction is important when interpreting helioscope limits: the same instrument can constrain the axion-photon coupling directly and, under additional model assumptions, products of photon and electron couplings.

Figure 2.2 shows the corresponding spectral components in the keV range relevant for helioscope searches.

This solar source is particularly attractive from an experimental perspective. First, the expected axion energies lie in the soft X-ray range, where efficient focusing optics and highly specialized low-background detectors are available. The Primakoff spectrum peaks around a few keV, while the electron-coupling channels have a relatively softer contribution, which motivates low-threshold detector options in addition to Micromegas, such as GridPix and cryogenic sensors. Second, the solar axion flux is large enough that helioscopes can probe parameter space beyond previous laboratory searches. Finally, helioscopes are directly sensitive to the axion-photon coupling through the inverse Primakoff process and can also probe scenarios involving the axion-electron coupling through the product \(g_{a\gamma } g_{ae}\).

2.1.2 Axion-Photon Conversion in a Helioscope

The basic working principle of a helioscope is illustrated in Figure 2.3. Solar axions enter a strong transverse magnetic field, where they can convert into X-ray photons through the inverse Primakoff effect. Those photons are subsequently focused by grazing-incidence optics onto a detector optimized for the 1–10 keV energy range. The entire system is mounted on a platform capable of following the Sun during the daily observation window.

For a homogeneous magnetic field of length \(L\), the conversion probability can be written as

where \(B\) is the magnetic field intensity and

is the coherence factor. In vacuum, \(q \simeq m_a^2 / 2E\) for relativistic axions of energy \(E\). The coherent regime corresponds to \(qL \ll 1\), in which case \(\mathcal {F} \simeq 1\) and the conversion probability grows as \(B^2 L^2\).

This coherence condition determines the mass range that can be explored in vacuum. At sufficiently large axion mass, the momentum mismatch between the axion and the photon suppresses the conversion probability. As in CAST, this coherence can be partially restored by introducing a buffer gas in the magnet bores, which gives the photon an effective mass and extends the accessible mass range. In a buffer gas, the photon acquires an effective mass \(m_\gamma \), so \(q \simeq |m_a^2-m_\gamma ^2|/(2E)\), with additional damping from photon absorption. Equations 2.1 and 2.2 are therefore the vacuum, negligible-absorption limit [59–61].

2.1.3 Experimental Figure of Merit

The helioscope signal rate is not determined by the magnetic conversion region alone. It also depends on the focusing efficiency of the optics, the background level and efficiency of the detector, and the fraction of time during which the instrument can track the Sun. These dependencies are conveniently summarized by the helioscope figure of merit [52, 54]

with

Here \(A\) is the bore cross-sectional area, \(\epsilon _d\) is the detector efficiency, \(\epsilon _o\) is the optics efficiency, \(b\) is the normalized detector background, \(a\) is the focal spot area on the detector, \(\epsilon _t\) is the tracking efficiency, and \(t\) is the total data-taking time.

This decomposition is particularly useful because it makes explicit how a next-generation helioscope should be designed. The magnetic term favors large aperture in addition to field strength and length, while the detector-optics term rewards efficient focusing onto a very small spot and an ultra-low background readout. The tracking term shows that a mobile platform with long daily observation time is an integral part of the physics reach. This FOM is a background-dominated sensitivity proxy; since the Primakoff signal scales as \(g_{a\gamma }^4\), improvements in \(f\) translate into coupling reach approximately as \(g_{a\gamma } \propto f^{-1/4}\). These are precisely the principles that motivated the transition from CAST to IAXO.

2.2 From CAST to IAXO

2.2.1 CAST as the Reference Helioscope

CAST established the helioscope technique as the leading laboratory search for solar axions [62]. It used a repurposed LHC test dipole magnet together with several low-background X-ray detector systems on its four magnet bores. One line was equipped with focusing X-ray optics and a pn-CCD detector, and later IAXO-pathfinder configurations explored Micromegas operation with focused optics, passive shielding, active vetoing, and upgraded readout [63–65]. Over its successive vacuum, \(\ce {^4He}\), and \(\ce {^3He}\) running periods, CAST demonstrated both the maturity of the helioscope concept and the practicality of restoring coherence with a buffer gas to extend the accessible axion-mass range [59–62].

The importance of CAST for IAXO is not limited to the exclusion limits it produced. CAST showed that very low detector backgrounds are achievable in helioscope conditions, that X-ray optics materially improve the signal-to-background ratio, and that long-term operation of a Sun-tracking magnet-detector system is feasible. In that sense, CAST provided the full experimental foundation on which the IAXO program was built. Its extended run with the IAXO pathfinder system and a Xe-based Micromegas detector found no axion signal and set \(g_{a\gamma }<5.8\times 10^{-11}\,\si {GeV^{-1}}\) at 95% confidence level for \(m_a\lesssim 0.02\,\si {eV}\) [66]. This result is especially relevant for the present thesis because it connects the best demonstrated helioscope performance directly to the same detector family, optics concept, shielding philosophy, and surface-background problem that motivate BabyIAXO.

2.2.2 Why a Dedicated Helioscope Is Required

At the same time, CAST made the main limitations of a repurposed installation evident. Its magnet was optimized for accelerator use rather than helioscope physics, which implies a small aperture, restricted geometrical freedom for optics and detectors, and limited tracking time. These are not secondary limitations. Because the helioscope figure of merit scales linearly with bore cross-sectional area \(A\) and strongly with the detector-optics term, a step change in sensitivity requires a dedicated experimental design rather than incremental upgrades of an existing accelerator component.

The comparison in Table 2.1 clarifies the design shift from CAST to the IAXO program. CAST maximized field strength by reusing a high-field accelerator magnet, whereas BabyIAXO and IAXO trade some field intensity for a much larger aperture, systematic use of focusing optics, and substantially longer daily tracking. Because \(f_M\) grows linearly with bore cross-sectional area \(A\), this change is decisive. The strategy of IAXO is therefore not to reproduce CAST at larger scale, but to optimize the full helioscope figure of merit in a balanced and purpose-built way [52–54].

2.3 The IAXO Experiment

2.3.1 Physics Reach and Design Philosophy

IAXO is conceived as a fourth-generation axion helioscope optimized for solar axions and axion-like particles [53, 54]. In the low-mass region, the full observatory is designed to improve the CAST signal-to-background ratio by approximately four to five orders of magnitude and to reach sensitivity to axion-photon couplings down to a few \(\times 10^{-12}\,\si {GeV^{-1}}\). In addition to Primakoff solar axions, it is also expected to probe scenarios involving the axion-electron coupling with sensitivity beyond previous laboratory experiments.

This projected reach is illustrated in Figure 2.5. In the language of the axion-photon parameter space, BabyIAXO is expected to begin probing the region where benchmark QCD axion models appear, while IAXO aims at a much broader advance through the unexplored low-mass domain. The essential design choice that makes this possible is that the entire experiment is optimized for the helioscope figure of merit. Instead of maximizing only the field strength, IAXO emphasizes aperture, simultaneous instrumentation of multiple bores, small focal spots, long tracking time, and detector backgrounds at the level required for rare-event searches. In this sense, IAXO should not be understood simply as a larger CAST, but as a dedicated observatory built around the needs of helioscope physics.

2.3.2 Magnet

The core of IAXO is a purpose-built superconducting toroidal magnet approximately 20 m long, formed by eight coils and providing eight bores of 60 cm diameter each [54]. The field at the bores is of order a few tesla, with peak values above \(5\,\si {T}\), but the central performance gain with respect to CAST comes from the large aperture rather than from field strength alone. This geometry is one of the defining differences with respect to previous helioscopes.

The toroidal layout has several advantages for a helioscope. It provides a large total conversion volume, leaves open and accessible bores for the insertion of optics and detectors, and naturally defines multiple parallel detection lines. In addition, the bores can be operated in vacuum or filled with a buffer gas when coherence recovery at higher axion mass is required. The magnet is therefore not simply a source of field, but the structural element that organizes the entire observatory.

2.3.3 X-ray Optics

The second key ingredient is the systematic use of focusing X-ray optics on every helioscope line [54, 68]. In IAXO, each bore is foreseen to be equipped with dedicated grazing-incidence optics that focus the converted photons onto spots of order \(0.2~\si {cm^2}\). This is a decisive improvement over CAST, where focusing optics were available only on part of the setup.

The function of the optics is not merely to image the source, but to compress the signal onto a very small detector area. Since the detector background roughly scales with the active area exposed to it, focusing the expected axion signal onto a compact spot directly improves the detector-optics figure of merit. This coupling between optics and low-background detectors is one of the defining features of the IAXO concept.

2.3.4 Detector Technologies

The low-background detectors located at the focal planes must combine high efficiency in the 1–10 keV region with stage-dependent background targets. BabyIAXO aims at the \(10^{-7}\,\si {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\) scale, while the full IAXO concept requires a further reduction toward \(10^{-8}\,\si {counts\,keV^{-1}\,cm^{-2}\,s^{-1}}\) [54, 55]. For a surface helioscope, reaching even the BabyIAXO target is nontrivial because the detector must reject cosmic-ray-induced backgrounds without relying on underground overburden. This requirement has driven a broad detector-development program within the collaboration, including surface-prototype studies with passive shielding and active veto rejection [54, 55, 69]. Several technologies are under study, including Micromegas, GridPix, metallic magnetic calorimeters, transition-edge sensors, and silicon drift detectors.

Among these options, microbulk Micromegas constitute the baseline gaseous detector technology because of their demonstrated performance in CAST and IAXO-D0, and because they combine radiopurity, topological discrimination power, stable operation, and compatibility with focused soft X-ray signals. At the same time, the BabyIAXO detector program has broadened to include other specialized concepts, in particular GridPix-based detectors, which aim at very fine-grained event reconstruction under the same low-background constraints [70, 71]. The detailed implementation of the Micromegas detector line addressed in this thesis is presented in the following chapters.

2.3.5 Tracking and Observatory Operation

IAXO is designed as a true observatory rather than a static test setup. The magnet, optics, and detector assembly are mounted on elevation and azimuth drives that allow solar tracking for up to about half of each day, corresponding to a tracking efficiency \(\epsilon _t \simeq 0.5\) in the conceptual design [54]. This is a very substantial gain with respect to CAST and is one of the reasons why the tracking system enters explicitly into the helioscope figure of merit.

The corresponding mechanical and cryogenic requirements are nontrivial. The structure must support a large cold mass, preserve alignment between bores, optics, and detectors during motion, and allow a reliable transition between Sun-tracking periods and off-Sun background measurements. These operational constraints are part of the experimental design, not merely engineering afterthoughts.

This has immediate consequences for the detector program. Unlike many rare-event experiments, a helioscope of this scale cannot simply be placed deep underground to suppress cosmic radiation. The expected installation is at surface level, and the required background suppression must therefore be achieved through detector design, passive shielding, topology-based analysis, and active veto systems. This constraint is central to the present thesis.

2.4 The IAXO Program and Collaboration Context

IAXO is inherently a collaboration-driven experiment. Its realization requires the integration of expertise from axion phenomenology, superconducting magnet engineering, X-ray optics, cryogenics, detector development, low-background techniques, and data acquisition. This breadth is already evident in the Letter of Intent and the conceptual-design documents, which frame IAXO as an observatory assembled from mature but previously separate technological lines [53, 54].

The staged realization through BabyIAXO reflects both physics logic and project logic. A medium-scale helioscope allows the magnet, optics, detector infrastructure, gas handling, alignment, and tracking systems to be commissioned together before scaling to the full toroidal observatory. In this sense, BabyIAXO is the bridge between subsystem R&D and the final experiment, and not simply a reduced-scale prototype [55, 71]. For the detector work of this thesis, the collaboration structure is not incidental: magnet geometry, optical focal-spot assumptions, readout constraints, radiopurity screening, and veto integration are defined across different working groups. The simulation and background-model tasks therefore act as an interface between detector development, mechanical integration, and physics sensitivity.

2.5 BabyIAXO as an Intermediate Stage

2.5.1 Role Within the IAXO Program

BabyIAXO was proposed as the intermediate stage between CAST and the full IAXO observatory [55, 56]. Its purpose is twofold. On the one hand, it provides a realistic environment in which the main IAXO subsystems can be integrated and validated: magnet, optics, detectors, cryogenics, tracking, alignment, and data acquisition. On the other hand, it is itself a fully-fledged helioscope with nontrivial discovery potential.

In the baseline vacuum phase, BabyIAXO is expected to reach sensitivities of order \(g_{a\gamma } \sim 1.5 \times 10^{-11}\,\si {GeV^{-1}}\) for masses up to \(m_a \sim 2\times 10^{-2}\,\si {eV}\). With a buffer-gas phase, the accessible mass range can be extended, allowing BabyIAXO to probe the KSVZ benchmark region approximately in the \(0.06\)–\(0.25\,\si {eV}\) interval [55]. In practical terms, this places BabyIAXO well beyond a mere engineering prototype. As indicated in Figure 2.5, it already begins to explore physically relevant parameter space associated with benchmark QCD axion models while simultaneously de-risking the construction of the full observatory.

2.5.2 Evolution of the DESY Site Scenario

The site assumptions for BabyIAXO evolved during the period in which the work presented in this thesis was being developed. At the beginning of the background-model and veto-simulation program, the reference implementation was the HERA South Hall at DESY. This was an underground accelerator hall rather than a deep-underground low-background laboratory, but it nevertheless implied a different environmental boundary condition from a fully outdoor surface installation: the hall structure, access shafts, and surrounding infrastructure could modify the cosmic-ray field seen by the detector. For this reason, early simulation work treated the cosmic-ray background as an important but site-dependent contribution, with attention to overburden, openings, and local shielding details.

During 2025 and 2026 the working site assumptions shifted in recent internal collaboration discussions toward an outside, on-surface location at DESY. The main arguments reported in the collaboration meetings were practical and programmatic: reduced civil-infrastructure effort, less dependence on overstretched DESY infrastructure groups, lower expected cost, and a faster route to site activation [72]. The change also has a physics and engineering advantage because it makes BabyIAXO closer to the expected surface conditions of the full IAXO observatory. By the 23rd IAXO Collaboration Meeting, the surface scenario had become the current internal working baseline for technical planning, and the DESY directorate had encouraged further site exploration and cost/schedule assessment, although formal full project and site approval still depended on the complete financial and construction review [73].

This change is directly relevant for the interpretation of the simulations in this thesis. The initial motivation included the question of whether the HERA South environment would provide enough passive reduction of cosmic-ray-induced backgrounds for a low-background Micromegas line. The shift toward an on-surface working baseline strongly motivates treating BabyIAXO background studies as surface-level studies, even when earlier simulations were developed with HERA South Hall boundary conditions in mind. The detector system must therefore be robust against sea-level muons, high-energy neutrons, and the secondary showers produced in the passive shielding. Consequently, the active scintillator–cadmium veto described in Chapter 5 becomes a central design element for the surface-detector concept rather than a secondary upgrade.

The outdoor site also introduces engineering constraints that feed back into detector-background studies. Recent site studies emphasize the larger outdoor turning circle, magnetic stray-field limits, the need for a fenced exclusion region of order 35 m diameter for BabyIAXO, and checks of possible interference with nearby DESY magnet-test activities [75]. In addition, the support and drive system must be validated for outdoor load cases such as wind, snow, ice, and temperature gradients. These developments do not invalidate the earlier simulation program; rather, they make the surface-cosmic component and the active-veto strategy the conservative and experimentally relevant reference for BabyIAXO.

2.5.3 Main Experimental Features

The BabyIAXO design follows the same experimental logic as IAXO, but at reduced scale [55]. Its magnet comprises two 10 m long bores of 70 cm diameter, each intended to host a complete detection line with optics and detector dimensions representative of the final observatory. The superconducting system is based on two parallel flat coils and conventional NbTi/Cu Rutherford cable technology, with the cold mass operated at about \(4.5\) \(\mathrm {K}\). In this way, the magnet aperture, cryogenic integration, and detector interfaces are all tested under realistic conditions before the transition to the larger toroidal concept.

The optics and detector strategy of BabyIAXO is also deliberately close to that of IAXO. Dedicated X-ray optics based on multilayer-coated segmented-glass Wolter-I concepts focus the expected signal from the full bore onto a spot of order \(0.2~\si {cm^2}\) [55]. The present BabyIAXO plan includes two telescope solutions with different focal lengths, one custom design and one based on an available XMM-Newton spare optic, both serving as technology and integration demonstrators for the final observatory.

On the detector side, Micromegas remain the baseline low-background technology for the helioscope line studied in this thesis, but the broader BabyIAXO program also includes GridPix and cryogenic detector developments [55, 71]. This diversification is scientifically valuable because different detector technologies probe complementary aspects of performance, such as energy threshold, topology, time structure, or energy resolution. The detector-side roadmap is also informed by the IAXO pathfinder program carried out at CAST, where an IAXO-oriented Micromegas line was already operated together with focused optics, passive shielding, an active muon veto, and AGET-based readout in a surface installation [65]. In parallel, the BabyIAXO infrastructure has motivated auxiliary axion-search concepts, including haloscope programs based on radiofrequency cavities integrated with the available magnet geometry [76].

The conceptual design places BabyIAXO at DESY in Hamburg [55]. The recent shift toward an outside surface working baseline, discussed in Section 2.5.2, makes the operating conditions especially relevant for the present work: a large moving magnet, full detector infrastructure, and no possibility of relying on underground shielding against cosmic rays. As a consequence, background modeling and active rejection become enabling technologies rather than secondary refinements. This point is emphasized repeatedly in recent BabyIAXO detector-development work, where veto design, material selection, and integration constraints are treated as central elements of the experiment rather than add-ons [69, 71].

2.6 Connection to the Present Thesis

The chapters that follow focus on one detector line within the broader IAXO program: the Micromegas-based BabyIAXO line, together with its software and background-reduction strategy. The need for realistic simulation, a quantitative background model, and an optimized active veto follows directly from the IAXO and BabyIAXO design choices described above.

The central challenge is the combination of focused keV X-ray detection, ultra-low background performance, and operation in a large surface-level moving apparatus. This thesis addresses that challenge through the Micromegas detector line, the REST-for-Physics/restG4 simulation chain, the background model, and the scintillator–cadmium veto strategy.

Chapter 3
Micromegas X-ray Detectors for BabyIAXO

Introduction

The Micromegas detector line studied in this thesis is the low-background x-ray detection system coupled to the BabyIAXO helioscope optics. Its task is narrow but demanding: it must convert a small number of soft x rays in the \(1\)–\(10\,\mathrm {keV}\) region into calibrated, position-sensitive waveforms while operating at surface level, close to passive shielding, active veto panels, gas services, high-voltage channels, and data-acquisition electronics. For that reason, the detector cannot be described only as an isolated gas volume. It is a coupled instrument in which gas transport, charge amplification, readout segmentation, calibration, slow control, and veto synchronization all determine the observables used later in the background analysis.

This chapter provides the detector foundation for the rest of the thesis. It first summarizes the signal-formation physics that is needed to interpret Micromegas waveforms, then describes the microbulk Micromegas technology and the IAXO-D0/IAXO-D1 prototype implementations. The final sections connect the detector to its operating services, data-acquisition chain, and calibration procedures, leaving the detailed software implementations and large-scale background simulations to Chapters 4 and 6.

3.1 The Time Projection Chamber (TPC)

Time Projection Chambers (TPCs) are gaseous detectors in which ionization electrons drift through an electric field toward a segmented readout plane. Large TPCs are often used as tracking detectors, but the BabyIAXO Micromegas detector is a shallow x-ray TPC: the relevant information is not a long momentum-measuring trajectory, but the amount of deposited charge, its two-dimensional distribution on the readout strips, and the relative timing of the digitized pulses. This compact topology is precisely what makes the detector useful for axion searches, because focused solar x rays should produce localized charge clusters while many background events produce more extended, asymmetric, or veto-correlated signatures.

A TPC typically consists of a gas-filled chamber subjected to a uniform drift field. An incoming particle or photon interaction produces electron-ion pairs in the gas. The electrons drift toward the anode, diffuse during transport, enter an amplification region, and finally induce signals on the readout electrodes. The ions drift more slowly toward the cathode. In the BabyIAXO detector, the readout plane is a microbulk Micromegas, which combines amplification and fine strip segmentation in a radiopure structure suitable for low-background operation.

3.1.1 Ionization in Gases

The Micromegas signal starts with an energy deposition in the gas. For the soft x rays relevant to BabyIAXO this deposition is dominated by photoelectric absorption, whereas charged particles usually produce extended ionization tracks and neutral particles contribute indirectly through recoils or secondary radiation. Only the aspects of these processes that determine the later waveform and calibration response are summarized here.

For photons, the attenuation through a material is described by

where \(\mu \) is the linear attenuation coefficient. Equivalently, \(\mu =\rho \mu _m\), with \(\mu _m\) the mass attenuation coefficient. Figure 3.2 shows the standard argon example: in the keV region the photoelectric effect dominates, while Compton scattering and pair production become important only at higher photon energies. Rayleigh scattering can redirect low-energy photons, but because it is elastic it does not by itself define the deposited-energy spectrum. The other photon interactions are nevertheless part of the detector background picture. Compton scattering transfers only part of the photon energy to an electron and can therefore generate lower-energy, spatially displaced deposits. Pair production is irrelevant for the few-keV calibration and axion-signal region, but it becomes part of the high-energy electromagnetic cascade description above threshold. Thus, the \(\ce {^{55}Fe}\) calibration response is governed mainly by photoelectric absorption, while the full background model must still transport Rayleigh, Compton, pair-production, and secondary-electron processes consistently.

The preference for noble gases follows directly from the strong \(Z\) dependence of the photoelectric cross section in the x-ray range, visible in Figure 3.3. The quencher is present at much lower concentration and has a smaller attenuation contribution, but it is essential for stable proportional operation. After photoelectric absorption, the atomic vacancy relaxes through Auger emission or fluorescence. If a fluorescent x ray escapes the sensitive volume, the measured energy is reduced and an escape feature appears in the calibration spectrum; this is particularly visible for argon-based \(\ce {^{55}Fe}\) calibrations.

Charged particles instead leave ionization along their path, with a topology governed by the stopping power, multiple scattering, and possible secondary radiation. In a Micromegas TPC this typically produces broader and more track-like charge patterns than a few-keV x ray. Neutral particles are relevant because they can generate nuclear recoils or secondary photons and charged particles in the gas or surrounding materials. This indirect character is one of the reasons why the background model treats radiation transport and detector-response reconstruction together rather than as separable problems.

3.1.2 Electron Transport

Primary Charge Production

An energy deposit \(E\) in the gas produces a finite number of electron-ion pairs. The electrons, referred to here as primary charge, are the carriers that drift toward the Micromegas readout and seed the avalanche in the amplification gap. The mean number of primary electrons is

where \(W\) is the average energy required to create one electron-ion pair in the mixture. The intrinsic fluctuation around this mean is smaller than Poissonian and is commonly written as

where \(F\) is the Fano factor [78]. This primary-charge statistics sets the best achievable energy resolution before transport, amplification, and electronics effects are included.

Electron Drift

The drift field transports the primary electrons from the conversion point to the amplification region. In the mobility approximation, the drift velocity can be written as

where \(\vec {E}\) is the electric field, \(p\) is the gas pressure, and \(\mu _e(E/p)\) is the effective electron mobility for the gas mixture at the relevant reduced field. In practice, drift velocities and diffusion coefficients are taken from gas-transport calculations such as Garfield++/Magboltz, because the response depends on the mixture, pressure, field, and quencher fraction. Typical electron drift velocities in noble-gas TPC mixtures are of order \(1~\mathrm {cm/\mu s}\), so the drift time is directly connected to the pulse timing in the digitized waveform. The gas-mixture dependence of the drift velocity and diffusion coefficients is discussed below in the context of the detector-response gas tables.

During transport the charge cloud also diffuses. The standard deviation \(\sigma _{\hat {u}}\) of the electron cloud in a given direction \(\hat {u}\) after a drift distance \(d\) can be written as

with separate longitudinal and transverse coefficients in the presence of the drift field. Diffusion controls the charge sharing between strips and the apparent width of a localized x-ray event. Recombination and attachment provide the competing loss mechanisms; in practice, oxygen and water contamination are the main operational concerns, which is why gas purity, material outgassing, and circulation are part of the detector response rather than purely auxiliary services.

Charge Amplification

The primary charge is too small to be measured directly, so the Micromegas gap operates in avalanche mode. The high amplification field converts each primary electron into a charge packet whose mean size is set by the gas gain.

The number of secondary electrons \(N_a\) produced by the amplification of \(N_e\) primary electrons in a region of length \(L\) is given by

where \(\alpha \) is the first Townsend coefficient, which depends on the gas medium and the electric field. The number of electrons after amplification of the primary charge \(N_a\) can be expressed as

If the gain fluctuations of individual primary electrons are described by a variance \(\sigma _G^2\), the variance of the number of secondary electrons after amplification, \(\sigma _a^2\), can be written as

where \(b\) is defined as

The resolution \(R = 2 \sqrt {2 \ln {2}} \sigma _a / N_a \approx 2.35 \cdot \sigma _a / N_a\) is more commonly used instead of the relative variance and is defined as the full width at half maximum (FWHM) of the amplified-charge distribution divided by its mean value.

where \(\sigma _{\mathrm {el}}\) represents additional electronic-noise contributions referred to the amplified charge. The resolution \(R\) is commonly expressed as a percentage.

Expression 3.10 shows that there is a lower limit to the detector resolution at relatively low energies, such as those of soft X-rays, and that this limit is dominated by the Fano factor and avalanche fluctuations. Simulations of the calibration of the BabyIAXO Micromegas detector with a \(^{55}\mathrm {Fe}\) source, shown in Figure 3.5, indicate that a resolution of around \(15\%\) is achieved for the \(5.9 \, \mathrm {keV}\) peak. These simulations only take into account the primary-charge generation; diffusion, amplification, and readout effects are not included. In practice, the detector resolution is therefore worse than the resolution obtained from primary-charge generation alone.

Besides avalanche multiplication, there is another significant charge-amplification process: electroluminescence. Electrons produced by the ionization of the gas medium can excite the gas molecules to higher energy levels without directly ionizing them. The excited molecules will eventually decay to their ground state by emitting a photon. The photon can ionize the gas medium and produce secondary charge. In the present detector context, this process can have a negative impact on the resolution of the detector, both in the energy and spatial domains, since the photons produced can travel long distances and ionize the gas medium far away from the primary charge production site.

This unwanted ionization is mitigated by adding a small fraction of quencher gas to the noble gas. The quencher gas absorbs the photons produced by the electroluminescence process without ionization and is usually a saturated hydrocarbon, such as isobutane. The addition of the quencher also modifies the drift velocity, diffusion, attachment, and amplification behavior of the mixture. For this reason, the choice of gas is both a detector-physics and an operations question, and the gas-transport calculations used to compare candidate mixtures are treated as part of the computational workflow in Section 4.5.6. Figure 3.6 illustrates this coupling for the two gas families considered for the IAXO Micromegas detectors: argon–isobutane and xenon–neon–isobutane. Increasing the isobutane fraction generally reduces the transverse diffusion coefficient, so the charge cloud arriving at the readout is less spread out after the same drift distance. The same scan also shows that the quencher shifts the drift-velocity curve and changes the longitudinal diffusion coefficient, both of which enter the conversion between waveform timing, drift position, and the expected longitudinal extent of a localized ionization cluster. The vertical dotted line in each row marks the representative reduced drift field used for the detector-response studies; it is a reference operating point for reading the curves, not a gas-optimization boundary.

3.1.3 Micropattern Gaseous Detectors: Micromegas

Micromegas (MICRO-MEsh GAseous Structure) detectors are micropattern gaseous detectors in which a thin metallic mesh separates the drift region from a narrow amplification gap [81]. Ionization electrons produced in the drift volume pass through the mesh when the field ratio between amplification and drift regions is favorable, and then avalanche in the high-field gap before being collected by the anode strips. This separation between a relatively low-field drift volume and a very high-field amplification region gives Micromegas detectors fast signals, good spatial granularity, and stable operation at gains suitable for soft x-ray detection.

For axion helioscopes and other rare-event searches, the relevant implementation is the microbulk Micromegas. In this technology the mesh, insulating pillars, and readout pattern are manufactured from copper-clad kapton using photolithographic processes, producing a thin and mechanically uniform amplification structure [82]. The small material budget, the use of radiopure copper and kapton, and the possibility of producing fine two-dimensional strip readouts are central advantages for low-background x-ray detectors. They also make the detector naturally compatible with a TPC analysis strategy: x-ray events produce compact clusters, while tracks from cosmic rays or radioactive backgrounds tend to be more extended in at least one strip projection.

The operating point of a Micromegas detector is defined by the drift field, mesh voltage, gas mixture, pressure, and readout threshold. The mesh transparency must be high enough that primary electrons enter the amplification gap efficiently, while the gain must be large enough to resolve keV deposits without approaching unstable discharge conditions. These two requirements are coupled: the field ratio controls electron focusing through the mesh, while the amplification field controls both signal size and discharge probability. Consequently, stable operation is not only a matter of setting a high voltage, but of choosing a consistent gas, voltage, and electronics configuration and monitoring it through calibration data.

The combination of radiopurity, segmentation, low threshold, and successful operation in CAST makes microbulk Micromegas the baseline detector technology for the IAXO Micromegas line [62, 66, 83].

3.2 The BabyIAXO Micromegas Detector Prototypes

The baseline detector technology for IAXO and BabyIAXO is the microbulk Micromegas. Its successful track record in the CAST experiment, where it was used to detect solar axions, makes it the ideal choice for the IAXO experiment.

The TPC design of the BabyIAXO Micromegas detector remains similar to the CAST Micromegas detectors, since both experiments are designed with the same goal of detecting solar axions. The gas volume is a cylinder with a diameter of \(10~\mathrm {cm}\) and a height of \(3~\mathrm {cm}\), with a total volume of \(235.62~\mathrm {cm}^3\). The microbulk micromegas readout has a square shape with a side of \(6~\mathrm {cm}\). The readout has 120 strips for each direction, for a total of 240 channels.

There are two distinct generations of detector prototypes: IAXO-D0 and IAXO-D1. Both prototypes share the same core design scale, including TPC dimensions, readout size, number of strips, and nominal lead-shielding thickness. The main differences are in the chamber and pipe design, shielding serviceability, Micromegas PCB implementation, and electronics.

3.2.1 IAXO-D0

The IAXO-D0 prototype is, in essence, the latest CAST-derived design. The chamber is cylindrical, with a large copper backplate that protrudes laterally from the shielding. The copper pipe is thinner in the middle and the shielding is made of lead bricks. In order to access or move the detector, the lead shielding must be partially removed brick by brick. The front-end electronic chips are four AGET chips and the back-end electronics is a Feminos card [84]. The front-end and back-end electronics are physically connected into a single FEC–Feminos unit, which is connected to the readout through flat cables.

A significant data-taking campaign was performed with the IAXO-D0 prototype in Zaragoza using the same Micromegas detector that had operated in CAST, shortly after it was decommissioned. This campaign validated the detector and tested the prototype veto system, with emphasis on the reduction of cosmic-ray-induced background. Earlier measurement campaigns with the same prototype family were also performed using other Micromegas detectors from the same generation [70]. Together, these measurements provided the experimental anchor for the simulation and background-rejection studies developed later in the thesis.

3.2.2 IAXO-D1

The IAXO-D1 prototype introduces significant improvements with respect to IAXO-D0. The shielding is a lead box with a square shaft in the middle. It is designed to sit on linear rails so that it can be moved laterally to access the detector, substantially reducing the time required for service operations. The chamber has a square footprint and the copper pipe is significantly thicker. The Micromegas PCB can be bent to fit the shielding aperture, and the readout strips exit the shielding hole in parallel to the pipe.

The front-end electronics are based on four STAGE chips, while the back-end electronics follow an ARC-compatible design. The front-end electronics (Figure 3.15a) are placed inside the shielding next to the pipe in order to minimize the length of the flat cables. The back-end electronics are placed outside the shielding (Figure 3.15b) and are connected to the front-end electronics through another set of flat cables.

3.3 Detector Ancillary Systems

3.3.1 Gas System

The gas system, shown schematically in Figure 3.17, is responsible for the circulation of the gas medium through the detector. The gas flows from a high-pressure gas bottle through a pressure reducer into the detector gas line. The gas flow into the detector is controlled by a set of computer-controlled pressure and flow controllers. The desired gas flow and pressure can be set to the desired values by the operator. A vacuum pump can be used to evacuate the gas from the detector and gas system in order to replace the gas medium.

A number of emergency relief valves are placed in the gas system to prevent overpressure in the detector. The window which separates the gas medium in the TPC from the outside (either atmospheric air or vacuum) is a critical detector component. The window is made of ultra-thin aluminized mylar and is placed in a very thin copper support frame. The window is designed to support up to \(1.5\,\mathrm {bar}\) of pressure difference between the inside and outside of the detector.

The IAXO Micromegas detectors are designed to operate with different gas mixtures. The gas mixtures considered at the time of writing are argon and a xenon-neon mixture, both using isobutane as the quencher gas. A mixture of argon with \(2\%\) isobutane at \(1.4\,\mathrm {bar}\) was successfully used in CAST during most of its operation [62]. A mixture of xenon and neon (equal parts in partial pressure) with \(2.3\%\) isobutane was also used in CAST during the last years of operation [66].

The xenon-neon mixture presents some theoretical advantages with respect to the argon mixture. The argon mixture results in a significant escape peak in the energy region of interest of the axion due to the argon \(K_\alpha \) line, as shown in Figure 3.5. Natural argon also contains the long-lived isotope \(^{39}\mathrm {Ar}\) at trace levels [85], which is relevant when evaluating intrinsic gas-background contributions.

The gas system is designed to operate in one of two modes: open loop or closed loop. In the open-loop mode, the gas is continuously replaced by a fresh gas flow from the bottle. The old gas is evacuated from the detector into an exhaust line. Operating under open loop is simple and should provide the best gas quality, assuming the gas bottle is of high purity. It has the disadvantage of consuming a large amount of gas, which is not an issue if the gas mixture is inexpensive, as is the case of the argon mixture, but not for the xenon-neon mixture. In the closed-loop mode, the gas is continuously purified by a filter and recirculated back into the detector. The closed-loop mode is more complex and requires a gas filter and a gas recirculation system. Closed-loop operation is more suitable for expensive gas mixtures, such as the xenon-neon mixture.

This design direction is consistent with the IAXO pathfinder detector operated at CAST, where xenon-compatible running motivated the installation of a recirculation and purification line including isolation electrovalves, flow controllers, pressure sensors, and dedicated moisture and oxygen filters [65]. The CAST experience is especially relevant here because it showed that closed-loop operation is not merely a gas-handling convenience, but a practical requirement when moving toward more expensive mixtures and longer stable surface campaigns.

For detector operation, the gas system is therefore not only a delivery line but also a monitoring and reproducibility system. Pressure, flow, oxygen and moisture content, filter status, and mixture composition determine the charge-transport properties summarized earlier in the chapter. These quantities also define the simulation input: the gas tables used by the detector-response model must correspond to the same mixture, pressure, temperature, and drift-field range used in data taking. The software workflow developed to generate and query these Garfield++/Magboltz gas files, including the gas-cli utility, is described in Section 4.5.6.

3.3.2 High-Voltage System

The Micromegas detectors require a high-voltage system to provide the drift field in the TPC and the amplification field in the Micromegas gap. Two high-voltage channels are used for each Micromegas detector: one for the drift region, applied to the cathode, and one for the amplification region, applied to the mesh. A CAEN high-voltage power supply is used to provide the detector bias.

The drift voltage must establish a sufficiently uniform electric field across the \(3\,\mathrm {cm}\) gas volume. In the IAXO-D1 chamber, the field quality is supported mechanically by the cathode, the PTFE liner, the copper-coated PCB region, and field-shaping elements around the active volume. These components are part of the detector response even though they do not directly read out charge: field non-uniformities can distort drift paths, change transparency through the mesh, and modify the apparent topology of low-energy events.

The mesh voltage defines the amplification field and therefore controls the gas gain. Because the amplification region operates close to discharge conditions, the voltage distribution includes filtering and protection elements that decouple high-voltage noise from the readout and limit the effect of short discharges. Stable ramping, current monitoring, and trip handling are therefore operational requirements rather than convenience features.

The active veto system also uses high voltage for the photomultiplier tubes coupled to the scintillator panels. Although the veto high-voltage settings are physically separate from the Micromegas mesh and cathode channels, they enter the same detector-operation problem: veto gain, trigger threshold, and timing stability determine whether a Micromegas event is correctly tagged as veto-coincident.

The CAEN high-voltage power supplies used can be controlled via a serial connection. This allows the high-voltage system to be managed by the Slow-Control, enabling the monitoring and control of the high-voltage levels remotely. In particular, automatic control of the detector high voltage is useful because trips can occur during long data-taking periods. The Slow-Control can be programmed to automatically turn back on the high-voltage in case of a trip, to send an alert to the operators, or to turn off the high-voltage in case of repeated trips. The software interface used for this type of operation was developed in this thesis as the hvps library [86], a reusable high-voltage power-supply control package described in Section 4.6.3.

3.3.3 Slow-Control System

The Slow-Control System is responsible for the monitoring and control of the ancillary systems of the Micromegas detectors. The Slow-Control continuously reads the status of the systems and can be programmed to take actions based on the readings. It can also be used to send alerts to the operators in case of a problem with the systems.

A web-based interface is used to interact with the Slow-Control, allowing the operators to monitor the status of the systems and to take actions such as turning on or off the high-voltage of the detectors. The data in this dashboard are updated in near real time, allowing the operators to quickly react to any issues that may arise. These data are also periodically stored in a database for later analysis.

The Slow-Control is built using node-red [87], a flow-based development tool for visual programming.

An instructive precedent was provided by the CAST pathfinder campaign, where a compact remote-control system was used to supervise detector high voltages, calibration-source position, readout power supply, muon-veto status, chamber pressure, and gas flow from a single interface [65]. That system also incorporated an automatic trip manager to recover the detector voltage after short discharges, a feature that became particularly important during xenon recirculation studies. This experience reinforces the view that slow control is not a secondary service, but an integral part of stable low-background operation.

3.4 Shielding and Veto Systems

The Micromegas detector is only one part of the complete low-background detection line. For BabyIAXO, the detector must operate inside a passive shield and in coincidence with an active veto system, so the mechanical envelope, signal feedthroughs, calibration access, gas services, high-voltage routing, and data-acquisition interfaces all have to remain compatible with the surrounding shielding. The detailed passive-shielding studies, cosmic-ray-induced background simulations, and scintillator–cadmium veto design are therefore treated in the dedicated shielding and veto chapter, Chapter 5. In the present chapter, the relevant point is the interface: Micromegas operation defines the x-ray-like event selection, timing reference, calibration strategy, and veto-coincidence information that the background model uses later.

3.5 Data Acquisition System

This section describes the detector-facing DAQ hardware: how the Micromegas strips and veto channels are connected to front-end electronics, back-end timing, and the DAQ computer. The acquisition software itself, including the feminos-daq refactor and online viewer, is treated in the software chapter.

The Data Acquisition (DAQ) system is responsible for the readout and storage of the detector signals. It is composed of three main components: the Front-End Card (FEC), the Front-End Module (FEM), and the Data Acquisition Computer (DAQ PC).

The overall architecture follows the same detector-readout philosophy adopted for the IAXO pathfinder line at CAST, where the 240 Micromegas strips were read through four AGET chips connected to a Feminos back-end board, with the external muon-veto signal routed to an otherwise unused AGET channel so that veto and TPC information could be recorded together on an event-by-event basis [65]. In this sense, the pathfinder operation serves as a practical bridge between the late CAST Micromegas generation and the more scalable BabyIAXO-oriented readout concepts.

Figure 3.19 is intentionally placed before the detailed hardware subsections because it summarizes the logic that connects the detector electronics to the later data analysis. At acquisition level, the important point is not only that the Micromegas strips are digitized, but that their waveforms are recorded in a timing-aware event structure that can also accommodate veto information. This common event record is what later allows one to compare Micromegas pulse-shape observables, reconstructed x-ray candidates, and veto coincidences within the same analysis chain. In other words, the DAQ architecture already encodes part of the future discrimination strategy.

Front-End Card

The Front-End Card is responsible for the amplification and digitization of the signals from the detector and is placed as close as possible to the readout. The FEC chips used in this work are the AGET (ASIC for Generic Electronics system for TPCs) chips [88].

Each AGET chip includes 64 channels, supports sample rates of up to 100 MHz, and provides 16 configurable shaping-time settings, ranging from 50 ns to \(1\,\mu \mathrm {s}\). It also features four adjustable gain levels, from 120 fC to 10 pC, and offers the option to select the signal polarity. Each channel has a 512-sample buffer.

These chips are based on the AFTER ASIC [89], which was used in the Micromegas detectors of the CAST experiment. A notable improvement of the AGET chips over the AFTER chips is self-trigger functionality, which allows the chip to automatically trigger the readout when a signal above a certain threshold is detected.

Front-End Module

The Front-End Card used with the IAXO Micromegas detectors consists of four AGET chips, each responsible for 60 channels, for a total of 240 channels. The FEC is connected to the Front-End Module (FEM) as shown in Figure 3.21. The board used is called Feminos [84] and it is responsible for the communication with the FEC and the Data Acquisition Computer (DAQ PC).

The Feminos board consists mainly of an FPGA module, different connection interfaces such as RS232 and Gigabit Ethernet and a few additional components.

The Feminos is connected to the DAQ PC through an Ethernet connection. Multiple Feminos boards can be connected to the same DAQ PC, allowing for the readout of multiple detectors. In this case a Trigger Clock Module (TCM) is used to synchronize multiple Feminos boards.

The configuration of the FEC’s AGET chips is done through the Feminos board via commands sent through the Ethernet connection from the DAQ PC. For instance, a command such as aget * time 0x1 sent to the Feminos sets the shaping-time register value for all AGET chips in the FEC; the corresponding physical shaping time is then determined by the AGET/Feminos configuration map used for that run.

Data Acquisition Computer

The Data Acquisition Computer (DAQ PC) is responsible for the communication with the Feminos boards and the storage of the data it receives. The DAQ PC runs a custom software (DAQ software) that communicates over the Ethernet link with all the connected Feminos boards.

During the initial setup, the DAQ software sends the configuration commands to the Feminos boards to set the AGET chips to the desired settings. After the configuration is done, the DAQ software starts the data acquisition by sending a start command to the Feminos boards. The Feminos boards then start the readout of the AGET chips and continuously send the data to the DAQ PC in the form of UDP packets. The data are encoded in the form of data frames. The DAQ software is responsible for decoding the data frames, which may come from multiple Feminos boards, and constructing the final data file.

The result of an acquisition run is a file or a set of files containing run metadata and waveform data, organized as a collection of events in which each event contains samples from the detector channels.

The custom acquisition software, including the feminos-daq refactor, ROOT output format, online monitoring, compression strategy, and event viewer, is described in Section 4.6.2.

3.5.1 Run configuration and waveform observables

At the detector-operation level, the relevant point is how a run is configured and how the digitized waveform encodes the quantities used later in reconstruction and monitoring. A typical acquisition with the FEC–Feminos chain proceeds as follows:

An instance of the acquisition software is started on the DAQ PC. The software is configured with the IP addresses of the Feminos boards and the desired acquisition settings.

The start sequence is initiated by the operator. The software sends the configuration commands to the Feminos boards to set the AGET chips to the desired settings, including the power-up sequence of the AGET chips.

A pedestal run is performed to measure the mean \(m_i\) and standard deviation \(\sigma _i\) of the channels when they are not triggered. The pedestal values are stored internally in the Feminos boards and are subtracted from the signal values during data acquisition, so that all signals have the same base level. This base level, corresponding to zero signal, can be set in the configuration and is usually set to 250 ADC counts, as recommended by the Feminos authors. Figure 3.22 shows a sample event with all channels at the same base level due to the pedestal subtraction.

Each channel can serve as a trigger. The trigger level, the value above which a signal is considered a trigger, can be configured and is set to three times the standard deviation of the pedestal values. The acquisition can be configured to return all signals or only the triggered signals.

Figure 3.23 summarizes the morphology of a typical single-channel waveform after pedestal subtraction. The relevant information is the pulse height, the collected charge, the time at which the pulse develops, and the width and symmetry of the shaped response. These quantities are not only electronics diagnostics: they are the first experimental handles used to separate compact x-ray-like events from extended tracks, pile-up, or pathological waveforms.

The most important run settings are therefore those that modify this pulse morphology. The gain sets the overall amplitude scale, the shaping time determines the width and asymmetry of the pulse, the sampling period fixes the time granularity of the waveform, and the trigger delay determines how much pre-trigger baseline and post-trigger tail are recorded. The trigger threshold also matters because it decides which channels enter the event and can therefore affect both the reconstructed charge and the timing pattern. Although some settings can in principle be adjusted channel by channel, they are normally chosen coherently for the full readout so that the event can be interpreted with a single response model.

After digitization, the reconstruction combines the channel-level pulse information into a smaller set of event-level quantities. For calibration, these are mainly energy estimators, such as the pulse height, the integrated charge around the maximum, the charge above threshold, or the reconstructed readout energy. For event selection, they are complemented by timing and topology descriptors that measure whether the active strips are compact and mutually synchronous. This is the level at which the raw waveform description becomes part of the later signal analysis: x-ray-like events should produce narrow, well-aligned strip responses, whereas background-like or poorly reconstructed events tend to be broader, more asymmetric, or less synchronous.

3.6 Detector Calibration

The operation of a Micromegas detector involves a set of coupled parameters that must remain under control in order to guarantee stable gain, reproducible energy calibration, and a well-defined trigger threshold. In the gas system, the most relevant settings are the gas flow, chamber pressure, and gas mixture. In the detector itself, the drift and amplification voltages determine the transparency of the mesh and the gas gain. At the readout level, shaping time, trigger delay, sampling configuration, and threshold settings define how the pulse is digitized and which events are retained. In addition to these explicitly configured quantities, environmental variables such as temperature, as well as slow drifts in gas quality, can also modify the detector response. For that reason, the relevant detector and DAQ settings are stored together with the run metadata and are monitored through regular calibration runs.

From the point of view of data taking, the acquisition is organized in runs, each one corresponding to a period with fixed detector and DAQ settings. The run duration may range from a few minutes to several hours depending on the purpose of the measurement. In practice, the most important distinction is between calibration runs and background or tracking runs. The former provide a controlled x-ray-like reference with which the detector gain, energy scale, resolution, and threshold can be monitored. The latter provide the physics data used for background characterization and, when relevant, for axion-sensitive exposure. In the CAST pathfinder campaign, the daily operating sequence was explicitly structured around this logic, with regular \(\ce {^{55}Fe}\) calibrations used to track the detector response and to associate each background or tracking period with the most representative nearby calibration [65].

3.6.1 Standard x-ray calibration

The standard calibration procedure uses a source of soft x rays placed in front of the detector window, typically through a dedicated calibration port. The most common choice is \(\ce {^{55}Fe}\), whose dominant manganese K-shell line at \(5.9\,\mathrm {keV}\) lies inside the energy region most relevant for the axion search and generates compact, x-ray-like events in the gas. Additional sources such as \(\ce {^{109}Cd}\) may be used for complementary checks at higher energy, but \(\ce {^{55}Fe}\) remains the reference source for routine operation. Since photons in this energy range interact predominantly through the photoelectric effect, the resulting signal is a localized ionization cluster that closely resembles the topology of a low-energy x-ray conversion in the Micromegas gas.

In routine operation, the calibration data are first used for a fast data-quality check. A reconstructed hit map verifies that the source illuminates the expected region of the detector and that no large-scale asymmetry or dead area has appeared. The corresponding energy spectrum is then inspected to verify the position and width of the main photopeak, which provides an immediate monitor of gain stability, energy resolution, and effective threshold. This daily quick-look procedure was an important part of the CAST pathfinder operation and is especially relevant for surface-running detectors, where small changes in gas quality, voltage settings, or noise conditions can translate into visible shifts of the calibration peak from run to run [65]. Figure 3.24 shows a representative IAXO-D0 \(\ce {^{55}Fe}\) calibration spectrum together with the corresponding simulated calibration spectrum after applying the same energy scale and detector-resolution broadening. The dominant structure is the manganese \(K_{\alpha }\) line at \(5.9\,\mathrm {keV}\), while the weaker \(K_{\beta }\) contribution appears at higher energy. The fit therefore uses the two \(\ce {^{55}Fe}\) lines rather than a single Gaussian, and the quoted FWHM refers to the fitted \(K_{\alpha }\) component.

The energy calibration itself is obtained from fits to the reconstructed calibration spectrum. For argon-based mixtures, the main \(5.9\,\mathrm {keV}\) photopeak and the argon escape structure around \(2.9\,\mathrm {keV}\) provide a convenient linear calibration of ADC units to deposited energy [65]. For xenon-based operation, where the argon escape feature is absent, the calibration can be anchored to the \(5.9\,\mathrm {keV}\) line alone with a linear relation through the origin. Repeating this procedure run by run makes it possible to quantify the long-term evolution of the gain and to propagate the appropriate calibration constants to the associated physics runs and selection studies.

The reconstructed calibration energy can be estimated in several ways, each one emphasizing a different aspect of the waveform or of the reconstructed hit. Table 3.2 compares a representative set of these energy estimators using the same calibration run and the corresponding simulated calibration sample. Integrated charge-like quantities give comparable resolutions, while a single-channel maximum-amplitude estimator performs significantly worse because it is more sensitive to charge sharing and local fluctuations. The simulated column is calculated after applying the same energy-scale and detector-response corrections used for Figure 3.24, so the comparison refers to the final experimental-like calibration spectra.

3.6.2 Experimental-like TPC signal production

The comparison in Figure 3.24 addresses the reconstructed energy scale and the width of the \(\ce {^{55}Fe}\) peak, but it does not fully describe the raw waveform population. At waveform level, measured Micromegas calibration events contain baseline fluctuations, coherent low-frequency structure, channel-to-channel correlations, and occasional noise excursions close to the signal region. These features are not reproduced by an idealized simulated waveform, even after the deterministic shaping time, signal timing, gain, and event-level smearing have been tuned. This distinction matters because the reconstruction does not operate on true deposited energy. It operates on peak lists, thresholds, timing windows, and baseline-corrected amplitudes derived from the raw traces.

For this reason, a data-driven residual-noise study was performed using real \(\ce {^{55}Fe}\) calibration waveforms as the reference sample. The approach separates the deterministic simulated signal from the stochastic residual response:

where \(c\) is the TPC channel index and \(t\) is the digitizer sample bin. The residual term \(N_{\mathrm {GAN}}\) was generated by a convolutional generative adversarial network trained to reproduce the difference between tuned simulated calibration traces and measured calibration traces. The generated residuals are applied to the full two-dimensional channel–time waveform, not only to quiet pre-trigger bins. This is important because real noisy structures can modify the reconstructed peak list itself, especially for low-amplitude channels near threshold.

The full detector-response chain used to produce experimental-like raw signals is summarized in Figure 3.25. The diagram should be read as a sequence of physical and operational transformations rather than as a strict list of individual REST processes. In an actual REST configuration some of these steps are combined inside the same process or controlled through metadata parameters. The important point is that the response parameters are not freely retuned to copy a calibration trace. The gas, field, readout, shaping, sampling, and other run settings are taken from the corresponding experimental configuration; only the energy calibration factor and the additional energy smearing are tuned to reproduce the \(\ce {^{55}Fe}\) peak position and resolution. The residual bank then adds the stochastic channel-time structure that is absent from the deterministic simulation.

Figure 3.26 shows the effect in a form close to the quantities used by the peak finder. For clarity, the measured event and the deterministic simulated event underneath the residual were chosen to have similar \(\ce {^{55}Fe}\) pulse timing, width, amplitude, and active-channel multiplicity, so the comparison isolates the remaining waveform-level discrepancy. This selection is only for the illustrative waveform comparison; the simulation chain uses the experimental-run settings, with spectrum-level tuning restricted to the energy calibration factor and smearing. In the signal region, the noisy simulation preserves the main pulse position and shape. The main missing ingredient is the stochastic component: measured active channels fluctuate around the pulse, and quiet channels show correlated excursions rather than perfectly flat baselines. The learned residual adds this missing texture to both active and quiet channels, making the simulated raw traces more representative of the data seen by the reconstruction.

These waveform-level checks support the use of an empirical residual bank as a practical detector-response correction. In the REST analysis chain the residual bank should be injected after conversion to raw TPC signals and before baseline correction and peak finding, so that noisy structures can affect the same reconstructed observables as in data. This ordering is essential: adding noise only to already reconstructed peak observables cannot reproduce changes in peak multiplicity, threshold crossings, or accidental noisy peaks. The implementation developed for this purpose is a raw-signal process that reads event-wise residual waveforms, maps them to the TPC channel IDs, and adds them to the simulated TRestRawSignalEvent before the standard peak-finding process.

The present result should be understood as a waveform-level validation of the method rather than a final calibration-spectrum closure test. The available dense waveform sample used for the GAN study contains a limited set of tuned simulated \(\ce {^{55}Fe}\) conditions, and the high-statistics spectral comparison must be repeated with a full REST reprocessing of simulated calibration events after the raw-level residual injection. Nevertheless, the study demonstrates that the missing electronic-noise component is not independent white noise. It has measurable channel–time correlations and can be reproduced in a way that preserves the simulated x-ray signal while producing more realistic raw Micromegas traces.

3.6.3 UV-light calibration R&D

A complementary calibration concept was explored during a three-month internship at CEA Saclay. This work is not part of the baseline BabyIAXO calibration strategy, which remains based on x-ray source runs, but it is worth retaining as detector R&D because it addresses a closely related problem: how to generate controlled, localized, and time-stamped primary electrons in a Micromegas gas volume. The idea is inspired by Micromegas-based photocathode detectors such as PICOSEC [90], where ultraviolet photons release photoelectrons that are subsequently drifted and amplified.

In the CEA setup, a pulsed ultraviolet source illuminated an aluminized cathode through a UV-transparent window. The lamp trigger provided a timing reference, while the anode pulse arrival time was measured after electron drift and amplification. By repeating the measurement with spacers of different thicknesses, the drift distance was changed in a controlled way and the drift velocity could be estimated from the variation of pulse arrival time with distance. The presentation study used argon–isobutane mixtures, several quencher fractions, and comparisons with Garfield++/Magboltz drift-velocity calculations. The measured velocities had the expected order of magnitude and qualitative field dependence, although offsets with respect to the simulation remained and were attributed to possible gas-settling, field, photocathode, or space-charge effects.

For the present thesis, the importance of this work is methodological rather than as a mature calibration proposal. A pulsed UV system could, in principle, provide single-electron or few-electron calibration, localized topological checks, timing studies, and gas-transport measurements without relying only on radioactive x-ray sources. However, the tested gas-discharge lamp had limited pulse stability, and a quantitative implementation for BabyIAXO would require a better-controlled UV source, calibrated photocathode response, stable gas conditions, and a dedicated comparison with the final detector geometry and readout. Supplementary figures from this R&D study are collected in Appendix 6.21.

Chapter 4
Computational Framework

4.1 Scope and software contributions of this thesis

This chapter describes the software tools and framework components that were developed, extended, or validated during the course of this thesis. It does not attempt to catalogue the full IAXO software stack; instead, it focuses on software that was either created as part of this work or modified in ways that directly enabled the background-model studies and veto analysis presented in later chapters.

The distinction between pre-existing infrastructure and thesis-specific contributions is important for understanding the role of each component. REST-for-Physics [91], Geant4 [92–94], ROOT [95], CRY [96], and the Kotlin GDML domain-specific language were already available when this work began. The contributions of this thesis lie in integrating these tools into a reproducible end-to-end simulation and analysis workflow, adding new generators and analysis processes, developing auxiliary tools for validation and monitoring, and scaling the production to the throughput required for an IAXO background model. Tables 4.1 and 4.2 summarize the main software components and their role in the thesis.

4.2 The ROOT Data Analysis Framework and Python interoperability

ROOT [95] is the data analysis framework developed by CERN and the foundation on which REST-for-Physics is built. For this thesis, the most relevant features of ROOT are its file format (.root), its TTree columnar storage, its Python bindings (PyROOT), and the serialization dictionary system that REST-for-Physics relies on for metadata persistence and versioning.

The simulations and analyses reported in this thesis used ROOT v6.34.04. The ROOT file format remains the primary data container for both Monte Carlo and experimental data within the IAXO collaboration. Every restG4 simulation, every restManager processing step, and every DAQ acquisition file uses the same underlying storage format, which is essential for maintaining a single analysis language across the full chain.

While ROOT provides extensive built-in visualization and analysis tools, most of the figures in this thesis were produced with Python libraries such as Matplotlib and Plotly. This was possible thanks to two developments: ROOT’s own PyROOT interface, which exposes C++ objects to Python, and Uproot [98], a pure-Python library that reads and writes ROOT files without requiring a ROOT installation.

4.2.1 Uproot and fsspec integration

Uproot is widely used for reading ROOT files in Python and underpins many Python-based HEP analysis workflows. A three-month IRIS-HEP fellowship during this thesis provided the opportunity to contribute to Uproot directly. At the time, Uproot supported local files and a few remote protocols (HTTP, XRootD), each requiring a hand-written implementation inside the library. The fellowship work delegated all file-I/O operations in Uproot to fsspec, a Python library that provides a uniform interface across local and remote file systems. This change, released in Uproot v5.2.0, simplified the codebase and made every fsspec-compatible protocol (including SSH, cloud object stores, and WebDAV) available to Uproot without additional maintenance burden.

This integration was directly useful for the present thesis in two ways. First, it enabled the feminos-viewer application to open remote DAQ files over SSH while they are being written, using the same code path as local files. Second, it allowed the Python-based background-analysis scripts to read simulation outputs directly from the NAF-IAXO dCache storage without copying them locally. The experience also provided a thorough understanding of the ROOT file format, which was important for designing the DAQ ROOT output and for debugging file-structure issues during analysis.

4.3 REST-for-Physics as the common event-processing framework

REST-for-Physics [91] (Rare Event Searches Toolkit for Physics) is an open-source, collaborative C++/ROOT-based framework that provides a unified environment for data acquisition, Monte Carlo simulation, detector-response emulation, and physics analysis. It was originally developed for experiments searching for rare phenomena such as neutrino interactions, dark matter, and axion signals, where precise detector modeling and reproducible analysis chains are essential.

The framework’s relevance extends beyond the present thesis. Cristina Margalejo Blasco’s recent thesis on the IAXO pathfinder detector at CAST independently demonstrates the same architecture being used for a Micromegas-based low-background line that is directly connected to the BabyIAXO and IAXO detector technology roadmap [65]. That work reinforces the claim that REST-for-Physics is most powerful when used as a common analysis language spanning transport, response, reconstruction, and event selection for Micromegas-based experiments.

REST-for-Physics is structured as a core Git repository with libraries and packages as Git submodules. It is strongly rooted in the ROOT ecosystem and follows ROOT conventions for class naming, I/O patterns, and dictionary-based serialization. The framework exposes three main executables: restG4, a user-configurable Geant4 application initialized via RML configuration files; restManager, which applies a sequence of processing stages to data; and restRoot, a ROOT interpreter wrapper that loads the REST-for-Physics environment for interactive data inspection.

4.3.1 Event-based processing and the EventTree/AnalysisTree model

REST-for-Physics follows an event-driven architecture. The abstract TRestEvent class is the central data container, with libraries defining their own derived event types (e.g. TRestGeant4Event, TRestRawSignalEvent, TRestTrackEvent). Each library also provides processes that transform one event type into another or compute scalar observables.

Data persistence is organized around two complementary TTree structures. The EventTree stores full event representations, preserving the physics content at each stage of the chain. The AnalysisTree, implemented as TRestAnalysisTree, stores scalar observables computed by the different processes and is used for cuts, control plots, efficiency studies, and background estimates. This separation is especially valuable in rare-event searches, where thresholds and selections are often scanned many times without regenerating the complete event representation.

For the IAXO-D0 and BabyIAXO studies, a common analysis.rml chain transformed Geant4 truth information into Micromegas and veto observables that could be treated with the same logic used for measured data. In the TPC branch this meant deriving reconstructed hit and track observables for X-ray/background discrimination. In the veto branch it meant generating realistic waveforms and applying peak finding to obtain timing, amplitude, and multiplicity observables. The event-type evolution is one of the key strengths of the framework, because it ensures that the final analysis is performed on reconstructed observables rather than on idealized Monte Carlo truth quantities.

The AnalysisTree approach also provides a systematic way of turning reconstruction outputs into reusable analysis products. Observables filled by each process can be inspected interactively, processed through ROOT macros or Python scripts, or consumed by dedicated REST-for-Physics plotting utilities. In this thesis many final figures were produced with external tools, but the underlying quantities were still derived from the common REST-for-Physics reconstruction chain, ensuring that simulation and experimental analyses remained aligned at the observable level.

4.3.2 Reproducibility and maintainability

REST-for-Physics stores the full analysis configuration as metadata objects inside the ROOT file, including framework version, dependency versions, and RML parameters. This allows any ROOT file to be re-analyzed with the original configuration or to be inspected for provenance. The source code is version-controlled and openly available on GitHub; periodic releases specify recommended versions of ROOT, Geant4, and Garfield++ to simplify reproducibility. Container images with pre-built dependencies are provided for users who want a consistent environment, and a comprehensive test suite with Google Test runs in GitHub Actions CI for every pull request. These practices were adopted throughout the production campaigns described in this thesis, and the CI infrastructure was migrated from GitLab to GitHub Actions during this work. Table 4.3 summarizes the practical provenance information that was preserved or recorded for the production campaigns used in this thesis.

4.4 Detector readout metadata and channel mapping

An essential intermediate layer between transport simulation and physics analysis is the detector readout description encoded in the TRestDetectorReadout metadata classes. In plain terms, this layer translates electronics channel numbers into physical detector positions and types, making it possible to know whether a signal came from a Micromegas strip, a veto scintillator panel, or a specific region of the detector. Without it, a waveform would remain only a list of ADC samples attached to an integer channel number. With it, the same processing chain can move consistently from raw signals to detector signals, and from detector signals to reconstructed hits and tracks, while preserving the physical interpretation of each channel.

The readout description is organized hierarchically. TRestDetectorReadout stores the full detector readout as a collection of TRestDetectorReadoutPlane objects. Each plane defines a position and orientation in world coordinates, the normal vector that identifies the drift side, the effective height of the active volume, and a semantic type such as tpc or veto. Each plane contains TRestDetectorReadoutModule objects, which define the local geometry of a readout module. Inside each module, TRestDetectorReadoutChannel stores the correspondence between the DAQ identifier and the physical channel identifier, while TRestDetectorReadoutPixel provides the elementary polygons representing the actual sensitive pattern. A physical channel may be composed of many pixels combined into a complex strip or pad geometry, which is important for the microbulk Micromegas pattern, where each strip is constructed from multiple pixels including the special edge pieces required by the real detector layout.

For the veto system, the effort was even more detector-specific. The scintillator panels do not form a single regular plane but a distributed system of individually oriented detector elements surrounding the shielding. Dedicated readout-generation code was developed to build one TRestDetectorReadoutPlane per veto panel, using the geometry information to determine the panel position, its outward normal, and the corresponding effective sensitive depth. Each panel was assigned a unique channel identifier and an alias matching the experimental naming convention. This mapping step was essential because the later analysis is formulated in terms of physical veto groups, layers, and aliases rather than arbitrary DAQ integers.

This metadata layer bridges the simulation-side and data-side representations of the detector response. On the simulation side, processes such as TRestDetectorHitsToSignalProcess use the readout geometry to decide which channels collect charge or light from a given interaction point. On the experimental side, TRestRawToDetectorSignalProcess and TRestDetectorSignalToHitsProcess use the same readout definition to transform digitized waveforms back into detector signals and then into reconstructed spatial hits. The auxiliary TRestRawReadoutMetadataProcess serializes channel-level information so that later waveform-analysis stages can distinguish TPC channels from veto channels without relying on external spreadsheets.

This was one of the most consequential software contributions of this thesis because it made the Micromegas and veto branches speak the same analysis language. That capability becomes especially important in the signal-analysis chapters, where waveform observables, strip topology, and veto coincidences must be combined in a single event-level selection strategy.

4.5 Geant4 simulation infrastructure

4.5.1 restG4 and Geant4Lib: the interface to Geant4

Geant4 [92–94] is a Monte Carlo toolkit for simulating the passage of particles through matter, widely used in high-energy physics, nuclear physics, and medical applications. Geant4 does not provide a command-line interface; users write a C++ application that instantiates the toolkit with a specific geometry, physics list, and primary generator. These applications share a large amount of boilerplate code, and Geant4 offers no built-in solution for serializing event data.

REST-for-Physics addresses this through restG4 (the executable) and Geant4Lib (the library): a modular, user-configurable Geant4 application that is driven by RML configuration files rather than recompilation. During this work, restG4 received over 600 commits and Geant4Lib over 370 commits. The most significant improvements are summarized below.

Geant4 event model and REST-for-Physics representation

In the Geant4 framework, a run is a collection of events sharing a fixed detector geometry and physics configuration. A run is initialized once (an expensive operation that loads geometry and cross sections) and then executes many events. A primary generation occurs at the beginning of each event, when one or more primary particles are created with specified energies, directions, and positions. Each primary particle is tracked through the geometry in a process called radiation transport, moving in discrete steps whose lengths are determined by the cross sections of active physics processes. Interactions can produce secondary particles, which are themselves tracked. The full chain of secondaries must be considered when calculating the energy deposited in a given detector region.

The principal Geant4 data structures (run, event, track, and step) are represented in Geant4Lib. Geant4 steps are stored as REST-for-Physics hits, which contain the position, momentum, time, energy, interaction process, and target information at a single point. Geant4 also provides user-action hooks at various levels (event, tracking, stepping); a stacking-action hook was added during this work to tag new tracks before processing, enabling long-lived secondaries to be isolated into separate sub-events with distinct sub-event identifiers while remaining traceable to the same Geant4 event.

Multi-threading and track pruning

Radiation transport is naturally parallelizable at the event level, since events are independent. During this work, support for Geant4 multi-threading was added to restG4, requiring a thread-safe event container and synchronization primitives with minimal performance impact. Support for interrupt-signal handling was also added, allowing a simulation to be stopped cleanly while preserving all output produced up to that point.

Track pruning was implemented to reduce output size and analysis time. The user specifies which detector volumes are of interest (e.g. the gas volume and the scintillator panels). Tracks and hits not associated with these volumes are removed, while the full track leading to a hit in a volume of interest is preserved, including intermediate steps through passive material, so that visualization tools retain all necessary information. This reduces output file size by a factor of 1–10, depending on the simulation configuration, without changing the observables used in the veto and TPC analyses, as checked in validation runs.

4.5.2 Geometry-generation infrastructure for IAXO simulations

The IAXO detector geometries used in this thesis—including the IAXO-D0 prototype, passive-shielding scans, and successive veto-layer designs—were defined through a dedicated geometry-generation workflow rather than hand-edited Geant4 C++ code. The Geometry Description Markup Language (GDML) [99] is an XML-based format for describing detector geometries, supported natively by both Geant4 and ROOT.

The complexity of the IAXO geometry (over 400 individual components in some veto iterations) made manually writing GDML impractical. A Kotlin-based domain-specific language (commonly referred to as gdml.kt) was developed within the collaboration to build GDML files from a higher-level, parameterized description. The author collaborated in its continued development, validation, and application to the IAXO-D0 and BabyIAXO simulation campaigns. The thesis contribution is not the invention of the Kotlin DSL itself, but the integration of that geometry-generation approach into the full simulation, analysis, veto-mapping, and visualization workflow.

The generated geometries are tracked in a dedicated Git repository, so each simulation can be associated with the commit hash of the geometry used to produce it. A hierarchical geometry description allows groups of related volumes to be enabled, disabled, or highlighted in the event viewer, connecting gdml.kt directly to the visualization package.

A technical challenge arose from Geant4’s handling of GDML assemblies: physical-volume names were converted into hashed identifiers during parsing, which prevented restG4 from mapping simulation properties (step-size limits, production cuts) to volumes by name. Significant effort was devoted to resolving these hashed names back to human-readable representations and to implementing support for logical-volume-name references, enabling properties to be assigned consistently to all instances of a repeated component. These developments made the complex IAXO geometries usable for production simulations in which detector materials, sensitive regions, and veto-channel definitions must remain traceable across many geometry versions.

The same semantic geometry information was used to validate the veto readout mapping. When the browser event viewer highlights a panel that received an energy deposit, the displayed panel, the Geant4 sensitive volume, the readout channel, and the analysis observable must all refer to the same detector element. Several iterations of the veto geometry and readout description were checked in this way, and the visualization package closed the loop: the Kotlin DSL produced the GDML, restG4 transported particles through it, the detector-response chain reconstructed signals using the readout metadata, and the browser viewer made it possible to inspect whether all these representations agreed event by event.

4.5.3 Python interface to REST-for-Physics

REST-for-Physics inherits ROOT’s PyROOT interface, which automatically generates Python bindings from the C++ class dictionaries. This allows REST-for-Physics objects to be used from Python with nearly identical syntax to the C++ API, as illustrated in Figure 4.4.

The Python interface makes it possible to prototype analysis code quickly, integrate with the Python scientific ecosystem, and use Jupyter notebooks for interactive data exploration. The performance penalty of interpreted Python loops can be mitigated by using optimized array libraries such as Awkward Array [100] or by relying on compiled C++ backends. In the present thesis, the Python interface was used extensively for generating plots, scanning cut thresholds, and performing statistical analyses that would have been more cumbersome to develop in C++ alone.

4.5.4 Probability Distribution Projection cosmic-ray generator

The cosmic-ray background simulations required for this thesis launch primary particles from the atmosphere toward the detector. The conventional approach—generating particles uniformly over a large plane above the detector and discarding those that miss—is physically intuitive but highly inefficient for compact geometries like the IAXO-D0 detector surrounded by shielding.

To address this, a new cosmic-ray generator was developed and published during this work [97]. The Probability Distribution Projection (PDP) method samples directly from the subset of trajectories that intersect a sphere enclosing the geometry of interest. For a fixed zenith angle, the allowed starting points are restricted to the ellipse obtained by projecting the enclosing sphere onto a plane tangent to it. The generator does not sample the original zenith distribution \(f(\theta )\) directly, but rather the conditional distribution \(f(\theta \mid \text {intersect sphere}) \propto f(\theta )\sec (\theta )\), which concentrates computational effort on useful trajectories only.

The method was validated against the standard Monte Carlo approach using two complementary observables: the zenith-angle distribution of intersecting trajectories and the distance distribution between the intersection point and the detector axis, which probes the spatial phase-space sampled by the generator. The comparison showed that the PDP method reproduces both observables within statistical uncertainties once the conventional Monte Carlo is run in its converged regime.

For the IAXO-D0 geometry, the PDP method improved the computation yield by a factor of approximately three compared with the fastest (and least accurate) conventional configuration. When compared at equal physical accuracy against the large generation disks needed for the conventional method to converge, the advantage reached up to a factor of about 37. This optimization was particularly valuable for the large cosmic-ray production campaigns discussed in the shielding and veto system chapter and the background model chapter, where the cumulative cost of low-efficiency simulations would otherwise have been prohibitive.

4.5.5 Cosmic-ray source generators

The simulation of cosmic-ray backgrounds involves two conceptually distinct tasks: generating the atmospheric secondary flux (performed with packages such as CRY [96] or CORSIKA [101]) and efficiently injecting those secondaries into the detailed IAXO Geant4 geometry. The PDP method addresses the second task; it does not replace shower generators but provides a more efficient way of sampling the already-modeled flux around the detector.

A dedicated auxiliary program was developed to precompute the cosmic-ray secondary distributions used as input for the Geant4 simulations [102]. The program runs CRY for a chosen site configuration, including latitude, date, altitude, and lateral generation box, and records the secondary particles crossing the generation surface. For each relevant particle species, the output is reduced to two-dimensional histograms in kinetic energy and zenith angle, \(H_i(E,\theta )\), stored in ROOT files for muons, electrons, positrons, photons, protons, and neutrons. The histograms carry the particle-dependent source term, while the later restG4 generator handles the geometry-dependent part of the problem: sampling a direction, choosing a valid entry point around the detector, and launching the particle into the detailed IAXO geometry.

This design deliberately decouples the atmospheric calculation from the detector transport. Instead of calling CRY inside every detector simulation, the atmospheric source term is computed once and reused across passive-shielding scans, veto-layer geometries, and production campaigns. It also makes the source term inspectable: the same ROOT histograms can be plotted, compared with EXPACS or HENSA measurements, or replaced by a different measured spectrum without changing the detector-response chain. In the final neutron studies, for example, the measured HENSA energy spectrum is passed through the same histogram-based interface, while the missing incident-direction information is supplied by the \(\sin \theta \cos ^2\theta \) angular model discussed in the veto-system chapter.

In the end, the production campaigns reported in this thesis relied predominantly on this CRY-based workflow for muons, photons, protons, electrons, and positrons. For neutrons, CRY remained essential as a generator-level cross-check and as the reference used to validate the angular prescription, while the final outdoor neutron energy source term was anchored to the HENSA measurement.

4.5.6 Radiation transport in gases: Garfield++

Garfield++ is a widely used software package for simulating the behavior of gaseous detectors. Within REST-for-Physics, it is an optional dependency used to precompute gas-transport parameters such as electron drift velocity, diffusion coefficients, and Townsend and attachment coefficients as a function of the applied electric field. These parameters (shown in the Micromegas detector chapter, Figures 3.4 and 3.5) are then used by REST-for-Physics to model the drift and diffusion of ionization electrons in the TPC gas volume without performing a full Garfield++ particle-by-particle transport, which would be computationally prohibitive.

A small companion tool, gas-cli, was developed to make this gas-table workflow reproducible and scalable [103]. The program provides a command-line interface for generating, reading, and merging Garfield++ gas files, including mixtures with several components, configurable pressure and temperature, and electric-field grids defined by explicit points or linear and logarithmic ranges. This was useful because gas-file generation with Garfield++/Magboltz is compute intensive. Once the calculation is expressed as a deterministic command or Docker invocation, large scans over gas mixtures and electric fields can be dispatched to high-throughput computing resources and later merged or queried in a uniform way. The same tool can extract gas properties such as drift velocity, longitudinal and transverse diffusion, Townsend coefficient, and attachment coefficient into JSON summaries, which makes it straightforward to compare physical properties across candidate mixtures while preserving the .gas files consumed by the detector-response chain.

The full Garfield++ microscopic transport was not integrated into the restG4 simulation chain; it was used only for generating the precomputed gas-parameter tables that the REST-for-Physics detector-response processes consume. Explicit integration of Garfield++ with Geant4, as described in [104], remains a potential future improvement, but was not required for the background-model studies presented in this thesis.

4.6 Visualization, online diagnostics, and detector operations

4.6.1 Browser-based Geant4 event viewer

REST-for-Physics provides a ROOT-based 3D event viewer using TEve, but this interface has significant limitations: CPU-based rendering leads to performance issues with complex geometries, the backend technology has not seen major updates in recent years, and the interface crashes frequently with large events.

During this thesis, a dedicated browser-based event viewer was developed for REST-for-Physics Geant4 output files. The package converts selected windows of REST-for-Physics ROOT files into a compact JSON scene representation and renders the detector geometry and event history in a web browser using three.js. The central design choice was to keep the heavy ROOT/REST-for-Physics dependency on the server or conversion side, while keeping the browser client simple and portable.

The viewer was developed with three primary use cases in mind:

1. Geometry and readout validation. The viewer renders the detector with a role-aware material model: gas volume, copper vessel, shielding, scintillator panels, cadmium layers, light guides, photomultipliers, and auxiliary elements are assigned distinct colors, transparency values, and visibility controls. This allowed systematic checks that the Kotlin-generated GDML, the restG4 geometry import, the sensitive-volume definitions, the readout metadata, and the reconstructed veto observables were mutually consistent. If the viewer showed a veto panel highlighted by the analysis but no plausible track or capture near that panel, the problem could be traced to the mapping, timing, or reconstruction rather than to the transport simulation.
2. Veto and delayed-capture topology debugging. The event history is displayed as a time-dependent object: particle tracks are colored by particle type, and the user can play the event in time with a configurable hit lifetime. This was particularly useful for cosmic-neutron studies, where the relevant signature can involve a prompt cascade, a delayed neutron capture, and energy deposits in different veto layers separated by microseconds. Several projection modes were added because the IAXO geometry is elongated and surrounded by a layered veto system; the four-panel orthographic view with compact veto maps immediately shows whether an event activates opposite sides, adjacent layers, a local cluster, or a delayed capture-like pattern.
3. Shareable event inspection and figure generation. The deployed viewer supports browsing a curated set of ROOT files, converting only the requested event window, and caching the resulting scene. The cache makes it possible to share stable URLs pointing to a particular file, event entry, and view direction, which is useful when discussing a suspicious topology with collaborators or preparing a thesis figure. Publication-oriented export tools include a single-frame export with veto projections attached and a sequence export that samples the event timeline and writes a reproducible set of frames. The neutron event sequence shown in the background model chapter was produced with this workflow.

The development of this package was closely connected to the geometry and readout work described in Sections 4.4 and 4.5.2. In this sense, the visualization package was not only a presentation tool but also a development instrument used to find geometry mistakes, volume-orientation problems, wrong particle color mappings, missing process labels, and inconsistencies in veto-channel interpretation.

The Phoenix event display [105], an open-source project supported by the High Energy Software Foundation (HSF), provided a useful reference during development. The IAXO viewer was not developed as a fork of Phoenix, but the Phoenix architecture demonstrated how modern browser-based event displays can replace traditional desktop-only visualization tools in high-energy physics.

4.6.2 feminos-daq: acquisition software and online viewer

The Micromegas readout hardware described in Section 3.5 requires a software layer able to configure the Feminos boards, receive UDP data frames, decode the AGET waveforms, store run metadata, and expose enough online information to diagnose the detector during data taking. The original program supplied with the Feminos electronics, mclient, was written in C and stored the received frames in a dedicated binary format, conventionally using the .aqs extension. That approach was sufficient for CAST and for the first IAXO Micromegas tests, but it made online inspection, long-term format maintenance, and integration with the later ROOT/REST-for-Physics analysis chain unnecessarily cumbersome.

During this thesis, the DAQ program was refactored into the feminos-daq repository [106]. The low-level communication with the Feminos boards was preserved where appropriate, while the surrounding software was reorganized around a modern CMake build, C++17, a clearer command-line interface, and direct output to regular ROOT files. The legacy binary output mode remains available for compatibility, but the ROOT format became the preferred output because it can be read with standard ROOT tools or with Uproot [98] without loading experiment-specific dictionaries. This makes raw acquisition data immediately usable from both the detector-control environment and the offline analysis notebooks.

The refactor also added a Prometheus exporter [107], so that acquisition counters and health information can be scraped by the slow-control and monitoring infrastructure. This is important operationally because DAQ failure modes are often visible before they appear in an offline file: malformed frames, missing boards, increasing queue occupancy, or abnormal trigger rates can all indicate detector or network problems during a run. In this sense, feminos-daq is not only a file writer, but part of the experiment-control layer that connects electronics status, detector conditions, and acquired data.

Data storage and file structure

The acquisition process is naturally I/O bound: the program must receive UDP frames from one or more Feminos boards, decode them, optionally compute lightweight online quantities, and write the result to disk without blocking packet reception. To reduce the risk of data loss, feminos-daq separates data reception from event processing and file writing. Incoming frames are passed through an internal queue to a processing thread, which writes the decoded events into the output ROOT file while the receiving thread remains available for new network data. The queue absorbs short processing delays, but it also provides a useful diagnostic because sustained queue growth signals that the writer cannot keep up with the incoming rate.

The output file is flushed periodically, so that an unexpected stop of the DAQ process does not make the entire run unrecoverable. Each file contains a tree of raw events with the event-level metadata and the waveform samples associated with each active signal. Since the file avoids custom ROOT dictionaries, it can be inspected with a plain ROOT installation, processed directly with Uproot, or converted into the REST-for-Physics raw-event format used by the later reconstruction chain.

ROOT compression

DAQ data have different storage regimes depending on the run type. Calibration runs can produce incoming rates of several MB/s because many channels are read out for source-driven events, whereas background runs are usually much lighter. The output format therefore has to balance acquisition safety, write speed, read speed, and long-term disk usage. The feminos-daq implementation exposes compression choices, with high-compression LZMA used as the default and a faster mode available for high-rate calibration conditions.

Table 4.4 summarizes a benchmark performed with a calibration run of 52 194 events, each containing approximately 272 signals with 512 samples per signal. The study compared sample storage types and compression settings using ROOT v6.32.02. The default LZMA setting reduced the file size relative to the default ZLIB output, while the maximum-compression setting saved additional space at a write-time cost too high for routine acquisition. The tested tightly packed unsigned char representation did not provide a practical advantage over unsigned short: although the uncompressed payload would be smaller, the compressed file size remained similar and the extra packing and unpacking logic would complicate the writer.

Processing tests showed no measurable difference in the downstream conversion to REST-for-Physics for the compression settings considered here. The compression choice is therefore mainly an acquisition and storage decision: fast enough writing is required during calibration, while compact files are preferable for long background campaigns.

Online event viewer

REST-for-Physics provides a ROOT-based event viewer for visualizing events throughout the processing chain, from raw signals to processed events. However, it lacks the ability to visualize events in real time as they are being acquired by the data acquisition system. For this reason, feminos-daq includes a dedicated viewer for raw acquisition files.

A Python application, feminos-viewer, was developed to visualize raw data in real time as it is being acquired. It uses Uproot to read the ROOT file and Matplotlib to render waveforms. It can display events from closed files as well as from files that are still being written, either by opening a local or remote file or by attaching to the output of a running acquisition process. The viewer uses readout mappings to translate signal identifiers into physical detector coordinates and includes online observables such as channel activity and energy-like summaries.

feminos-viewer is complementary to the browser-based Geant4 event viewer: the former is an acquisition and waveform-quality monitoring tool, while the latter is a simulation and event-history tool. Both share the broader goal of making detector information inspectable without writing ad hoc analysis code for every diagnostic question. During data taking, feminos-viewer was used to identify detector and acquisition issues quickly, including malformed events, inactive or noisy channels, and inconsistencies between waveform activity and detector-coordinate mapping.

4.6.3 High-voltage control library: hvps

Stable Micromegas operation depends on the high-voltage system as much as on the gas and readout chains. The drift field, amplification field, current limits, ramping behavior, and trip-recovery policy must remain accessible during long background runs, and the relevant quantities should be readable by the same slow-control environment that supervises pressure, flow, temperature, and acquisition status. In practice, however, high-voltage power supplies expose device-specific serial protocols, with different command names, channel conventions, response formats, and status registers. This makes direct integration into detector-control software fragile if every dashboard or script sends raw vendor commands.

To address this problem, a dedicated high-voltage power-supply library, hvps, was developed during this thesis [86]. The package provides a common Python interface for serially controlled high-voltage supplies and currently supports CAEN and iseg devices. Its design follows the physical hierarchy of the instrument: an HVPS object manages the serial connection, a Module object represents the crate or board, and a Channel object exposes the monitor and control quantities associated with one output. Typical channel-level operations include reading the set and monitored voltages, reading the monitored current, switching a channel on or off, configuring ramp parameters, checking status words, and handling trip or interlock-related states. The purpose of the abstraction is not to hide the safety behavior of each device, but to make routine control actions explicit and reusable.

The library was also packaged as an operations tool rather than only as an importable module. A command-line interface allows operators and scripts to query or set high-voltage parameters from the terminal, while keeping the same validation and response-parsing layer used by the Python API. Bindings for Node.js and a Node-RED node were added so that the same backend could be used from web-based slow-control dashboards. This choice is directly connected to the IAXO detector-control model described in the Micromegas chapter: the high-voltage backend can be called from automation flows without duplicating low-level serial-command logic in the graphical interface. The repository also includes a graphical prototype for CAEN N1471H supplies, with real-time voltage and current monitoring, channel switching, alarm indicators, interlock information, and queued command execution to avoid simultaneous serial transactions.

From a software-engineering point of view, hvps occupies a different layer from feminos-daq. feminos-daq is responsible for event acquisition and online waveform inspection, whereas hvps belongs to detector operation and slow control. Both were developed with the same practical objective: reducing the number of ad hoc scripts needed to run and diagnose the detector, and replacing them with tested, version-controlled tools that can be reused in IAXO-D0, IAXO-D1, and future BabyIAXO-oriented setups. The package was released through PyPI, with corresponding Node.js/Node-RED packages distributed through npm, and includes tests for command construction, response parsing, and device-interface behavior. For the purposes of this thesis, its relevance is therefore not only that it can set a voltage, but that it makes high-voltage operation a reproducible software component of the detector system.

4.7 Monte Carlo production at scale

The background-model studies required large-scale Monte Carlo campaigns spanning multiple particle species, shielding configurations, and veto designs. This section describes the production infrastructure that made these campaigns feasible.

4.7.1 End-to-end simulation and analysis chain

The complete workflow used for production simulations follows a fixed sequence of stages:

1. Source generation. Atmospheric secondary distributions (muons, neutrons, photons, electrons, protons) are computed with CRY at the relevant site coordinates and stored as ROOT histograms.
2. restG4 transport. The source histograms are sampled by the primary generator inside restG4, and particles are transported through the IAXO detector geometry using Geant4. The output is a TRestGeant4Event stored in the EventTree.
3. Detector response. Geant4 energy deposits are converted into TRestDetectorHitsEvent and TRestDetectorSignalEvent representations, where quenching, light attenuation, diffusion, and smearing are applied.
4. Raw-signal emulation. Signals are converted to TRestRawSignalEvent through waveform shaping, sampling, trigger positioning, and dynamic-range effects.
5. Reconstruction. Waveforms are reconstructed back into detector hits and tracks, yielding event representations directly comparable to experimental data.
6. AnalysisTree observables. Each processing stage appends scalar observables (hit multiplicities, energies, positions, veto peak times and amplitudes) to the AnalysisTree.
7. Cuts and background-rate extraction. The observables are used to apply fiducial, topological, and energy cuts; the surviving events are normalized by the simulated exposure to produce background rates.

This chain is configured through two RML files stored in the collaboration repository iaxo-simulations [108]: a source-specific simulation.rml and a common analysis.rml. This separation made it possible to treat source generation, transport, response emulation, and final selection as distinct but reproducible stages.

4.7.2 Production workflow with HTCondor

Simulations were orchestrated using HTCondor, a workload management system designed for High-Throughput Computing (HTC) [109]. Unlike traditional HPC environments that optimize for instantaneous floating-point performance, HTCondor maximizes total computational work over long periods through dynamic matchmaking between job requirements and available resources.

A dedicated Python script, restG4ToCondor.py, was developed to facilitate the submission of restG4 jobs to the HTCondor system. The script automates the creation of job description files and manages output data including log files, error reports, and the resulting ROOT files. Its command-line interface extends the restG4 interface, making it easy for users familiar with restG4 to adapt to batch submission.

Table 4.5 summarizes the typical workflow steps for a large Monte Carlo production campaign, from job splitting to the final extraction of analysis observables.

The multi-job productions used in this thesis were run on the National Analysis Facility (NAF) at DESY, referred to here as NAF-IAXO, which provides a centralized computing environment with dCache storage [110] and a HTCondor batch system. Typical campaigns involved 300 parallel jobs of 2–8 hours each, producing tens of thousands of saved events per particle species. The production infrastructure was validated with cosmic-neutron and cosmic-muon campaigns totaling approximately 40 000 final events across 600 Condor jobs.

4.8 geant4-python-application: Python prototyping with Geant4

geant4-python-application is a project developed during this thesis to make small Geant4 studies accessible from Python notebooks and scripts. It is a teaching and prototyping tool, not a replacement for the restG4 production pipeline.

The standard Geant4 workflow is based on user-written C++ applications. Although Python bindings and third-party Python interfaces exist, they do not provide the specific restG4-like, pip-installable, process-isolated application wrapper targeted here for notebooks, teaching, and rapid prototyping. The project wraps a generic user-configurable Geant4 application using Pybind11 to generate Python bindings. Because a Geant4 application cannot be reinitialized once started, process isolation was implemented with Python’s multiprocessing module, allowing each worker process to run its own independent Geant4 instance.

The following concrete outputs were demonstrated with this tool:

• A Jupyter notebook computing the X-ray attenuation length in a given material by running 5 000 Geant4 events and analyzing the results with Awkward Array [100] (Figure 4.13).
• Parallelization of independent simulations through Python’s concurrent.futures interface, with each task launching an isolated Geant4 worker process rather than attempting to reinitialize Geant4 inside a single process.
• Distribution as a pip-installable package on PyPI (Python Package Index), with pre-compiled binary wheels for Linux, Windows, and macOS across multiple Python versions, built via a GitHub Actions CI pipeline.

While geant4-python-application was not used for the production simulations of this thesis, it demonstrated the feasibility of embedding Geant4 inside a Python workflow and contributed to the broader goal of improving the accessibility and maintainability of HEP simulation software.

4.9 Summary and role in the thesis

This chapter has described the software framework and tools that enabled the background-model and veto-system studies presented in later chapters. The contributions can be summarized as follows:

• REST-for-Physics provided a reproducible event-processing architecture in which the same analysis chain could be applied to Monte Carlo and experimental data, ensuring that observables remained aligned across both branches.
• Readout metadata linked detector geometry to electronics channels and analysis observables, making it possible to move from raw waveforms to physically meaningful detector hits and veto peaks within a single framework.
• restG4 and Geant4Lib provided the Geant4 transport layer, extended with multi-threading, track pruning, sub-event splitting, and geometry-name resolution to support the demanding IAXO detector geometries and the throughput required for background-model campaigns.
• The PDP cosmic-ray generator accelerated the simulation of atmospheric secondaries by concentrating computation on trajectories that actually intersect the detector, enabling large-scale cosmic-background productions that would otherwise have been computationally prohibitive.
• The browser-based Geant4 event viewer served as a validation tool for geometry, readout mapping, and veto topology, and as a means of producing publication-quality event figures and sharing event topologies with collaborators.
• feminos-daq and feminos-viewer provided live waveform monitoring and detector-coordinate mapping for the acquisition system, supporting real-time data-quality assessment during IAXO-D0 and IAXO-D1 operation.
• The HTCondor production infrastructure enabled large Monte Carlo campaigns on the NAF-IAXO batch system, with automated job submission, processing, merging, and output staging.
• Python tools (Uproot + fsspec integration, PyROOT, and geant4-python-application) supported interoperability between the C++ simulation framework and the Python analysis ecosystem, enabling rapid prototyping, monitoring, and interactive data exploration.

Collectively, these components formed the computational backbone of the thesis. They allowed the background model to be constructed from reproducible simulations with validated geometry, calibrated detector response, and statistically meaningful event samples, and they ensured that the veto tagging strategies could be developed and tested within the same analysis environment used for the experimental data.

Chapter 5
Shielding and Veto System

Introduction

This chapter describes the design, optimization, construction, and validation of the shielding and active veto system developed for the BabyIAXO/IAXO-D0 Micromegas detector line. The central background problem addressed here is the surface-level cosmic-ray-induced background, in particular the high-energy neutron component that cannot be sufficiently suppressed by passive lead shielding alone. The chapter follows the evolution of the veto concept from the initial source-term studies and passive-shielding simulations to the final multilayer scintillator–cadmium design, waveform-level veto observables, prototype construction, commissioning, and comparison with experimental data.

The design strategy is driven by the fact that high-energy cosmic neutrons are difficult to detect directly. Instead, the lead shielding converts part of the primary neutron flux into showers of lower-energy secondary neutrons and photons. The veto system is therefore optimized not only as a muon veto, but also as a neutron-sensitive active shield exploiting prompt scintillation signals, delayed neutron-capture signatures, and event multiplicity.

The general REST-for-Physics/restG4 simulation infrastructure and the full cosmic-source-generation workflow are described in the software and background-model chapters. Here, only the aspects directly relevant to the shielding and veto design are summarized. The radiation transport studies discussed below were performed with Geant4 through restG4 [91–94].

The chapter is organized around four linked claims. First, the surface source term makes high-energy neutrons a design-limiting background for a low-threshold Micromegas detector. Second, passive lead shielding remains essential for photons but cannot by itself remove the neutron component, and can even transform it into a more distributed secondary shower. Third, repeated scintillator–cadmium stages provide a practical way to tag that shower through prompt, delayed, and multiplicity-rich veto observables. Finally, the commissioned IAXO-D0 prototype validates the same waveform-level logic in data, although the absolute neutron fraction remains limited by source-normalization and detector-response systematics.

5.1 Motivation: surface backgrounds and veto requirements

5.1.1 Design requirements and constraints

Before presenting the simulations and prototype results, it is useful to state explicitly the requirements that shaped the veto concept. The active shielding was not designed as an independent detector placed around the Micromegas chamber. It is part of the same background-rejection chain as the passive shield, the X-ray entrance geometry, the Micromegas reconstruction, and the waveform-level veto analysis. The design problem is therefore constrained by three coupled goals: preserve the low-energy X-ray acceptance, suppress the surface cosmic-ray background, and remain compatible with the available scintillator modules, mechanical envelope, and readout electronics.

Several of these requirements pull in opposite directions. Increasing the lead thickness improves gamma attenuation but increases the importance of neutron multiplication in the shield. Extending the delayed window recovers more capture-like activity but raises the accidental-coincidence probability. Increasing segmentation improves topology and channel-level diagnostics but is limited by the number of available readout channels and by the inherited scintillator geometry. The rest of this chapter follows these trade-offs in order: first the surface source term and material interactions, then the limits of passive shielding, and finally the active scintillator–cadmium veto response at waveform level.

5.1.2 Surface cosmic-ray source term

The veto design studies rely on a common description of the atmospheric-secondary background at surface level. Only a short summary is given here, since the CRY-to-REST source-generation workflow is described in Section 4.5.5 and the component normalization is part of the broader background-model effort. For the veto studies, the relevant secondary populations are muons, neutrons, photons, electrons, and protons. The photon, electron, proton, and mixed-secondary source-term comparisons were generated primarily with CRY [96], stored as two-dimensional energy–zenith histograms, and then reused as external sources in the restG4 simulations. For muons, the production simulations use the correlated sea-level CosmicMuons parameterization implemented in REST, while CRY provides an independent generator-level cross-check. For neutrons, the final surface simulations use the measured HENSA outdoor spectrum discussed below as the nominal energy source term, while CRY and EXPACS provide spectral and angular guidance. This separation allowed the same atmospheric source term to be propagated through many alternative shielding and veto geometries.

The CRY source terms correspond to sea level, with latitude settings appropriate to Zaragoza (\(41.65^\circ \) N) and DESY (\(53.34^\circ \) N), a reference date of 2024-01-01 for the solar-modulation setting, and the maximum available lateral generation box of 300 m. For the veto studies, the most relevant output of this stage is the spectral shape of the atmospheric secondaries reaching the laboratory level, rather than the exact event-by-event ancestry of the primary cosmic ray.

The histogram and formula source terms generated in this way were reused as inputs to the detector simulations, which made it possible to compare alternative shielding layouts and veto geometries under a common source definition. The resulting CRY-based distributions were checked against EXPACS, the sea-level neutron measurements of Gordon et al., and the HENSA measurement campaign in Zaragoza [111–114]. This comparison is used in two different ways: CRY and EXPACS establish a stable generator-level reference, while HENSA anchors the measured neutron field used for the final neutron simulations.

The CRY and EXPACS distributions are in good agreement for the broad energy range relevant to the veto studies, which provides confidence that the simulated source term captures the main features of the atmospheric-secondaries flux. This agreement is especially important for cosmic neutrons, whose absolute rate is difficult to normalize but whose spectral shape largely determines the energy region that dominates the detector response.

Muon source term. The production muon simulations use the CosmicMuons source in restG4, which implements the sea-level parameterization of Guan et al. [115]. This model is a Gaisser-like atmospheric-muon flux with an effective zenith-angle correction, sampled as a two-dimensional distribution in kinetic energy and zenith angle rather than as independent one-dimensional marginals [116]. This is useful for a surface veto because inclined and high-energy muons are not equivalent to vertical low-energy muons: both the detector path length and the shielding traversal change with angle. CRY is therefore kept as a consistency check and as the source model for several historical scans, while the final muon production uses the correlated CosmicMuons input shown in Fig. 5.2.

HENSA neutron source term. The nominal neutron source used in the final surface simulations is the outdoor HENSA spectrum unfolded up to 10 GeV. HENSA is an extended-energy neutron spectrometer based on moderated \(\ce {^3He}\) counters and the Bonner-sphere principle; it measures the inclusive neutron field and obtains the energy spectrum through an unfolding of the detector count rates [117]. This point is important for BabyIAXO: at ground level, the neutron field is not a pure atmospheric-cascade component, but also contains neutrons produced, moderated, and scattered in the surrounding soil, concrete, and laboratory structures. The HENSA outdoor spectrum therefore includes the environmental, or ambient, neutron component to which the measurement technique is sensitive, and is closer to the field that a surface experiment sees than a generator-only cosmic-neutron spectrum.

Since HENSA provides the energy spectrum but not the incident direction of each neutron, the spectrum is paired in restG4 with the analytic downward angular model

where \(\theta \) is measured from the downward vertical axis. This form corresponds to a \(\cos ^2\theta \) zenith intensity multiplied by the \(\sin \theta \) solid-angle factor. It is implemented through the SinCos2 angular generator and was validated with a geantino sample. For CRY-based source terms, the simulations use the sampled two-dimensional energy–zenith histograms directly, while for HENSA the measured energy spectrum is combined with Eq. 5.1. The comparison in Fig. 5.4 shows that this analytic model reproduces the marginal neutron angular distribution obtained from CRY to the accuracy needed for the veto-design source term.

5.1.3 Relevant interaction processes in the shielding and veto materials

The veto concept is motivated by the different roles played by the materials surrounding the Micromegas detector. The relevant question is not only whether a material has a large cross-section for a given particle, but whether the resulting interaction helps to reduce, transform, tag, or accidentally produce a signal-like event. For this reason, the material discussion is kept focused on the components that directly determine the shielding and veto response.

Lead illustrates the central compromise. Its high density and atomic number make it an efficient attenuator for environmental photons in the keV–MeV range, as quantified by photon attenuation data such as NIST XCOM [77]. For fast cosmic neutrons, however, lead is not an efficient moderator. In an elastic collision with a nucleus of mass number \(A\), the maximum fraction of neutron kinetic energy that can be transferred is \(4A/(1+A)^2\). This fraction is unity for hydrogen, about 0.28 for carbon, and only about 0.019 for lead. Consequently, elastic scattering in lead removes little energy per collision, while inelastic and neutron-emission reactions become important at MeV energies. The event display in figure 5.24a shows the transport-level origin of the veto signature, but the veto does not identify the incoming primary neutron directly. The operational signature is instead the correlated secondary shower produced after the lead shielding has converted a hard neutron into softer neutrons, photons, and charged secondaries. This motivates a detector response that preserves two complementary components: prompt scintillation from charged secondaries and recoil protons, and delayed activity from neutrons that moderate and capture in cadmium. The concept is summarized in figure 5.24b.

5.1.4 Geant4 physics validation against evaluated data

The veto simulations rely on Geant4 for coupled neutron transport, nuclear interactions, prompt-gamma production, electromagnetic transport, and detector response. For the veto design, the relevant validation question is therefore not whether every final-state detail is reproduced spectroscopically, but whether the physics inputs that drive the design conclusions are consistent with evaluated data and whether the model-dependent parts are identified explicitly. Three checks are used for that purpose. The first compares the high-precision neutron cross-section tables used by Geant4 with evaluated nuclear data for the materials that control moderation, capture, and secondary production. The second compares inclusive neutron emission from lead with experimental double-differential production data, because this is the final-state observable most directly connected to neutron multiplication in the passive shield. The third compares the prompt gamma cascade emitted after cadmium capture with evaluated prompt-gamma production data, because this part of the simulation directly affects the delayed scintillator response.

Neutron-transport cross sections

The nuclear data underlying the lead-shower interpretation were checked against the data actually used by the Geant4 high-precision neutron transport. For natural lead, the reference curves were computed from the ENDF/B-VIII.0 incident-neutron evaluations by weighting the ²⁰⁴Pb, ²⁰⁶Pb, ²⁰⁷Pb, and ²⁰⁸Pb isotope files by their natural abundances [118]. The Geant4 comparison points were extracted from the G4NDL4.6 high-precision neutron tables distributed with Geant4 11.0.3, using the same natural-abundance weighting [119, 120]. Elastic, inelastic, and capture channels were read from the corresponding HP cross-section tables, while the \((n,2n)\) contribution was read from the HP inelastic final-state channel because Geant4 treats it as a channel inside the inelastic process rather than as an independent hadronic process. This procedure isolates the physics-list nuclear data from detector-geometry effects; it is therefore a validation of the transport inputs, not a replacement for the full detector simulations.

The same ENDF/B-VIII.0 versus G4NDL4.6 procedure was also applied to the two active-veto materials that control neutron tagging after the lead shower has formed: BC408, approximated as \(\mathrm {C}_9\mathrm {H}_{10}\), and natural cadmium. Those material-comparison studies are kept as supplementary validation plots in appendix 6.6, figures 6.29 and 6.30, because they support the scintillator–cadmium design choice without changing the main lead-multiplication argument.

Lead secondary-neutron production

The cross-section comparison validates the interaction probabilities, but it does not by itself validate the neutron energy and angle distribution emitted after an interaction in lead. This final-state information is the part of the model that matters for the veto concept, because the active panels tag the secondary shower produced after a hard neutron enters the passive shield. A separate thin-target benchmark was therefore performed against the EXFOR natural-lead \((n,xn)\) double-differential neutron-emission data of Takahashi et al., measured with \(14.1~\mathrm {MeV}\) incident neutrons at the OKTAVIAN facility [121, 122]. The benchmark uses a \(1~\mathrm {mm}\) natural-lead target and scores outgoing neutrons in the same \(20^\circ \)–\(160^\circ \) angular range and \(0.4\)–\(16~\mathrm {MeV}\) energy range covered by the experimental data. The simulated yields are normalized by the lead areal density, \(3.30\times 10^{-3}\) atoms per barn for the chosen target thickness, so the comparison is expressed directly as a production cross section.

Figure 5.7 compares four Geant4 reference physics lists: QGSP_BIC_HP, QGSP_BERT_HP, FTFP_BERT_HP, and Shielding. Each model was run with \(2.0\times 10^{6}\) incident neutrons, giving about \(3.5\times 10^{4}\) scored outgoing neutrons in the experimental acceptance. The model spread is small: all four physics lists predict an angle- and energy-integrated cross section of \(5.36\)–\(5.40~\mathrm {b}\) in the measured acceptance, compared with \(5.87~\mathrm {b}\) from the EXFOR data. Thus the integrated yield is about \(8\%\)–\(9\%\) low, while the energy and angular shapes are reproduced at the level needed for the veto-design interpretation.

The practical conclusion is that the low-energy lead-neutron final state is not a useful knob to tune the veto result within the tested HP physics lists. At \(14.1~\mathrm {MeV}\), changing from the binary-cascade list to Bertini, FTFP–Bertini, or Shielding changes the integrated neutron-emission yield by less than \(1\%\), because the relevant neutron interactions remain inside the ParticleHP energy domain. The benchmark therefore supports the physical picture used in this chapter: lead converts fast neutrons into a softer outgoing neutron population that is well matched to the moderator and cadmium layers of the veto. It also identifies the remaining model uncertainty correctly. For the higher-energy part of the HENSA surface spectrum, where intranuclear cascade models rather than HP final states control secondary production, the appropriate treatment is a model-envelope systematic in the full detector geometry rather than a retuning of the low-energy lead data.

Cadmium capture and prompt-gamma de-excitation

Cadmium enters at the opposite end of the neutron-energy scale. It is not a shield for the primary MeV–GeV cosmic neutrons. Its purpose is to absorb neutrons after they have been slowed in the scintillator and surrounding low-\(Z\) materials. Natural cadmium is especially effective in this regime because the ¹¹³Cd isotope has a very large thermal neutron-capture cross-section. A 1 mm natural-cadmium sheet is already optically thick for thermal neutrons: using \(\rho _{\mathrm {Cd}}=8.65\,\mathrm {g\,cm^{-3}}\), \(A_{\mathrm {Cd}}=112.4\,\mathrm {g\,mol^{-1}}\), and a thermal natural-cadmium capture cross-section of about \(2.5\times 10^3\) barn gives an uncollided transmission of order \(10^{-5}\) through 1 mm at 0.025 eV. This is consistent with the practical use of millimeter-scale cadmium as a thermal-neutron cut-off absorber [123]. The design requirement is therefore not to make the cadmium thicker, but to place it where enough neutrons have first been moderated and where the resulting capture gamma cascade can be detected by nearby scintillators. The corresponding Geant4 nuclear-data cross-check for natural Cd is shown in appendix figure 6.30; the same appendix also includes the BC408 scintillator comparison in figure 6.29, documenting the elastic, inelastic, and capture inputs used for moderation and prompt scintillator response.

The same capture process also explains why cadmium can produce an observable veto signature rather than merely remove moderated neutrons from the transport. Evaluated prompt-gamma data for ¹¹³Cd show a cascade of characteristic photons after neutron capture, with strong lines in the few-hundred-keV to MeV range [124, 125]. Figure 5.9 compares those evaluated prompt-gamma lines with the photon energies emitted by Geant4 using the PhotonEvaporation cascade model in the HENSA-driven three-layer veto simulation. The recovered PhotonEvaporation sample records \(30{,}791\) cadmium captures and \(207{,}146\) emitted prompt-gamma tracks, corresponding to an average of \(6.73\) photons and \(9.01~\mathrm {MeV}\) emitted as gamma energy per capture. The relevant design consequence is that the cadmium sheets should be placed close to active scintillator, because the useful signal is the transport and partial absorption of this gamma cascade in nearby panels. At the same time, this comparison is treated as a validation diagnostic rather than as a claim that Geant4 reproduces all cadmium line intensities. The high-energy \(\sim 9.04~\mathrm {MeV}\) ¹¹³Cd line is present in evaluated data and is strongly model-dependent: the default ParticleHP cascade overproduces this line, while the PhotonEvaporation option suppresses it to the same order of magnitude as the evaluated yield. This is consistent with the more general limitation discussed in recent work on data-driven neutron-capture cascade models: the standard Geant4 capture/de-excitation modules are useful transport tools, but they do not necessarily reproduce all measured prompt-gamma lines and correlations in the MeV range [126]. For this reason, the cadmium study includes a dedicated Geant4 physics-model comparison rather than a single production configuration. The comparison separates three choices that affect different parts of the calculation. First, the neutron transport and capture probabilities are governed by the high-precision neutron data used by the QGSP_BIC_HP hadronic list and the associated elastic HP model [119, 120]. Second, the exact isotope-data policy is controlled by requiring ParticleHP to skip missing isotope data instead of silently falling back to a nearby element or natural composition. Third, the prompt-gamma cascade after capture can be generated either from the default ParticleHP final-state data or through the PhotonEvaporation de-excitation model [119]. The last choice is the most relevant one for cadmium, because it changes how the capture \(Q\)-value is partitioned among emitted photons while leaving the preceding neutron moderation and capture geometry largely unchanged.

The campaign is enabled through an extension of the restG4 physics-list interface that forwards the usePhotoEvaporation and skipMissingIsotopes options to G4ParticleHPManager before the hadronic neutron processes are constructed. This distinction is important for the veto optimization because the design does not rely on a single gamma line being simulated with spectroscopic accuracy. It relies on three more robust ingredients: moderation of secondary neutrons in hydrogen-rich material, high capture probability in cadmium once those neutrons are thermalized, and emission of an MeV-scale photon cascade close enough to nearby scintillators to deposit detectable energy. The model comparison therefore tests whether the veto conclusion survives a different de-excitation prescription, while also identifying which line-level predictions should be treated as a physics-model systematic. In the recovered HENSA physics-model comparison, the default and strict-ParticleHP variants give nearly the same cascade: \(3.75\) and \(3.78\) photons per cadmium capture, respectively, and \(8.69\) and \(8.74~\mathrm {MeV}\) of emitted gamma energy per capture. The PhotonEvaporation variant gives \(6.73\) photons per capture and \(9.01~\mathrm {MeV}\) per capture, while reducing the \(9.043~\mathrm {MeV}\) line-window yield from about \(0.34\) photons per cadmium capture to \(5.8\times 10^{-4}\). This result motivates the default physics convention used for the veto study: HP neutron transport is kept as the nominal treatment for neutron propagation and capture rates, strict isotope handling is enabled for production runs, and PhotonEvaporation is used as the nominal cadmium-capture cascade model when prompt-gamma energy partition is part of the observable. The default ParticleHP cascade is retained as a systematic comparison and for continuity with earlier productions.

The selected line-window comparison in table 5.5 gives the quantitative scale of the agreement. The strongest \(558~\mathrm {keV}\) line is reproduced within about \(22\%\), while several weaker branches remain below the evaluated PGAA yields by factors of about three to five. This level of agreement is sufficient for the detector-design question, which depends mainly on the existence and transport of a multi-MeV capture cascade, but it is not a substitute for a data-driven cascade generator if precision line spectroscopy were required.

As a detector-level cross-check of the same model choice, the recovered HENSA campaign was also scanned directly at EventTree level. Because these validation outputs were not processed through the waveform and peak-finding chain, the comparison uses the total energy deposited in scintillator volumes as a truth-level veto proxy rather than the final reconstructed veto observable. Figure 5.11 shows that the three-layer veto response is stable under the cascade-model change. At a \(10~\mathrm {MeV}\) truth-level scintillator-energy threshold, the rejected fractions are \(0.908\pm 0.006\), \(0.914\pm 0.006\), and \(0.927\pm 0.007\) for default ParticleHP, strict ParticleHP, and PhotonEvaporation, respectively. At \(30~\mathrm {MeV}\), the corresponding values are \(0.699\pm 0.009\), \(0.703\pm 0.010\), and \(0.719\pm 0.012\). The modest increase for PhotonEvaporation is consistent with the softer, higher-multiplicity cascade, but the effect is small compared with the line-level spectral difference.

A second comparison was then made by replaying the recovered Geant4 files through the same detector-response and raw-signal processing chain used in the veto simulations. This produces the reconstructed rawPeaksVETO observables, including the number of VETO peaks, the number of hit channels, and the visible-energy sum of the reconstructed peaks. The default ParticleHP sample contains \(2{,}368\) usable events after this replay because one recovered ROOT file was corrupted; the strict-ParticleHP and PhotonEvaporation samples contain \(2{,}120\) and \(1{,}502\) events, respectively. Figure 5.12 shows that the probability of producing at least one reconstructed VETO peak is stable at the level of the available statistics: \(0.719\pm 0.009\), \(0.742\pm 0.010\), and \(0.720\pm 0.012\) for default ParticleHP, strict ParticleHP, and PhotonEvaporation. Fixed visible-energy thresholds are more model-dependent. At a \(10~\mathrm {MeV}\)-equivalent reconstructed peak-energy threshold, the rejected fractions are \(0.375\pm 0.010\), \(0.383\pm 0.011\), and \(0.314\pm 0.012\), respectively. Thus, the PhotonEvaporation cascade improves the prompt-gamma spectrum while tending to distribute the energy into lower-amplitude reconstructed VETO peaks. This is the relevant detector-level systematic for threshold choices. The operating points in Fig. 5.12 are summarized in table 5.6. They separate the binary question of whether the veto reconstructs any signal from the more analysis-dependent question of whether the summed reconstructed peak energy exceeds a chosen threshold.

These validation studies are used here to establish the physics convention and the associated model systematic. The quantitative veto optimization still depends on geometry, shielding gaps, secondary-particle multiplicity, capture position, capture time, gamma transport, scintillator quenching, light attenuation, PMT thresholds, and Micromegas topology. Those coupled effects are the reason why the design is evaluated with the full Geant4/restG4 simulation chain rather than with cross-section estimates or gamma-line yields alone.

5.1.5 Interaction of high-energy neutrons and photons with the detector

Atmospheric neutrons span many orders of magnitude in energy, from thermal and environmental energies to the GeV scale. The source spectra discussed above show that the integrated flux is large at low energy, but this is not the same as saying that low-energy neutrons dominate the detector background. The relevant question for the veto design is which primary-neutron energies survive the shielding and produce activity in the Micromegas sensitive volume.

This was studied in two complementary samples. The first is the original CRY-based baseline lead-shielding simulation, used to establish the high-energy response of the detector-plus-shield system. The second uses the recent outdoor-HENSA neutron source propagated through the three-layer cadmium veto configuration. The baseline configuration consists of a 20 cm thick lead shield surrounding the copper chamber, as shown in figure 5.13; a thin layer of copper is used as inner shielding.

Figure 5.14 and Table 5.7 show the same qualitative behavior for both source models. Sub-MeV neutrons are an important part of the measured or generated source term, especially for the HENSA outdoor spectrum, but they do not dominate the detector-triggering population. The events that reach the Micromegas sensitive volume are concentrated in the \(100~\mathrm {MeV}\)–\(10~\mathrm {GeV}\) region, where neutrons are energetic enough to create secondary activity in the lead and copper surrounding the detector. This justifies keeping the high-energy part of the neutron source in the veto simulations even though its integral flux is small, and it also motivates the active veto: the problematic neutron background is not simply a low-energy moderation problem, but a secondary-shower problem produced by fast primaries interacting in the shielding.

For the original CRY baseline study, the ratio between the detector-reaching and input primary-energy distributions can be used as a relative detector-response diagnostic. This ratio should not be interpreted as an absolute detection efficiency: each bin compares the fraction of detector-reaching events with the fraction of generated primaries in that same energy interval, and the vertical normalization is arbitrary. It is nevertheless useful for identifying which primary energies are preferentially converted into Micromegas activity.

Figure 5.15 shows that, above the MeV scale, the relative response grows approximately as

with \(\alpha \) close to unity for both neutron and photon primaries in the simulated range. This trend is physically reasonable: more energetic primaries create more secondary particles in the shielding and therefore have a larger probability of transferring energy into the Micromegas sensitive volume. The photon case was studied in the same baseline detector-plus-shielding configuration [114]; its similar response shape does not imply similar mitigation behavior, because the electromagnetic component is still much more efficiently attenuated by additional lead, as discussed in Section 5.2. For neutrons, the same lead that suppresses photons becomes the material where energetic primaries can multiply and generate the correlated secondary shower seen by the TPC and the veto system.

Secondary-particle production in the lead shielding

The lead shield should therefore not be regarded as a passive absorber only. For high-energy neutrons it is also the main site of secondary-particle production. Dedicated simulations with the HENSA outdoor neutron spectrum and the nominal three-layer veto geometry confirm that the population emerging from the shield is dominated by neutrons with significantly lower energies than the primaries, with a spectrum that peaks around the MeV scale. In the current sample, 1,745 detector-reaching events contain \(9.19\times 10^{4}\) neutrons produced in the lead, of which \(6.58\times 10^{4}\) leave the lead volume and \(1.83\times 10^{4}\) do so with a momentum direction pointing toward the TPC. This shift toward lower energies is important because it makes the secondary shower much better matched to moderation and detection in the hydrogen-rich scintillator panels of the veto system.

This behavior clarifies why the veto can be effective even though the primary cosmic neutrons themselves are difficult to detect directly. The relevant observable is not the high-energy primary neutron in isolation, but the correlated shower of secondaries generated when it interacts in the lead.

Figure 5.17 shows that the final interaction responsible for the TPC signal is very often produced by a secondary particle created in the surrounding shielding and detector materials. The event count is dominated by gamma/electron routes, whereas the deposited gas energy is dominated by recoil and fragment routes. This result provides the physical justification for designing the veto system to tag the shower as a whole, rather than attempting to identify only the incoming primary neutron. It also motivates the later use of veto observables based on prompt energy, delayed activity, multiplicity, and spatial correlations, since these quantities are sensitive to the topology of the full secondary cascade.

A separate topology appears when the neutron first creates an unstable residual nucleus in the detector or shielding materials and the Micromegas trigger is produced only by the later radioactive decay. In this delayed-activation channel, the gas deposit is caused by a beta, positron, or decay-gamma descendant rather than by the prompt neutron-induced shower. The original neutron interaction may still have produced scintillator activity, but that activity is separated from the TPC trigger by times far longer than the veto coincidence window. This makes the channel effectively invisible to prompt and delayed veto selections. In the available nominal three-layer-cadmium HENSA histories, this topology accounts for \(120/4594\) TPC-selected events and \(42/1392\) events after the fiducial \(2\)–\(7~\mathrm {keV}\) readout-energy cut, defining the class by a RadioactiveDecay ancestor later than \(100~\mu \mathrm {s}\). The aggregate machine-learning veto leaves \(39\) of these \(42\) delayed-activation events, while none survive the subsequent X-ray-like topology BDT in the scanned subset. This is therefore a useful boundary case for the analysis: the active veto tags correlated neutron-shower activity, whereas delayed activation products must be controlled by the Micromegas topology selection and by the source normalization.

5.1.6 Effect of detector inclination during solar tracking

As a solar axion helioscope, BabyIAXO must track the Sun across the sky during its daily observation window. This tracking is achieved by physically rotating and tilting the entire magnet and detector assembly, so that the optical axis remains pointed toward the Sun. Consequently, the detector does not operate in a fixed orientation: the inclination angle with respect to the horizontal plane changes continuously during each tracking period.

This raises a natural question for the background model: does the cosmic ray-induced background depend significantly on the detector orientation? For the muon component, some dependence might be expected on physical grounds, since the muon flux has a strong zenith-angle dependence and the effective cross-sectional area of the TPC presented to vertically incident muons varies with inclination. For the neutron component, the situation is less clear, as the secondary neutron shower produced inside the lead shielding is largely isotropic.

To address this question, dedicated Geant4 simulations were performed for the horizontal detector orientation and for tracking inclinations spanning the \(-25^\circ \) to \(+25^\circ \) range. The full three-layer veto geometry was retained, while the incident cosmic field was rotated with respect to the detector axes. This is equivalent to tilting the detector with respect to the downward cosmic-ray field, but avoids modifying the GDML geometry for each angular point. The scan was performed for both cosmic muons and HENSA-driven neutrons, and the convention and response are summarized together in Fig. 5.18.

The TPC-selected rates in Fig. 5.17b show no monotonic or operationally significant dependence across the tracking-angle range. For HENSA neutrons, the relative response spans from \(0.982\pm 0.024\) at \(+12.5^\circ \) to \(1.057\pm 0.024\) at \(-25^\circ \), compared with the horizontal configuration. For muons, the corresponding range is \(0.988\pm 0.020\) to \(1.028\pm 0.022\). The excursions remain at the few-percent level, so detector inclination is not a leading effect for the cosmic-background studies presented in this chapter. The result justifies using a fixed horizontal geometry for the larger production campaigns, while treating residual orientation effects as a subdominant systematic.

5.2 Limits of passive shielding

The passive shield defines the boundary conditions for the veto design. Lead is retained because it is highly effective against environmental photons in the keV–MeV range, while copper provides a radiopure inner layer close to the detector. At the same time, the detector line cannot be enclosed by a perfect passive castle: the X-ray entrance path, gas services, readout cabling, and mechanical supports introduce openings and penetrations. For a surface helioscope, passive shielding must therefore be evaluated not only as an absorber, but also as part of the geometry in which cosmic-ray-induced secondary particles are produced.

Neutron shielding is qualitatively different from gamma shielding. Hydrogen-rich materials such as polyethylene or water are useful moderators because neutron elastic scattering on hydrogen can transfer a large fraction of the neutron energy, as discussed in Section 5.1.3. Boron- or lithium-loaded materials can then absorb moderated neutrons through neutron-capture or absorption reactions. Such captures may also generate gammas or charged particles, so the absorber must be placed in a geometry where those secondaries do not become a new detector background. These constraints make passive neutron shielding a design trade-off rather than a simple matter of adding more material.

In the IAXO-D0/BabyIAXO geometry, the passive shield must also remain compatible with the X-ray optical axis. A copper pipe connects the detector to the vacuum beam line and produces the most important intentional weakening of the shielding. The lead-thickness and moderator studies presented below therefore ask a narrow design question: can practical passive shielding suppress the remaining cosmic-ray-induced background, or must the detector rely on an active veto?

5.2.1 Lead-thickness scan: electromagnetic suppression versus neutron multiplication

A parameterized lead-shield geometry was used to scan the passive-shielding thickness with two variants: an idealized \(4\pi \) coverage and a more realistic configuration including the beam-pipe opening. The atmospheric-secondary distributions generated with CRY (Figure 5.1) were used as input. The scan was designed to motivate the original shielding choice and, just as importantly, to test whether lead alone could be a complete solution for a surface detector. The full per-particle scans are preserved in Appendix 6.12; the main text keeps only the photon and neutron trends because they drive the design decision.

The photon response confirms the expected role of the lead castle. In the idealized \(4\pi \) configuration the photon-induced background drops by more than four orders of magnitude over the scanned range; with the beam-pipe opening the suppression is weaker, about a factor \(3\times 10^2\), because leakage through the opening becomes comparatively important once the rest of the solid angle is shielded. Lead therefore remains part of the baseline design, but the geometry of penetrations matters.

The neutron response leads to the opposite conclusion. High-energy neutrons interact in the lead and can produce secondary neutron showers, so the residual detector background is not removed simply by increasing the lead thickness. In this scan the neutron level remains within the same order of magnitude across the full range and even rises at intermediate thickness before decreasing mildly at large thickness. The beam-pipe configuration changes the neutron rate less dramatically than it changes the photon rate and does not alter the design conclusion. The shield is therefore both a necessary gamma attenuator and a source of correlated neutron-induced activity that must be tagged by the active system.

5.2.2 Borated-HDPE moderation studies

The lead-thickness scan motivates the consideration of passive materials specifically aimed at neutron moderation and absorption. High-density polyethylene (HDPE) is a standard hydrogen-rich moderator, and borated HDPE adds neutron absorption through the ¹⁰B reaction

after the neutron has been slowed in the polymer matrix. This makes borated HDPE an attractive passive candidate in principle: hydrogen can reduce the neutron energy, while boron can absorb part of the thermalized population. The question for BabyIAXO is whether this mechanism remains effective for the relevant surface-neutron problem, where many of the problematic events are produced by MeV–GeV primaries interacting in and around the lead shield.

A dedicated simulation study tested whether 5% borated HDPE could be used as an additional passive layer without abandoning the 20 cm lead shield required for gamma suppression [114]. A single external borated-HDPE layer produced only a small reduction in the neutron-induced background. A layered Pb/borated-HDPE/Pb configuration was therefore tested, keeping the total Pb thickness fixed at 20 cm while scanning both the borated-HDPE thickness and the partition of lead between the inner and outer sides of the moderator. The geometry is shown schematically in Figure 5.20. In the scan notation used below, \(L_1\) is the inner lead thickness, \(L_2\) is the borated-HDPE thickness, and the remaining outer lead thickness is \(L_3=200~\mathrm {mm}-L_1\).

The best sampled configuration reduces the neutron-induced background by about \(40\%\) with respect to the plain 20 cm Pb reference, corresponding to a suppression factor of only about 1.6; the most favorable lead partitions give reductions of order \(30\)–\(40\%\). The reduction is largest when a substantial fraction of the lead remains outside the moderator, so that the moderator acts on neutrons produced upstream in the shield. For configurations with most of the lead inside the moderator, the gain is much smaller, and thin moderator layers can even increase the residual rate within the statistical precision of the scan. This behavior is consistent with the energy scale of the source term: a practical moderator thickness does not fully thermalize the MeV–GeV neutron component before it has already produced secondaries in the lead or surrounding materials.

Borated scintillator layers, acting simultaneously as active and passive shields, were also explored and gave only modest additional improvement for the highest-energy neutron component. Borated HDPE was therefore not adopted as a baseline passive layer. The study nevertheless defines the boundary condition for the active-veto design: lead is kept because it efficiently suppresses photons, but neither more lead nor practical borated-HDPE moderation reduces the high-energy neutron background to the required level. The active shield must instead detect the correlated secondary shower produced in and around the passive shield.

5.3 Neutron-sensitive active veto concept

This section follows the evolution of the veto concept from a conventional surface muon shield to a neutron-sensitive active system coupled to the passive lead shielding. The emphasis is not only on the final geometry, but on the sequence of questions that connected the source-term studies, the passive-shielding limits, the neutron-tagging mechanism, the choice of three scintillator layers with cadmium, and the subsequent validation with prototype data.

Detailed campaign metadata, including the response level and timing convention used in each scan, are collected in Appendix 6.7. The main text keeps only the design consequences, so that the reader can follow how the veto evolved from a prompt muon counter into a neutron-sensitive, waveform-level system.

5.3.1 Plastic scintillators

Plastic scintillators were a natural choice for the active shielding because they combine large-area coverage, good timing performance, and a high hydrogen content, which is advantageous for neutron moderation. In the BabyIAXO/IAXO-D0 case, the collaboration also had access to a substantial stock of NE-110 panels and photomultipliers from a former time-of-flight spectrometer [127]. The veto design was therefore developed around this existing hardware, with segmentation and panel lengths constrained by the available modules. Several material names appear in the simulation studies: NE-110 for the reused prototype bars, EJ-208 as the modern datasheet reference used for optical properties, and BC408 as the PVT-like scintillator used in the simplified material scans. For the neutron-transport argument these are treated as closely related polyvinyltoluene-like organic scintillators; the exact optical constants matter for the light-collection model, while the moderation and recoil-proton response are driven mainly by the hydrogen and carbon content [128, 129].

A scintillator converts the kinetic energy of ionizing radiation into detectable light, which is subsequently collected and amplified by a photomultiplier tube. The fundamental figure of merit is the scintillation efficiency, defined as the ratio of photons produced to the energy deposited.

For standard calibration purposes, plastic scintillators are exposed to gamma sources (e.g., \(^{60}\)Co or \(^{137}\)Cs), which induce energetic electron recoils via Compton scattering. Since the light yield for electrons is approximately linear with energy, this establishes an ”electron-equivalent” energy scale (\(E_{ee}\)), typically measured in units of MeVee (MeV electron equivalent).

However, the scintillation efficiency is strictly dependent on the particle type and its specific energy loss (\(dE/dx\)). This is particularly relevant for the detection of neutrons, which is a primary focus of this work. Neutrons interact within the plastic scintillator primarily by elastic scattering off hydrogen nuclei, producing recoil protons. Unlike the electrons from gamma interactions, these recoil protons are heavily ionizing. The resulting high density of ionization centers along the proton track leads to a saturation of the fluorescent molecules, causing a significant reduction in light output known as quenching.

In organic scintillators such as NE-110, this non-linear response is semi-empirically described by Birks’ law [130, 131]. Consequently, a neutron-induced recoil proton depositing 10 MeV of kinetic energy will produce significantly less light than an electron depositing the same amount. This necessitates the application of a quenching correction factor in simulation studies to accurately predict the veto efficiency for neutron backgrounds.

It is worth noting that while Birks’ law governs the quenching in the solid scintillator, the visible-signal reduction for nuclear recoils in the gaseous Micromegas volume is driven by a different mechanism and is treated through Lindhard-type models [132]. During this work both effects were incorporated in the simulation chain, since a realistic veto/background comparison requires the scintillator and the gas detector to be treated consistently at the level of visible signal rather than only at the level of deposited energy.

5.3.2 From prompt muon veto to neutron-sensitive stages

Given the IAXO background requirements and the limits of passive shielding, the key remaining challenge is the high-energy cosmic-neutron component [70]. The early active-shielding concept inherited from previous detector configurations was essentially a single-layer muon veto: effective for prompt charged tracks, but not yet optimized for the softer, more distributed, and often delayed signatures expected from neutron-induced secondary showers.

The next design question is where the active material should sit relative to the lead and moderator volumes. Rather than retaining the older deposited-energy limiting scans as a separate result, the comparison was repeated with the same Birks-corrected visible-energy response used in the current simulation chain. The simplified geometry reduces the veto to a 10 cm scintillator slab, treated as the only sensitive volume, and places lead, borated HDPE, and thin capture/moderator sheets before and after it along the neutron direction. The purpose is not to predict the final veto performance, but to isolate whether the active layer benefits mainly from direct neutron interactions, from secondaries produced in lead, or from local capture/moderator sheets before the segmented multi-layer waveform response is introduced.

Together these scans give the design lesson that replaces the older deposited-energy limiting studies. The scintillator should not be treated as an isolated neutron counter: its useful response comes from sampling the secondary shower generated by the surrounding shielding. The fixed-threshold energy projection shows the same point from the source-term perspective: the bare slab is most effective for low-energy neutrons that can interact directly in the scintillator, whereas the lead-coupled geometries are the ones that remain efficient for the harder primaries relevant to the surface cosmic-neutron spectrum. This is the essential reason for placing the veto around, and not instead of, the lead shielding.

Neutron-tagging mechanism

Additional simulation studies presented during the IAXO collaboration meetings clarified the relevant energy and time scales of this problem [114, 133, 134]. Although the input cosmic-neutron spectrum extends from sub-MeV energies to the multi-GeV range, the detector-triggering events are dominated by primary neutrons in the MeV-to-GeV region, with the effective primary-energy distribution peaking around the GeV scale for the detector-plus-shielding system. After interacting in the lead shielding, however, the shower that emerges toward the veto is strongly softened: the outgoing secondary neutrons are concentrated at much lower energies, typically around the MeV scale. This separation of scales is central to the veto concept.

The relevant microscopic processes were introduced in Section 5.1.3. Here the same physics can be summarized operationally. Lead is a poor moderator but an efficient converter for fast neutrons: inelastic scattering, \((n,xn)\) channels, and high-energy nuclear reactions create a softer secondary shower distributed through the shielding volume. The hydrogen-rich scintillator then samples the moderated and charged part of that shower through recoil-proton and charged-secondary light, while cadmium samples the thermalized tail through capture-gamma cascades. The veto is therefore designed to observe the history of the neutron-induced cascade, not the incoming neutron itself.

This mechanism is the central reason for using a multilayer active veto rather than a single passive moderator or a single scintillator counter. The lead shielding increases the probability that a high-energy neutron creates detectable secondaries, while the hydrogen-rich scintillator and cadmium sheets sample different stages of the moderation history. A neutron-induced background event need not look like a clean through-going track. It can instead appear as a moderate prompt signal, several delayed peaks, and a spatially distributed multiplicity pattern. The analysis is therefore designed to retain these correlated waveform-level observables.

The timing structure of the event is as important as its topology. The interaction that gives rise to the Micromegas trigger is essentially prompt on the timescale of the detector: in the dedicated simulations, the relevant activity in the shielding and the first interaction in the sensitive volume occur within less than about \(1\,\mu \mathrm {s}\) from the primary neutron generation [114, 133]. By contrast, neutron capture is delayed by the stochastic moderation chain. The capture-time distribution follows approximately an exponential law with characteristic constant \(\tau \simeq 45\,\mu \mathrm {s}\), measured relative to the Micromegas trigger time [133, 134]. An ideal post-trigger delayed window of \(100\,\mu \mathrm {s}\) would therefore contain approximately \(1-\exp (-100/45)\approx 89\%\) of delayed captures before threshold and acceptance effects are considered. In the prototype-like acquisition mode used later in this chapter, however, the veto is read out in a \(100\,\mu \mathrm {s}\) total window with the Micromegas trigger placed at \(30\,\mu \mathrm {s}\), corresponding to approximately \([-30,+70]\,\mu \mathrm {s}\) relative to the trigger. The practically accessible post-trigger delayed fraction is then \(1-\exp (-70/45)\approx 79\%\). This is the reason why the veto analysis is not restricted to a narrow prompt coincidence: doing so would discard a large fraction of the cadmium-capture information that motivated the multilayer design.

The same mechanism can be inspected directly in the recent HENSA-driven three-layer cadmium simulation. The diagnostic summarized in Appendix 6.10, Fig. 6.36, scans the Geant4 history of the 2,706 neutron events that survive the common TPC selection and records explicit neutron-capture processes together with the reconstructed veto peaks. In total, 73,295 neutron-capture steps are found. At the event level, \(99.3\%\) of the selected events contain at least one neutron capture, and \(98.3\%\) contain at least one capture in a cadmium sheet. Cadmium is also the dominant capture site in the full population of capture processes: \(78.9\%\) of all explicit captures occur in the cadmium sheets, while \(19.3\%\) occur in the plastic scintillator. Within the cadmium sheets, the capture isotopes are dominated by ¹¹³Cd, which accounts for about \(98\%\) of the recorded cadmium captures in this sample.

For events whose first TPC activity is prompt, \(79.7\%\) of cadmium captures occur within the first \(70\,\mu \mathrm {s}\) after the TPC time, and \(88.8\%\) within \(100\,\mu \mathrm {s}\). This reproduces at truth level the same time-window scale inferred from the exponential capture-time model. The bottom-right panel also shows why capture truth cannot be used as a direct analysis observable: about one quarter of the selected events contain a cadmium capture but no reconstructed veto peak, while another quarter produce only prompt or near-trigger peaks. The useful experimental signature is therefore not the capture process itself, but the subset of captures and secondary shower activity that survives gamma transport, scintillator response, thresholds, and waveform reconstruction.

The delayed component is therefore physically central, but it is not sufficient by itself as an analysis cut. Late veto peaks also occur in calibration and mixed-background samples through accidental activity, electronic noise, and unrelated environmental coincidences. This can be seen in a simple event-mixing test in which veto peak trains are time-scrambled with respect to the TPC trigger. A requirement of at least one late peak accepts about \(52\%\) of the simulated neutron/TPC events but also about \(56\%\) of the mixed accidental sample. Adding a prompt requirement reduces the accidental acceptance to about \(14\%\) while retaining about \(46\%\) of neutron events; requiring the late activity to span at least two veto groups gives a cleaner, more topology-aware tag with about \(25\%\) neutron acceptance and about \(7\%\) accidental acceptance. The practical capture strategy is therefore to combine prompt activity, delayed peaks, multiplicity, visible energy, and spatial distribution rather than to search for an isolated delayed pulse.

This is the principal design strategy followed in the remainder of the section: repeated scintillator–cadmium stages are used to increase the probability of recording at least one prompt or delayed signature from the neutron-induced shower, while the event selection uses the waveform-level context to reject accidental delayed activity.

A dedicated neutron-history check on the waveform-level cosmic-neutron sample confirms that the veto must be interpreted as a tag of the full secondary cascade, not only of the incoming neutron. The study followed the Geant4 ancestry of the particle that deposited energy in the Micromegas gas for 879 simulated neutron events with nonzero TPC energy. The classification is a truth-level diagnostic used to understand the detector response; it is not used as a selection variable in the final analysis. Most TPC deposits are produced by electromagnetic descendants, which explains why a neutron-initiated event can pass an x-ray-like Micromegas selection while still carrying a neutron-like prompt or delayed veto history.

5.4 Multilayer veto optimization

The geometry study compared 1-layer (19 panels), 2-layer (39 panels), 3-layer (59 panels), and 4-layer (79 panels) configurations. The first optimization was performed with an idealized deposited-energy observable in the scintillator volumes [133]. That scan was useful for design intuition, but the final comparison was repeated with the outdoor HENSA neutron source term and the detector-response chain used in the background-model simulations: multilayer Geant4 transport, quenching, light attenuation, waveform generation, and reconstructed veto observables. The threshold in this final scan is therefore a calibrated visible-energy proxy, not the same quantity as the older truth-level deposited-energy threshold.

The response-chain comparison preserves the original design conclusion but gives more conservative absolute rejection values. For example, the earlier idealized scan gave approximate 3-layer rejection values of \(0.85\) and \(0.52\) at 4 and 8 MeV, whereas the final HENSA response-chain scan gives \(0.58\) and \(0.42\) at the same nominal thresholds. For the 4-layer configuration the corresponding values change from about \(0.88\) and \(0.54\) to \(0.63\) and \(0.48\). This difference is expected: quenching, attenuation, waveform-level thresholds, and reconstruction losses all move the analysis away from a perfect deposited-energy observable. The relevant stability check is the ordering, which is unchanged. The second and third scintillator–cadmium stages give the large improvement, while the fourth stage adds only a smaller residual gain.

Relative to the one-layer cadmium configuration, the event rate after the common TPC selection is reduced to about \(0.54\), \(0.37\), and \(0.32\) for the two-, three-, and four-layer cadmium configurations, respectively. At the same time, the fraction of events with a reconstructed veto tag increases from about \(47\%\) in the one-layer geometry to \(74\%\) in the three-layer geometry and \(77\%\) in the four-layer geometry. This confirms the design interpretation: three layers do not maximize rejection in an unconstrained sense, but they capture most of the available veto information before the mechanical complexity, readout channel count, and accidental-coincidence exposure increase further. The capture-material comparison reinforces the same interpretation. A three-layer gadolinium variant gives a similar neutron-tagging response to cadmium in this observable set, whereas replacing the capture sheets with stainless steel strongly reduces the reconstructed veto-tag fraction and the \(10~\mathrm {MeV}\) rejection.

The detailed threshold-only and geometry-only plots from this scan are kept in Appendix 6.9, where they serve as provenance for the compact design summary in Fig. 5.29.

Layer optimization cannot be based only on the neutron rejection curve, because each additional instrumented layer also increases the number of channels that can contribute accidental veto activity. This effect was estimated by using experimental calibration-triggered data as an empirical accidental-veto template and scaling the amount of independent accidental activity with the number of active layers. For the measured veto-noise environment, a threshold of about \(10~\mathrm {MeV}\) in calibrated visible-energy proxy gives approximately \(90\%\) calibration acceptance for the three-layer configuration, while a more conservative threshold around \(14\)–\(15~\mathrm {MeV}\) gives approximately \(95\%\) acceptance. When this accidental component is included, the optimization becomes a balance between neutron rejection and calibration acceptance rather than a search for the lowest possible threshold.

The same conclusion appears when the veto observables are treated as an event-selection problem rather than as a single threshold. As discussed in Section 5.6.1, a boosted veto BSD trained on aggregate waveform observables rejects substantially more HENSA neutron events than a single visible-energy threshold at the same calibration acceptance. Thus the veto design is not only a matter of adding active material; it is also a matter of retaining enough multiplicity and quality information in the readout to distinguish neutron-correlated veto activity from ordinary accidental peaks.

These results also clarify the role of delayed peaks. Delayed activity is physically central to the scintillator–cadmium design, but a late peak by itself is not a clean neutron tag because real calibration data already contain abundant accidental late activity. The useful signature is more specific: prompt or near-trigger activity together with delayed veto peaks, visible energy, and multiplicity distributed across the veto system. In the peak-level cosmic-neutron study discussed later in this chapter, the condition “prompt plus late” rejects nearly half of the neutron sample while preserving about \(96\%\) of calibration-like events, whereas the mere existence of late peaks has little discrimination power. This is the analysis counterpart of the geometry choice: the multilayer scintillator–cadmium structure is designed to create prompt and delayed opportunities for detection, while the event selection must combine timing, multiplicity, and energy information to keep accidental coincidences under control.

5.5 Final veto geometry and readout

The final simulated geometry comprises 59 scintillator volumes arranged in six groups — Top, Bottom, Left, Right, Front, and Back — with three layers per group. The nominal symmetric layout would contain 60 panels. In the implemented 59-panel design one short inner top panel is absent, so that Top L1 contains three panels rather than four. The asymmetry is treated consistently in the Geant4 geometry and reflects the mechanical/service accommodation of the realized design. The group/layer logic is summarized in table 5.14; the detailed per-channel PMT serial map used during integration is not reproduced here because it is not needed for the design argument and evolved during prototype commissioning.

5.5.1 Prototype construction and commissioning

The final simulated geometry discussed in the optimization sections uses long 150 cm panels on the sides and bottom together with short 80 cm modules on the front, back, and inner-top positions. The commissioned IAXO-D0 prototype, by contrast, was built from re-used NE-110 bars originally 3 m long and then cut to lengths of 150 cm or 65 cm for the first surface implementation [69]. Each panel is 20 cm wide and 5 cm thick, with a PMT coupled through a light guide at one end. This distinction between the later 59-panel simulated design and the earlier 57-signal commissioned prototype should be kept in mind whenever simulation and data are compared.

In the simulated design, the veto is described as repeated scintillator–cadmium stages, with thin cadmium capture sheets placed between successive scintillator layers so that moderated neutrons emerging from one active volume can be captured close to the next one. In the commissioned prototype, 1 mm cadmium sheets were physically installed between neighboring panels and layers around the detector [69], thereby realizing the same scintillator–cadmium stage concept in the mechanically accessible layout. The overall arrangement follows the multi-layer shielding logic described above, with overlapping panels around the lead shield but unavoidable openings associated with the beam pipe, support structure, and service routing.

The commissioned IAXO-D0 veto did not yet realize the full 59-panel BabyIAXO geometry. In the prototype data-taking configuration up to 57 veto signals could be recorded per event, corresponding to the installed panel set [69]. This distinction is important when comparing simulation and data: the design studies in this chapter refer to the final 59-panel simulated geometry, whereas the first experimental validation was carried out with the slightly reduced commissioned prototype implementation.

Commissioning relied strongly on atmospheric-muon calibration. For a flat 5 cm scintillator panel with density close to \(1\,\mathrm {g\,cm^{-3}}\), the most probable muon signal corresponds to about 10 MeV visible energy [69]. This Landau-like reference was used for gain equalization across the installed channels. At the same time, dedicated measurements on the long panels confirmed that the light collected at the far end of a 150 cm bar can be attenuated by roughly a factor of two, which sets a practical limit on how directly calibrated veto amplitudes can be interpreted as deposited energies.

The construction and commissioning were carried out within the BabyIAXO detector team. The work presented in this thesis is centered on the simulation framework, the analysis strategy, and the interpretation of the veto response, together with contributions to the detector integration and commissioning tasks required to connect the simulation program with the first surface data.

5.5.2 Electronics and readout

Each scintillator panel is read out by a dedicated photomultiplier tube coupled through a light guide. In the BabyIAXO prototype both the Micromegas detector and the veto system were instrumented with four AGET ASICs each, with 64 channels per chip [69, 88]. The readout architecture is therefore a design constraint, not a mere implementation detail: segmentation, timing windows, and channel mapping must all fit within a synchronized dual-branch electronics system.

A relevant feature of the scintillator response is the attenuation of the collected light along the panel length. Measurements reported for the prototype show that, at the far end of a 150 cm scintillator, the collected light can be reduced by about a factor of two with respect to interactions close to the photomultiplier [69]. Consequently, the pulse height measured in a veto channel cannot be interpreted as a direct deposited-energy estimator without accounting for the interaction position, and the calibrated veto energy should be regarded as a lower limit on the true deposited energy. This effect is incorporated in the detector simulations through light-attenuation models applied to the scintillator and light-guide system, allowing a more realistic description of the waveform amplitudes expected in each channel.

The shaped analog signals are digitized and stored in an adjustable acquisition window. Internally, each channel is sampled continuously over 512 bins by a circular buffer, which makes it possible to choose freely the delay between the start of the time window and the trigger [69]. This flexibility is particularly important for the present application because the Micromegas and veto signals evolve on very different timescales.

In order to operate both subsystems with independent readout settings, the Micromegas and veto signals are handled as separate AGET-based branches synchronized by a common trigger and clock reference [69]. During prototype operation the Micromegas time window was set between 10 and 30 \(\mu \)s depending on the configuration, whereas the veto system was read out in a 100 \(\mu \)s total window with the Micromegas trigger located at 30 \(\mu \)s inside that window [69]. In trigger-centered coordinates this corresponds approximately to \([-30,+70]\,\mu \mathrm {s}\). This common timing architecture allows veto observables and Micromegas candidate events to be merged offline into a single event record with a shared time reference.

For neutron-tagging studies, the veto acquisition window must extend well beyond the prompt response, since delayed signals produced after moderation and capture in the scintillator–cadmium structure are expected on timescales of several tens of microseconds [69, 133, 134]. The precise per-channel high-voltage and AGET mapping evolved during commissioning and are therefore not tabulated here, but the stable group/layer geometry is summarized in table 5.14. The electronics design is thus a central ingredient of the discrimination strategy itself.

5.6 Waveform-level veto observables

At analysis level, the waveform information recorded in the veto channels is reduced to a set of observables characterizing the presence of prompt or delayed activity. This distinction is important for the logic of the chapter. The early geometry-optimization studies used idealized deposited-energy thresholds to compare alternative layouts, while the HENSA layer validation and the performance figures use waveform-level observables extracted from shaped traces.

For this reason, the simulation framework is designed to propagate the detector response up to waveform level. In the REST-for-Physics chain developed for IAXO-related studies, each scintillator is treated as a dedicated readout channel coupled to one photomultiplier, so the position of the Geant4 energy deposit can be translated into a propagation distance along the panel and through the light guide. The optical attenuation is then applied using the measured attenuation length of about 400 cm, after which the signal is mapped to the corresponding veto channel and converted into a shaped waveform [133]. In the configuration adopted for the veto studies, the simulated waveforms were sampled in 500 ns bins with a shaping time of 3000 ns, while dedicated TPC timing studies used finer values of 20 ns and 1200 ns for the Micromegas branch. This approach allows simulated veto data to be analyzed with essentially the same logic as experimental data, which is particularly valuable for validating cuts and estimating the rejection power of different veto configurations.

In the production analysis chain, the shaped traces are processed with TRestRawPeaksFinderProcess, which operates on the selected channel type and identifies local maxima using configurable baseline, threshold, distance, and window parameters defined in the common analysis.rml file. The process returns the time, amplitude, and multiplicity of the relevant peaks that are later used for veto decisions. Working at waveform level is essential because neutron-tagging events are not characterized by a single large deposited energy. Instead, they often produce a sequence of prompt and delayed peaks with weak amplitude–time correlation, and the most useful observables are therefore the peak times, multiplicity, and channel distribution rather than the total integrated energy alone.

In practice, the use of waveform-based observables provides a more robust description of veto activity than a simple energy-in-volume treatment. This is especially relevant for neutron-induced backgrounds, where the topology of the event in the veto system may contain delayed signals associated with moderation and capture rather than a single prompt pulse. The discrimination capability of the veto system therefore depends not only on its geometrical coverage, but also on the achievable threshold, timing performance, and segmentation of the readout.

The same reconstructed observables were used to classify the 879 TPC-depositing neutron events by their veto pattern. Explicit neutron capture was present in nearly all of these events at truth level, but a reconstructed veto tag is not guaranteed because the visible response depends on capture-product transport, quenching, light attenuation, waveform shaping, and peak finding. The resulting classes show why a single geometry-only coincidence is insufficient: the useful information is distributed across prompt activity, delayed peaks, multiplicity, and the occasional absence of a reconstructed veto signal.

5.6.1 Boosted veto BSD selection

The waveform observables described above can be used either as explicit cuts or as inputs to a multivariate selection. In this thesis the latter approach is treated as the veto analogue of the background-signal discrimination (BSD) selector used for the Micromegas analysis. The purpose is not to assign a unique particle identity to each event, but to build a calibrated ranking variable that separates neutron-correlated veto activity from signal-like accidental veto activity. Only reconstructed analysis observables are used as inputs; truth labels, generator information, event number, and run number are not used by the classifier.

Two related implementations were studied. The design-facing version is a binary boosted-tree selector trained on the three-layer HENSA outdoor-neutron simulation and on experimental calibration-triggered veto activity. For the neutron class, each simulated neutron event is overlaid with one calibration event sampled from the measured accidental-veto template, so that the classifier sees neutron-correlated signals on top of a realistic random-veto environment. For the signal-like control class, the input is the calibration-triggered veto activity itself. The five aggregate inputs are the total visible veto-energy proxy, the reconstructed peak multiplicity, the number of unique veto channels, the number of high-quality veto signals, and the integrated above-threshold waveform response. This is intentionally a compact feature set: it tests how much discrimination can be obtained from observables that are robust against details of the final channel mapping and do not require truth-level information.

The discriminator output is treated as an ordering variable, not as a calibrated neutron probability. Operating points are defined by the calibration acceptance, i.e. by the fraction of calibration-like events that are not vetoed by a given score threshold. At \(90\%\) calibration acceptance, a single visible-energy threshold rejects about \(51\%\) of the HENSA three-layer neutron sample. The boosted veto BSD increases the rejection to about \(76\%\), and still rejects about \(68\%\) of the neutron sample at \(95\%\) calibration acceptance. The maximum of the relative \(S/\sqrt {B}\) proxy occurs at a less conservative calibration acceptance of about \(83\%\), where the neutron rejection reaches about \(82\%\). The feature-ranking study shows that the dominant information is carried by the total visible veto-energy proxy and by the number of good veto signals, with peak multiplicity providing a smaller but non-negligible contribution. The unique-channel count is much less important in this aggregate study, consistent with the weak track-like topology of neutron-induced veto activity.

The distinction between muon and neutron inputs is also important. Muon-induced events are dominated by prompt, high-amplitude scintillator coincidences associated with a through-going track. In the aligned 20,000-event muon simulation, the median event has five veto peaks, five unique channels, and essentially no delayed-window activity. Neutron-induced events are more heterogeneous: the median event has three veto peaks and three unique channels, but the delayed window contains a median of two high peaks and a visible-energy proxy of about \(986\) in the analysis units. The neutron response also has a broader time distribution because the veto is sensitive not only to prompt secondaries but also to moderation and capture-related activity. This is why delayed peaks are physically important, but also why they cannot be used alone: the calibration data already contain accidental late activity, so the useful signature is the combination of timing, energy, multiplicity, and signal quality.

An expanded machine-learning study was also performed for the experimental IAXO-D0 data. That study uses three training classes: calibration data, muon simulation with calibration-noise overlay, and neutron simulation with calibration-noise overlay. The input vector extends the aggregate veto variables with prompt-window, neutron-window, delayed-window, and pre-prompt veto observables, together with a small set of Micromegas topology quantities. The Micromegas variables are included only for the experimental candidate-ranking study, where the goal is to identify events whose full detector record resembles the neutron+noise template; the design-facing veto discriminator described above uses only veto observables. The held-out validation gives recalls of \(99.2\%\), \(95.8\%\), and \(91.7\%\) for calibration-like, muon-like, and neutron-like classes, respectively. The largest confusion is between neutron-like and muon-like events, which is expected because energetic neutron showers can contain prompt secondaries, while atypical muons can leave weak or delayed residual activity after the prompt-veto selection.

This multivariate analysis should therefore be interpreted as a structured extension of the explicit veto cuts, not as an independent truth label. For the design study it quantifies the gain available when the full waveform-level veto information is retained. For the experimental comparison it provides a way to rank neutron-enriched event populations while preserving a direct calibration-data estimate of accidental acceptance. The final veto interpretation remains anchored to control samples and to explicit efficiency points, rather than to an unqualified classifier probability.

5.7 Simulation performance

Unless explicitly stated otherwise, the performance results in this subsection correspond to the final 59-panel simulated geometry, atmospheric secondaries generated with CRY at Zaragoza latitude, and the full waveform-level analysis chain including quenching, light attenuation, shaping, and peak finding. The veto readout is treated with the prototype-like 100 \(\mu \)s total acquisition window and trigger placement at 30 \(\mu \)s, so that the simulated observables can be compared directly with the data-taking mode of the commissioned IAXO-D0 prototype.

Definitions. In table 5.17, raw denotes the particle-specific background rate before Micromegas event selection. Energy + topo + window denotes the residual rate after the Micromegas energy-region, topological, and readout-window cuts. + veto denotes the same analysis-selected sample after adding a simplified waveform-level veto requirement. The veto efficiency is therefore the fraction removed by the veto from the analysis-selected sample, not from the raw particle flux. The residual background is the surviving rate after all applied cuts. Unless stated otherwise, times in this subsection are quoted relative to the Micromegas trigger at \(t=0\). The threshold refers to the veto-peak threshold used to define a triggerable veto signal; the prompt window denotes activity around the Micromegas trigger, and the delayed window the later part of the 100 \(\mu \)s total acquisition used to retain capture-related peaks. When the experimental cut windows are quoted later in the original publication convention, they are given explicitly from the start of the veto acquisition window.

Muon-dominated component

Cosmic muons dominate the raw background rate by a wide margin because of their large flux and high penetration power. Their veto signature is correspondingly robust: they traverse one or more scintillator layers and deposit large signals, typically well above any practical threshold. Figure 5.39 is a deposited-energy diagnostic illustrating this separation between muon signals and the threshold region. Figure 5.41 shows the same behavior at channel level in the segmented detector. The TPC-triggered muon population is compared with the full sample of veto-intersecting muons, showing how the TPC coincidence selects a more geometrically constrained subset while preserving the track-like correlation bands across opposite veto groups.

The same conclusion can be inspected at the level of the main veto groups. Figure 5.40 separates the deposited energy by detector side for the muon events that also produce a TPC signal. These distributions are not used as independent cuts in the final analysis, but they are useful diagnostics of the veto geometry: through-going muons usually illuminate more than one scintillator group, and the relative response of the groups reflects the direction and acceptance of the segmented enclosure. This group-resolved view provides the bridge between the integrated energy spectrum and the channel-level correlation matrix shown next.

With a simplified waveform-level veto condition requiring at least one veto peak above threshold, more than \(99\%\) of the muon-induced candidates remaining after the Micromegas analysis cuts are rejected [135]. The much larger reduction from the raw muon rate to the final post-veto rate in table 5.17 is therefore not a contradiction: it reflects the combined action of the Micromegas energy, topology, readout-window, and veto cuts.

Neutron- and proton-dominated component

The neutron case is more difficult because the veto signals are softer, more distributed, and often delayed. High-energy primary neutrons interact in the lead shielding and produce showers of secondaries concentrated around the MeV scale. Their recoil-proton signals in the scintillator are strongly quenched, and their spatial pattern is weak compared with the muon case. Figure 5.42 shows the corresponding waveform-level response. Muons and proton-induced cascades usually produce large veto signals once they reach the scintillators, whereas neutron events have a broad low-energy component and gamma events frequently produce no triggerable veto peak. This is why neutron rejection is much more sensitive to the practical veto threshold and to delayed peak recovery than muon rejection.

The same loss of clean spatial structure is visible in figure 5.43, where the strong track-like bands seen for muons are replaced by a more diffuse channel-correlation pattern.

The delayed component is therefore essential. In the simplified waveform-level performance studies, the prototype-like 100 \(\mu \)s total acquisition window captures both prompt fast-neutron activity and a large fraction of the delayed capture signal. Because only about \(70\,\mu \mathrm {s}\) of this window lie after the trigger, it retains roughly \(79\%\) of an exponential delayed component with \(\tau \simeq 45\,\mu \mathrm {s}\) before threshold and acceptance effects. Under this definition, the veto reduces the residual neutron-induced background by about \(30\%\) after the Micromegas analysis cuts [135]. A further important finding was that cosmic-ray protons are not negligible: because they can also generate secondary cascades in the shielding, the same veto logic suppresses the residual proton component by about \(70\%\) [135].

5.8 Experimental validation with IAXO-D0 data

The prototype system was operated together with the IAXO-D0 Micromegas detector at surface level in Zaragoza, providing the first direct validation of the veto concept under realistic background conditions. This comparison is especially relevant because the experimental analysis uses waveform-level veto observables, including peak time, peak amplitude, multiplicity, and channel pattern. It therefore tests the same class of quantities emphasized in Sections 5.6 and 5.7, rather than only idealized deposited-energy thresholds.

The scope of the comparison must be defined carefully. The simulations presented above correspond to the final 59-panel geometry, while the first experimental implementation was a commissioned 57-signal prototype based on the same scintillator–cadmium concept. The experimental setup also includes detector effects that are only approximately represented in the simulation, such as channel-dependent gain calibration, light attenuation along the scintillator bars, evolving threshold settings during commissioning, mechanical gaps, and the exact readout configuration. For this reason, the data should not be treated as a one-to-one measurement of the simulated neutron-veto efficiency. Instead, they provide a validation of the physical discrimination strategy: prompt tagging of muon-like events, together with delayed and multiplicity-based rejection of events compatible with neutron-induced activity.

Published surface cut-flow validation

Starting from the full raw acquisition, the Micromegas analysis selects events in the 2–7 keV region of interest, inside the focal-spot region, and passing the standard topological selection. This reduces the data set to 257 X-ray-like candidates with a calibration efficiency of 81.9%. The application of the prompt muon-veto selection then reduces this sample to 56 events. This is the dominant rejection step in the experimental data, corresponding to a reduction of

with respect to the Micromegas-selected sample. This behavior is consistent with the simulation picture: muons dominate the raw surface background and, when they produce events that survive the Micromegas cuts, they are usually accompanied by large and prompt scintillator signals.

The advanced veto selection removes 7 additional events from the 56 events left after the prompt veto, leaving 49 events in the final sample. This corresponds to an additional rejection of

after the prompt-veto stage. The associated binomial uncertainty is approximately 4.4 percentage points, so the effect is statistically visible but not yet precise enough to extract a detailed neutron-rejection efficiency. The final measured background level is

where the quoted uncertainty is dominated by counting statistics. The calibration efficiency decreases from 81.9% after the Micromegas cuts to 79.4% after the full veto selection, corresponding to a relative efficiency of \(79.4/81.9 \simeq 97\%\). This is an important result because it shows that the delayed and multiplicity-based selection can provide additional rejection without introducing a large penalty for signal-like X-ray events.

The advanced veto cuts reject events with unusually high veto multiplicity or with substantial veto activity in delayed sub-windows, both of which are difficult to reconcile with an isolated X-ray-like Micromegas signal. In the original publication convention, the windows [23,53] \(\mu \)s and [35,68] \(\mu \)s are quoted from the start of the 100 \(\mu \)s veto-acquisition window. Since the Micromegas trigger is placed at 30 \(\mu \)s, these correspond approximately to \([-7,+23]\,\mu \mathrm {s}\) and \([+5,+38]\,\mu \mathrm {s}\) relative to the trigger. The first window therefore straddles the prompt region and early delayed activity, while the second isolates the delayed component more cleanly. This timing convention is important when comparing the experimental cuts with simulation results, where times are generally expressed relative to the Micromegas trigger. The veto-energy variable entering these cuts is a calibrated scintillator-energy proxy rather than a direct local deposited energy, because light attenuation and channel-dependent gain corrections are folded into the observable.

Interpretation limits of the published selection

The interpretation of the advanced veto selection should be made with some caution. Although the original analysis refers to this stage as a neutron cut, the experimental observable is not a direct neutron identifier. The veto does not detect the primary neutron itself in an event-by-event sense. Instead, it tags activity expected from neutron-induced cascades: secondary particles produced in the lead shielding, moderation in the plastic scintillator, and delayed capture-related signals in the scintillator–cadmium structure. The rejected events occupy a region of moderate veto-energy proxy and delayed activity, rather than the high-amplitude prompt signals characteristic of through-going muons. It is therefore more precise to describe the advanced selection as a delayed/multiplicity-rich veto selection enriched in neutron-like activity.

This distinction is also consistent with the Monte Carlo studies. In the full waveform-level simulations, the muon component is strongly suppressed by the prompt veto, while the residual neutron-induced background is reduced only partially. The simulation predicts that, after Micromegas cuts, the neutron component is reduced by about 30% by the simplified waveform-level veto, while proton-induced residuals are reduced more strongly, by about 70%. These simulated values are not directly comparable to the 12.5% additional rejection observed in data, because the experimental sample contains a mixture of background components and because the prototype geometry, thresholds, and calibration are not identical to the final simulation configuration. Nevertheless, the data show the expected qualitative structure: the prompt veto provides the dominant rejection of muon-like events, and a second class of delayed or high-multiplicity veto observables provides additional background discrimination.

The published cut flow is therefore kept as the experimental reference point for the veto-analysis discussion. It provides a baseline against which the refined selections developed in this thesis can be tested: at comparable calibration acceptance, a new delayed, multiplicity, likelihood, or machine-learning selection should reject more of the post-prompt background sample, or provide a clearer physical separation between prompt muon-like, accidental, and neutron-like veto activity. This comparison is more informative than replacing the published figures, because it keeps the first experimental validation and the later simulation-driven optimization conceptually separate.

The comparison can therefore be summarized in four points. First, the experimental data confirm that waveform-level veto observables are operationally useful and can be applied to real Micromegas candidate events without a large loss of calibration efficiency. Second, the prompt-veto response behaves as expected for muon-induced backgrounds, giving the largest reduction in the measured cut flow. Third, the advanced veto selection removes an additional population of events with delayed or multiplicity-rich scintillator activity, supporting the design motivation of the scintillator–cadmium veto. Finally, the limited size of the published data set and the differences between the commissioned prototype and the final simulated geometry prevent a direct extraction of an absolute neutron-tagging efficiency.

Thesis extension: neutron-enriched score comparison

For this thesis, the published comparison was extended with a higher-statistics reanalysis designed to answer a more specific question: which events in the experimental background sample are most compatible with the veto signatures expected from cosmic neutrons? The goal is not to assign a unique physical origin to every background event. Instead, the analysis constructs a controlled neutron-like score using calibration data, muon simulations, and neutron simulations, and then studies the experimental events that populate the neutron-enriched tail of that score. This approach makes the comparison more transparent than a single hard multiplicity cut because it keeps the calibration-derived accidental response, the prompt muon component, and the neutron-like delayed component as separate ingredients.

Three terms are used throughout the rest of this section. A neutron-like event is an event whose observables resemble the neutron+noise template more than the calibration or muon+noise control templates. A neutron-enriched population is a statistical sample with a larger expected neutron contribution than the parent sample, but with possible contamination from other backgrounds. A neutron-enriched candidate is an experimental event selected by the neutron-like score; this label does not imply event-by-event proof that the primary particle was a neutron. This terminology is intentionally conservative because the veto observes correlated scintillator activity and capture-related signatures rather than the incoming neutron directly.

The experimental input consists of the same prototype data used for the first veto publication. Two flat analysis trees were used: a calibration sample with \(139454\) events and a background sample with \(777752\) events. The calibration events are essential because they contain signal-like Micromegas triggers together with accidental veto coincidences produced by the real detector environment. They therefore provide an empirical model of random veto activity, including channel correlations, nonuniform channel noise, and occasional multi-peak structures. The background file contains the surface physics data in which most raw events are expected to be muon related, with a smaller population of events produced by other external or detector-internal backgrounds. Both files correspond to the commissioned 57-signal veto implementation, while the simulation templates described below use the 59-volume design geometry. This mismatch is a known systematic limitation, but it is acceptable for the present purpose because the comparison is based mainly on global timing, multiplicity, and energy-proxy observables rather than on a channel-by-channel efficiency extraction.

The simulation input consists of two dedicated 20,000-event production campaigns run with the same waveform-level analysis chain used for the veto studies. The muon production yielded \(21569\) analyzed events and the neutron production yielded \(20274\) analyzed events. In both cases the analysis tree includes the reconstructed veto peak vectors and the Micromegas observables needed to compare the simulated events with the experimental flat trees. Because the REST simulation stores the peak times in a physical time convention while the experimental analysis stores the veto waveform in binned acquisition coordinates, the simulated peak times were aligned according to

where \(t_{\mathrm {REST}}\) is the REST peak time in microseconds and \(t_{\mathrm {bin}}\) is the experimental waveform-bin convention. This alignment was validated with the muon sample: the prompt-muon tag selected \(97.65\%\) of the aligned muon simulation, consistent with \(97.84\%\) in the earlier reference sample. The corresponding fraction in the experimental background file is \(91.13\%\), while the calibration file has an accidental prompt-tag probability of \(11.00\%\). These numbers show both that the simulated prompt timing is correctly aligned and that the experimental background sample is indeed dominated by prompt muon-like activity before veto rejection.

The same prompt definition can be used to inspect the experimental channel topology directly. Figure 5.48 shows conditional channel-coincidence matrices built from veto peaks above 200 analysis units. Events are split according to whether they satisfy the prompt-muon tag \(N_{\mathrm {prompt}}\geq 2\). The muon-like background population has broad, high-probability channel coincidences, as expected for through-going or showering cosmic activity crossing several veto panels. The non-muon-like and calibration samples are less uniformly correlated and retain visible channel-dependent accidental structure. This comparison is not used as an efficiency calibration for individual scintillators, but it is a useful check that the prompt tag separates a topologically distinct experimental population before the delayed neutron-sensitive score is applied.

The prompt-candidate comparison makes the calibration role explicit. The prompt definition selects \(902484\) of \(995271\) experimental background events, \(21062\) of \(21569\) simulated muon events, and \(21134\) of \(21569\) simulated muon+noise events. Adding calibration accidentals brings the simulated multiplicity closer to the data, with a median of ten reconstructed veto peaks in both samples, but it does not fully reproduce the delayed tails. This supports the interpretation that the experimental prompt population is dominantly muon-like while still containing real detector accidentals and non-muon activity that must be treated separately in the neutron-enriched comparison.

The calibration sample was also used to add an empirical accidental-veto component to the simulations. For each simulated event, one calibration event was sampled with replacement and its veto-peak vectors were concatenated with the simulated veto peaks. This procedure does not attempt to model the electronics from first principles. Rather, it preserves the measured accidental veto environment, including the real distribution of random channels and amplitudes, while retaining the simulated correlation between the TPC event and the physical muon or neutron shower. The resulting templates are denoted below as muon+noise and neutron+noise. This step is important because a pure simulation sample has too little random veto activity compared with the experimental data, especially in the delayed windows used for neutron-sensitive selections.

Figure 5.49 illustrates the central distinction exploited by the comparison. The muon simulation has a compact prompt response, with a median of five veto peaks, five unique veto channels, and essentially no delayed activity after the prompt window. The neutron simulation is less sharply prompt and more heterogeneous: the median event has three veto peaks and three unique channels, while the delayed window contains a median of two peaks and a median delayed energy proxy of about \(986\) in the analysis units. The absolute veto-energy scale should not be overinterpreted, but the timing pattern is robust. Muon-like events are identified by large prompt coincidences; neutron-like events are enriched by delayed and moderate-multiplicity activity.

Likelihood score and candidate definition

The event classification was performed with a deliberately simple likelihood score. For each event, an observable vector \(\vec {x}\) was constructed from six global quantities:

where \(E_{\mathrm {nwin}}\) and \(N_{\mathrm {nwin}}\) refer to a neutron-sensitive delayed window, \(E_{\mathrm {delayed}}\) and \(N_{\mathrm {delayed}}\) refer to the full post-prompt delayed window, \(N_{\mathrm {unique}}\) is the number of unique veto channels with peaks, and \(E_{\mathrm {TPC}}\) is the reconstructed Micromegas energy observable. The score is the log-likelihood ratio

where the second term represents the non-neutron control population constructed from calibration events and muon+noise simulation. The score is not a proof that an event was caused by a neutron. It is a ranking variable: large positive values identify events whose veto and TPC observables are more compatible with the neutron+noise template than with calibration-like or muon-like activity.

Before applying this score, two quality selections were imposed. Events with a prompt-muon tag were removed using the condition \(N_{\mathrm {prompt}}\geq 2\) for veto peaks with amplitude above 200 analysis units in the prompt window \(190 \leq t_{\mathrm {bin}}\leq 210\). Events with extreme veto activity, defined as \(N_{\mathrm {peaks}}\geq 100\) or \(N_{\mathrm {unique}}\geq 50\), were treated as burst-like and excluded from the clean comparison sample. The neutron-enriched candidate threshold was then set by the calibration control sample: the default requirement is that an event lies above the upper \(1\%\) tail of the clean calibration score distribution. This gives

By construction, this threshold accepts approximately \(1\%\) of clean calibration events and therefore provides a direct empirical estimate of accidental acceptance for a signal-like X-ray control population.

Table 5.20 summarizes the resulting populations. After prompt-muon suppression and burst removal, \(65990\) background events remain from the original \(777752\) experimental events. Applying the \(1\%\) calibration-tail threshold selects \(3877\) events. This corresponds to \(0.50\%\) of all experimental background events, \(5.62\%\) of the prompt-muon-suppressed background sample, and \(5.88\%\) of the clean prompt-muon-suppressed sample. The same threshold selects only \(12\) events in the muon+noise simulation, corresponding to \(0.056\%\) of all simulated muon events and \(2.77\%\) of the clean prompt-muon-suppressed muon+noise subset. In contrast, it selects \(1722\) neutron+noise events, or \(8.49\%\) of all simulated neutron events and \(17.8\%\) of the clean prompt-muon-suppressed neutron+noise subset.

The accidental acceptance is therefore not an abstract estimate; it is measured from the calibration data themselves. At the chosen threshold, a signal-like calibration event has a \(1\%\) probability of entering the neutron-like tail after the prompt-muon and burst selections. Equivalently, the neutron-enriched candidate definition would reject or tag about \(1\%\) of calibration-like X-ray events because of random veto coincidences or calibration-event structures that resemble neutron-like activity. This value is the appropriate accidental scale for the score-based selection. The muon+noise leakage is smaller in the full simulated muon sample because most muon events are removed by the prompt tag, but it is not zero in the clean prompt-suppressed subset. This residual leakage corresponds to muons with atypically weak prompt signatures, muon-induced secondaries that survive the prompt cut, or accidental-noise configurations that populate the delayed windows.

It is useful to compare this result with the published advanced-veto reduction. The published cut flow removed \(7\) of \(56\) events after the prompt muon veto, an additional reduction of \(12.5\%\) in the final 2–7 keV focal-spot sample. The score-based study quoted above is broader: it is applied to the full available flat background sample and uses a likelihood threshold anchored to the calibration tail rather than the exact published focal-spot cut flow. With a looser threshold defined by the upper \(5\%\) calibration tail, the score selects \(9039\) of \(65990\) clean prompt-muon-suppressed background events, or \(13.7\%\). This is close to the scale of the published \(12.5\%\) post-muon-veto reduction, although the two numbers should not be interpreted as a direct reproduction of the same selection. Their agreement in scale is nevertheless encouraging: both analyses indicate that a delayed/multiplicity-rich veto observable identifies an additional background population after prompt muons have been removed, while preserving most calibration-like events.

Properties of the neutron-enriched experimental population

The selected experimental events are not simply high-energy muons that escaped the prompt veto. Their veto signatures are characterized by substantial delayed activity and moderate neutron-window activity. The median selected experimental candidate has \(47\) veto peaks, \(12\) unique veto channels, one peak in the neutron-sensitive delayed window, and seven delayed peaks over the full delayed window. The median delayed energy proxy is \(6822\), while the median prompt-count observable is zero. This pattern is qualitatively different from the prompt muon template and is the reason these events are assigned large values of \(S_{\mathrm {n}}\).

The comparison with selected neutron+noise simulations is more nuanced. The neutron+noise events selected by the same score have a median of \(9\) veto peaks, \(8\) unique veto channels, one neutron-window peak, and four delayed peaks. Their median delayed energy proxy is \(2707\), lower than in the selected experimental population, while their median Micromegas energy and hit multiplicity are larger than in the experimental candidates. Thus, the experimental candidates are neutron-like according to the global score, but they are not perfectly described by the present neutron simulation. The data show stronger delayed veto multiplicity, whereas the simulation shows more energetic and more extended TPC topologies.

Representative event rasters for the neutron-enriched experimental sample and selected neutron+noise simulation are shown in Appendix 6.11, Fig. 6.38. They are kept out of the main text because they are useful visual diagnostics, but the quantitative argument is already captured by the score distribution, population table, and delayed-observable comparison.

Several conclusions follow from these comparisons. First, the score-based candidate population is plausibly enriched in cosmic-neutron-induced activity, because it is selected by delayed and neutron-window veto features that are inefficient for ordinary calibration events and strongly suppressed in prompt muon simulations. Second, the population is not a pure neutron sample. The present templates include calibration-like accidentals, muons, and neutrons, but the experimental background may also contain gamma-induced events, radon- or activation-related activity, residual proton or hadronic secondaries, muon-induced secondaries with weak prompt veto response, unstable channels, and DAQ artifacts. Any of these components can be partially absorbed into the neutron-like likelihood tail if their observables resemble delayed veto activity. Third, the mismatch in Micromegas topology between selected experimental candidates and selected neutron simulation suggests that the current neutron production does not yet fully reproduce the response of the experimental prototype. This may arise from the gas mixture and analysis configuration, differences between the 57-signal prototype and the 59-volume simulation, threshold and gain effects, or incomplete modeling of the full environmental background composition.

The corresponding Micromegas-energy and hit-multiplicity diagnostics are also deferred to Appendix 6.11, Fig. 6.39. Their role is to document the main residual mismatch: the neutron template reproduces the delayed-veto character better than the full TPC topology.

The safest interpretation is therefore statistical rather than categorical. At the \(1\%\) calibration-tail threshold, approximately \(0.50\%\) of all experimental background events, and \(5.9\%\) of the clean prompt-muon-suppressed background, form a neutron-enriched candidate population. This fraction is not the cosmic-neutron background fraction in the detector. It is the fraction of events that pass a particular neutron-like selection whose accidental acceptance is fixed from calibration data. The true neutron contribution could be smaller if other backgrounds populate the same delayed/multiplicity-rich region, or larger if a significant fraction of neutron-induced events have weak veto signatures and remain outside the selected tail. Nevertheless, the result is consistent with the published observation that delayed and multiplicity-based veto cuts remove a measurable fraction of the post-muon background while preserving most calibration events.

5.9 Systematic limitations and remaining work

5.9.1 Design-level systematics

The veto-performance values quoted above should be interpreted as design-level estimates rather than as final absolute background predictions. Several systematic effects remain relevant, both in the source term and in the detector response.

The dominant uncertainty for absolute neutron-background rates is therefore no longer the existence of a measured source term, but the transfer of the HENSA outdoor spectrum to the DESY site and the differences between measured and generator-level descriptions. At fixed source term, the dominant uncertainty for veto efficiency is the effective threshold, which combines quenching, light attenuation, PMT gain calibration, and peak-finding settings into a single observable-level response. Geometry gaps and finite Monte Carlo statistics mainly affect the tails of the residual distributions and the precision with which small surviving components can be quoted.

A full accidental-veto and dead-time estimate requires the measured single-channel rates together with the final online veto logic. In general, for a representative veto-trigger rate \(R_{\mathrm {veto}}\) and coincidence window \(\Delta t\), the accidental probability scales approximately as \(P_{\mathrm {acc}} \simeq 1 - \exp (-R_{\mathrm {veto}}\Delta t)\). This quantity is not quoted here because the relevant single-channel rates evolved during commissioning and were not yet fixed in the configuration used for the first prototype analysis. Empirically, however, the advanced experimental veto cuts preserve about \(97\%\) of the calibration events relative to the prompt-veto stage, which provides a first bound on the live-time penalty associated with delayed and multiplicity-based veto observables.

5.9.2 Limitations of the neutron-enriched comparison

The main limitations of the present data–simulation comparison are summarized in Table 5.23. They are narrower than the general systematics listed in Table 5.22: the question here is not the absolute uncertainty of the full veto design, but the degree to which the experimental neutron-enriched population can be interpreted with the currently available templates.

The extended comparison also identifies the measurements needed to convert this neutron-enriched selection into a quantitative neutron-background estimate. The most important improvement is a fully matched experimental and simulated analysis chain, including the exact 57-channel prototype mapping, run-dependent thresholds, channel gains, and broken-channel configuration. The second requirement is a broader simulation library that includes not only cosmic muons and neutrons but also protons, gammas, environmental radioactivity, and muon-induced secondaries under the same waveform analysis. The third requirement is a run-by-run accidental model rather than a single calibration-overlay template, because the delayed-window candidate rate is sensitive to channel noise and burst-like periods. Finally, the HENSA-based neutron source term must be transferred to the DESY site conditions before the candidate fraction can be translated into a BabyIAXO background prediction.

The same list defines what would be required for a publication-quality neutron-population measurement. A robust result should use the exact experimental geometry and readout map, a blinded validation period independent of the data used to tune the score, a run-by-run veto calibration and accidental model, and a complete template set including protons and environmental backgrounds. The neutron template should then be normalized with the measured or otherwise constrained cosmic-neutron source term, and the resulting candidate rate should be propagated through the same Micromegas region-of-interest and topological selections used for the final background model. Under those conditions, the neutron-enriched score could become not only a tagging variable but also a control region for constraining the cosmic-neutron component of the surface background.

In conclusion, the surface data validate the main design logic of the active shield and provide the first experimentally grounded handle on neutron-like veto signatures. The veto behaves as a conventional prompt muon veto and, in addition, provides a measurable delayed/multiplicity-based rejection channel that is consistent with the expected response to neutron-like residual backgrounds. The extended reanalysis shows that a calibration-controlled neutron-like score selects a small but significant experimental population with delayed veto activity, while also revealing systematic differences between data and the current neutron simulation. This result supports the use of a multi-layer scintillator–cadmium veto for BabyIAXO and motivates the next step: a larger and more stable data set, with fixed thresholds and a fully matched simulation geometry, to convert the present neutron-enriched population into a quantitative neutron-veto efficiency and background estimate. The neutron-enriched population defined here will also be useful in the background-model chapter as a validation target for the simulated cosmic-neutron and muon-induced components, because it provides an experimentally selected control sample anchored to the real veto response.

5.10 Summary and outlook

The shielding and veto studies lead to a clear design conclusion. Lead remains necessary for suppressing external photon backgrounds, but it is not a complete surface-background solution: for high-energy neutrons it acts partly as a converter, producing a softer and more distributed secondary shower. The veto concept must therefore be coupled to the passive shield rather than treated as a separate muon counter.

The final design response is a three-stage scintillator–cadmium veto surrounding the lead shield. The hydrogen-rich scintillator provides prompt and moderated-neutron sensitivity, the cadmium sheets convert the thermalized component into capture-gamma cascades, and the waveform analysis retains prompt, delayed, multiplicity, and topology information. The HENSA-driven layer scans support the three-layer cadmium configuration as the practical compromise: most of the available neutron-tagging gain is obtained before the fourth layer, while the additional layer increases channel count and accidental-veto exposure. The default physics configuration for this interpretation is high-precision neutron transport with strict isotope handling; PhotonEvaporation is used as the nominal cadmium-capture cascade model when prompt-gamma energy partition matters, with the default ParticleHP cascade retained as a systematic comparison.

The commissioned IAXO-D0 prototype validates the same strategy in data. The prompt veto gives the dominant muon-like rejection, and delayed/multiplicity-rich selections provide an additional measurable reduction with only a small calibration-efficiency penalty. The extended neutron-enriched comparison strengthens this interpretation by selecting a calibration-controlled population with delayed veto activity, while also showing where the present simulation is incomplete. The next improvements are therefore well defined: a matched 57-channel prototype geometry, run-dependent threshold and noise modeling, broader background templates, and transfer of the measured HENSA neutron source term to the BabyIAXO site conditions.

Chapter 6
Background Model

Introduction

As a rare-event search experiment, IAXO requires a detailed background model to distinguish signal candidates from background events. The purpose of the model is to translate measured activities and external particle fluxes into reconstructed, X-ray-like survivor rates in the Micromegas region of interest. This translation is non-trivial because the same source activity can produce different accepted rates depending on geometry, detector response, topology cuts, veto response, and normalization uncertainty.

This chapter describes the background model developed for IAXO-D0 and BabyIAXO, while noting that many of its components are also relevant to the future IAXO experiment. The model remains a collaborative effort that continues to evolve as new measurements and simulations become available. The work presented here builds on the previous iteration of the IAXO-D0 background model [70], which itself was informed by the CAST background-model studies. The chapter should therefore be read as a definition of the current source catalogue, detector-response chain, and component maturity status, rather than as the final absolute background-rate budget for BabyIAXO. The latter requires the final master rate table, with source normalizations, geometry version, exposure, selection window, surviving rate, and uncertainties fixed for all components.

6.1 Simulation and Analysis Methodology

The background model simulations and the subsequent event reconstruction were carried out with REST-for-Physics [91], using the restG4 and restManager applications described in the software chapter. The Monte Carlo transport stage was defined through source-specific configurations, while the detector-response emulation and event reconstruction were performed with a common analysis chain. This same reconstruction chain is also used for the analysis of experimental data, since the simulated detector response is converted into the same reconstructed event format as real detector acquisitions. This common data model allows the same observables, selection criteria, and background-discrimination procedures to be applied consistently to both simulated and measured events.

6.1.1 Workflow overview

The methodology followed for the background model is summarized in Figure 6.1. The first stage consists of defining a source term and the corresponding detector geometry. The source term depends on the origin of the background contribution under study: radioisotope contamination in a detector component, environmental radiation entering from outside the shielding, or cosmic-ray secondaries. These inputs are then propagated with restG4, which performs the Geant4 transport and stores the event-level truth information.

In a second stage, restManager processes the simulated event through a detector-response chain designed to reproduce the experimental readout observables as closely as possible. This response chain includes both the Micromegas detector readout and the active-veto readout, which are described in REST-for-Physics through dedicated readout definitions. Although both systems are handled within the same analysis framework and are ultimately stored in a common event structure, they represent physically different detector subsystems: the Micromegas readout reconstructs the charge signal produced in the gaseous TPC, while the veto readout reconstructs scintillation signals produced in the surrounding veto modules. Consequently, their channel mapping, signal formation, timing, shaping, and reconstructed observables are treated with subsystem-specific parameters and processes.

The reconstructed output is then used to derive the observables employed for the background studies and for the X-ray-like event selection. In this way, the simulated events can be compared with experimental data at the level of reconstructed quantities, rather than only at the level of idealized energy depositions.

This separation between transport and reconstruction was particularly important in the present work. It allowed the same reconstruction chain to be applied consistently to different background sources, while at the same time making it possible to update detector-response parameters, electronics settings, veto thresholds, or analysis cuts without repeating the full Geant4 transport stage. The same strategy also ensured that simulated events and experimental data were compared using the same reconstructed observables and selection criteria, while preserving the distinct detector-response models required by the Micromegas and veto readout systems.

6.1.2 Source-specific simulations

The Monte Carlo transport stage was configured with a family of source-specific source descriptions. Each one defined the source term for one background component, but the structure of the simulations was kept common: a detector geometry, a primary-event generator, the sensitive detector volumes, and the physics lists required for electromagnetic interactions, radioactive decays, and, when needed, hadronic transport. This organization isolates the physical origin of each background contribution while preserving a common interface to the reconstruction chain.

For internal contaminations, the simulated source was defined from the detector volume corresponding to the material under study. This category includes detector materials such as copper, electronics, gas, kapton, mylar, shielding elements, and radon or plated-out progeny. The primary positions were sampled uniformly inside the selected volume, or on its surface when the measured contamination was given as a surface activity.

The activity assigned to each source was obtained from radiopurity measurements performed by the collaboration at the Laboratorio Subterráneo de Canfranc. Depending on the sample, these measurements provide either activities per unit mass or per unit surface. To avoid inconsistencies in the normalization, the component mass or surface was taken from the same detector description used in the simulation. The measured activity and the simulated mass or surface were then used to compute the total activity assigned to the source. This activity provides the normalization factor used to convert the simulated event sample into a background rate.

When the measured activity referred to a parent isotope assumed to be in secular equilibrium, the full radioactive decay chain was simulated. In this way, the generated events preserve both the spatial distribution of the contamination in the detector geometry and the correct normalization to the measured activity of the material.

Environmental backgrounds were also considered in the simulation campaign, although they became less central to the final background model. At the time when these studies were developed, the experimental layout under consideration assumed that the detector would operate inside a laboratory environment, with at least partial underground overburden. Under those assumptions, radiation from the surrounding laboratory materials, such as concrete gammas and neutrons, was a relevant contribution to evaluate.

These backgrounds were treated as external fluxes incident on the detector and shielding system. When a direct simulation from the laboratory boundaries was inefficient, the source term was factorized into two stages. First, energy and angular distributions were obtained for particles emerging from the surrounding materials. These distributions were then used as input spectra for the detector-level simulation, avoiding the need to repeat the expensive laboratory-scale transport for each detector-response or selection study.

In the final experimental scenario, where the detector is expected to operate essentially at surface level and not inside a deep underground laboratory, these environmental contributions are less important than the cosmic-ray-induced and intrinsic-radioactivity backgrounds discussed in the following sections. Nevertheless, they are included here for completeness, since they were part of the background-model development and provide a useful cross-check of the simulation workflow.

Cosmic-ray-induced backgrounds required a separate set of source generators because their normalization and event topology depend strongly on the particle species, angular distribution, energy spectrum, and exposed surface of the apparatus. Dedicated configurations were prepared for the main secondary components at surface level: muons, neutrons, protons, gammas, and electrons. Depending on the study, the primary distributions were defined either analytically or from histograms produced with CRY. For the largest production campaigns, geometry-aware sampling strategies developed during this work [97] were used to avoid spending most of the computation time on particles whose trajectories would not intersect the detector geometry. The detailed modelling of the cosmic-ray sources is discussed later in this chapter. The relevant point for the present methodology is that, once the transport stage is completed, cosmic-ray and non-cosmic samples are treated with the same detector-response and reconstruction philosophy.

The detector description used in these simulations was derived from detailed geometrical models of the BabyIAXO/IAXO-D0 Micromegas detector, passive shielding, active-veto system, and auxiliary volumes. Different geometry variants were selected depending on the purpose of each sample. Full geometries including shielding and veto volumes were used for cosmic-ray and shielding studies; reduced geometries were used for isolated material-contamination studies; and chamber-focused geometries were used for X-ray calibration, detector-response validation, or cut-efficiency studies. The active gas volume above the Micromegas readout was the main sensitive region used to compute the detector background rate. Additional sensitive volumes, such as plastic scintillators or neutron-capture layers, were included when the goal was to study veto response, neutron-tagging performance, or the history of particles contributing to a reconstructed event.

The Geant4 transport configuration was kept as uniform as possible across the different source classes, so that differences between samples were driven mainly by the source term and geometry rather than by changes in the physics list. Electromagnetic interactions were described with G4EmLivermorePhysics, which is appropriate for low-energy photon and electron transport. Hadronic interactions were handled with the high-precision neutron and binary-cascade models required to describe neutron transport, inelastic interactions, and secondary production in the shielding. For internal-contamination samples, radioactive-decay processes were enabled, including the associated atomic de-excitation mechanisms such as internal conversion, fluorescence, and Auger-electron emission. Production cuts were generally kept at the millimetre scale for charged particles and photons, while the gas volume was assigned a smaller maximum step size to preserve the topology of low-energy depositions in the X-ray region of interest.

6.1.3 Background-model component catalogue

The background model was built as a catalogue of independent source components rather than as a single combined Monte Carlo sample. Each component describes one physical origin of background: cosmic-ray secondaries, environmental radiation, intrinsic radioactivity of detector materials, or radon-related activity. For each source, the simulation defines where the particles are generated, which spectrum or decay chain is used, and how the resulting event sample is normalized to an expected rate.

This organization keeps the model modular. A new material-screening result, an updated cosmic-ray flux, or a revised detector geometry can be incorporated by updating only the affected source component. The simulated events from all components are then passed through the same detector-response and reconstruction chain before being compared at the analysis level.

Table 6.3 summarizes the main source classes considered in the model. The first four entries correspond to physical background-rate components. The final entry is an auxiliary sample used to define the detector response and the X-ray-like selection efficiency applied when the rate components are combined.

The individual source components are combined only after detector-response emulation, event reconstruction, and event selection. In practice, each simulated sample is first reduced to the number of events that survive the analysis cuts in the reference energy window. That number is then scaled by the appropriate physical normalization: the measured activity of a material, the activity density of a surface contamination, the radon activity in the gas, or the incident particle flux for external and cosmic-ray sources.

The final background estimate is therefore assembled from reconstructed and selected events, not from idealized energy depositions. This is important because the same source can have a very different impact depending on where the interaction occurs, how the charge or veto signal is reconstructed, and whether the event passes the X-ray-like topology selection. Keeping the source generation, detector response, and normalization as separate steps also makes the calculation easier to update as new measurements or improved detector descriptions become available.

6.1.4 Event types and detector-response chain

The output of the transport stage is not analyzed directly from the Geant4 truth information. Instead, it is converted step by step into event representations that progressively resemble the information delivered by the experimental readout. Figure 6.2 summarizes this chain.

The initial container is the Geant4 event, implemented as TRestGeant4Event. In the following discussion this object is referred to simply as the truth event. It preserves the essential transport information: the primary particle, the hierarchy of secondaries, and the hits produced in the relevant detector volumes. At this stage the event still corresponds to an ideal Monte Carlo description and is therefore not directly comparable to the output of the data acquisition system.

Figure 6.3 shows a representative cosmic-muon event at this stage, pairing a compact print-style event summary with the corresponding geometrical event display.

The first conversion produces a detector-hits event, TRestDetectorHitsEvent. At this response-level hit stage, the Geant4 hits are rewritten as detector hits associated with a detector category, in particular TPC or veto. This is the appropriate point to apply processes that modify the deposited energy before digitization, such as quenching in nuclear recoils or attenuation of the light collected in the veto scintillators. It is also the stage where geometrical corrections, such as the rotation between the Micromegas sensitive volume and the readout coordinates, are applied.

The detector hits are then projected onto readout channels, producing a detector-signal event, TRestDetectorSignalEvent. These signals are still idealized: they describe the charge or light response assigned to detector channels before the electronics response has been applied. The next conversion produces a raw-signal event, TRestRawSignalEvent, which emulates the digitized waveform format delivered by the readout electronics. This step incorporates shaping, sampling, trigger position, dynamic range, and channel-dependent calibration factors. The raw waveform stage is therefore the key bridge between Monte Carlo truth and experimental-like data.

Figure 6.4 shows detector-event views for the same simulated cosmic-muon event after the response has been projected onto the detector readouts. The Micromegas panel uses the readout-channel geometry to show the charge pattern in the TPC, while the veto panel shows the corresponding scintillator modules with visible energy deposits.

The waveform representation itself is shown in Fig. 6.5. At this stage the event is stored as a TRestRawSignalEvent, with separate digitized traces for the Micromegas and veto channels. The native waveform coordinates are the ADC amplitude and acquisition bin, while the same information can be expressed in physical units using the sampling periods, trigger delays, and calibration factors defined in the analysis configuration.

The raw-signal stage is also the point at which simulated and experimental data can be compared most directly at waveform level. Figure 6.6 shows such a comparison for an experimental muon candidate and a simulated cosmic-muon event processed through the same raw-signal representation. The two events are not expected to be identical, since they correspond to different physical particles and trajectories. The relevant validation point is instead that the shaped Micromegas and veto pulses have comparable time ordering, widths, and amplitude scales once the detector-response parameters have been applied.

Once the raw waveforms have been generated, the reconstruction proceeds in the same direction as the analysis of experimental data. The raw signals are converted back into reconstructed detector signals after thresholding and zero suppression, and then into reconstructed detector hits, where the hit coordinates are recovered from strip identities, timing information, and drift velocity. These hits are grouped into a track event, TRestTrackEvent, which stores the topological information used for background discrimination. For the strip readout used here, this representation is naturally expressed as two projected track views rather than as the original three-dimensional Monte Carlo trajectory.

Figure 6.7 shows the reconstructed track representation for the same event sequence. The two panels correspond to the XZ and YZ projections stored in the track event. The colored points show the reconstructed hits and their associated energy, while the solid line is an energy-weighted projected fit added only as a visual guide to the reconstructed topology.

The corresponding scalar observables are finally written to the analysis tree, TRestAnalysisTree, where the analysis cuts are applied and the accepted events are used for the background-rate estimate.

Detector signals and detector hits therefore appear twice in the chain, but with different physical meanings. The first occurrence corresponds to the ideal detector response predicted by the Monte Carlo before electronics digitization. The second occurrence corresponds to the reconstructed information that would be available to the analyst after the same signal-processing and reconstruction stages used for experimental data. Distinguishing between these two stages is essential when validating the detector-response model and when interpreting the effect of the analysis cuts.

6.1.5 Analysis processes and observables

The common analysis chain was kept in a single version-controlled configuration. Its purpose was to define one reconstructed observable space for both simulated and measured events. Simulation-only stages emulate the detector response before digitization, while experimental-input stages import measured DAQ waveforms. After these input-specific branches, both event classes follow the same raw-waveform reconstruction, peak finding, hit reconstruction, and topology analysis.

For simulated events, the first stages apply visible-energy corrections, record Monte Carlo truth observables for validation, and convert Geant4 energy deposits into detector hits assigned to the TPC or veto volumes. The roles of these Geant4-level processes are not equivalent. TRestGeant4QuenchingProcess is the only process in this block intended to modify the detector response itself. It converts nuclear-recoil energy deposits into a visible-energy estimate before the event is interpreted as detector response. The other Geant4-level analysis processes provide truth-level observables, such as the primary particle, the direction and energy of the source particle, the first interaction in the sensitive volume, or auxiliary veto-truth diagnostics. These quantities are useful for debugging, validating the simulation chain, and understanding individual events, but they are not used as final selection variables. They are too idealized for that purpose, because equivalent information is not available in experimental data.

In the current configuration the quenching process is applied to both the Micromegas gas volume and the scintillator volumes. A visible-energy correction is needed because the energy deposited in Geant4 is not generally equal to the detector signal. In the Micromegas gas, nuclear recoils lose part of their energy to atomic motion rather than ionization, motivating a Lindhard-type ionization yield [132]. The process uses the hadronic target information stored by restG4 and evaluates this yield from the recoil energy and from the target isotope mass and atomic numbers. The visible energy assigned to the hit is

with

Here \(E_{\mathrm {R}}\) is expressed in keV, \(A\) is the target mass number, and \(Z\) is the target atomic number. For the veto scintillators, the relevant non-linearity is scintillation saturation: highly ionizing recoil protons and light fragments produced during neutron moderation yield less light per deposited MeV than electron-like deposits. The same process therefore applies a first-order Birks-law correction [130, 131]. In differential form, the scintillation light yield is approximated as

or, for an individual Geant4 hit with deposited energy \(E_{\mathrm {dep}}\) over an effective step length \(\Delta x\),

The production configuration uses a configurable Birks constant initialized to \(k_{\mathrm {B}}=0.126\,\mathrm {mm}/\mathrm {MeV}\), and estimates \(\Delta x\) from the local spacing of neighboring Geant4 hits when an explicit step length is not stored. This value is used as a nominal organic-plastic-scintillator setting, adequate for a first-order veto light-yield model and consistent with values commonly adopted in Geant4-style plastic-scintillator simulations [136]. It should not be interpreted as a dedicated calibration of the BabyIAXO scintillators. Direct measurements in plastic scintillators report material-dependent values, including a somewhat larger value for BC-408, so \(k_{\mathrm {B}}\) remains configurable and should be varied in detector-response systematic studies [137]. Using a smaller \(k_{\mathrm {B}}\) corresponds to weaker quenching and therefore larger visible energies for recoil-proton-like deposits, which is relevant for veto-threshold studies. The corrected visible energy is written back to the copied Geant4 hit collection before the detector-hit and raw-waveform stages, so the downstream response simulation receives the quenched detector energy rather than only an auxiliary Geant4 diagnostic summary.

The size of this correction was checked with a representative cosmic-neutron validation sample. In that sample, the energy-weighted visible energy in the Micromegas gas was reduced by only about \(0.22\%\) on average, because Lindhard quenching is applied only to the small subset of gas hits identified as nuclear-recoil-like hadronic deposits; the median event was unchanged, although individual argon recoil hits could be reduced by factors of a few. In the veto scintillators the effect was much larger: the Birks correction reduced the energy-weighted visible signal by about \(25.7\%\), consistent with the high ionization density of recoil protons and other charged secondaries. Photons, including neutron-capture gamma-cascade hits recorded as photon deposits, are explicitly left unquenched by this process; in the same validation sample, the total energy carried by those hits was unchanged within numerical precision.

After this visible-energy correction, the event is converted from the truth-event representation into the detector-hit representation. The corresponding conversion and the subsequent projection onto detector channels depend on the detector readout metadata described in the software chapter and illustrated in Fig. 6.4. For this reason the conversion is not described here as a separate physics model: its role is to make the detector geometry, sensitive-volume aliases, and readout-channel geometry consistent before the response processes act on the event. The detector-response stage then introduces the effects that separate an ideal energy deposit from a measurable detector response: scintillator light attenuation, coordinate alignment, electron diffusion in the gas, finite resolution, and readout-plane diagnostics before digitization.

The first of these effects is the attenuation of light in the active-veto scintillators. A veto hit in Geant4 is a local energy deposit in a plastic panel, but the measured veto signal is produced only after scintillation light has propagated through the panel and light-guide system to the photomultiplier. The amount of light collected therefore depends not only on the deposited energy, but also on where the interaction occurred within the scintillator. This point is particularly important for the IAXO-D0/BabyIAXO veto geometry because many panels are long bars read out from one end. The same recoil-proton or capture-gamma energy deposition can produce a different waveform amplitude depending on whether it occurs close to the photomultiplier or near the far end of the panel. Consequently, a fixed peak threshold in the analysis corresponds to a position-dependent deposited-energy threshold in the scintillator.

This effect is implemented with TRestDetectorLightAttenuationProcess. The process acts only on hits identified as veto hits; TPC hits are passed through unchanged. For each veto hit, the readout metadata is used to determine the veto readout plane and channel associated with the hit position. The distance \(d\) from the hit to the effective readout end of the corresponding panel is then used to attenuate the hit energy according to

where \(E_{\mathrm {vis}}\) is the visible energy after quenching and \(\lambda _{\mathrm {att}}\) is the effective light-attenuation length. The same geometrical path length also gives a propagation-time correction,

with \(v_{\mathrm {eff}}\) the effective light speed used for the veto channel. The nominal attenuation length used in the veto studies is of order \(400\,\mathrm {cm}\), consistent with the measured and datasheet-scale attenuation behavior discussed in the shielding and veto chapter. This is not a full optical-photon simulation; reflections, surface treatments, coupling details, and channel-to-channel gain variations are absorbed into effective parameters. Nevertheless, it captures the leading geometrical effect that controls whether neutron-related activity in a long scintillator panel remains above threshold after light collection.

The second major response effect is electron diffusion in the Micromegas gas. Whereas light attenuation modifies the veto amplitude, diffusion modifies the spatial and temporal distribution of the TPC charge cloud before it is projected onto the strip readout. Ionization electrons created far from the Micromegas plane drift for a longer time and undergo a larger random walk than electrons created close to the readout. This broadens the charge distribution both transversely, in the readout plane, and longitudinally, along the drift-time direction. Diffusion is therefore directly connected to the reconstructed width, cluster multiplicity, hit spread, and track-shape observables that enter the X-ray-like selection. It also provides the practical link between the detector-response chain and the gas-transport calculations performed with Garfield++/Magboltz, summarized in the software chapter.

In the analysis chain this is handled by TRestDetectorElectronDiffusionProcess. The process reads the gas pressure, drift field, work function, Fano factor, and longitudinal and transverse diffusion coefficients from the TRestDetectorGas metadata when those values are available. These gas parameters are precomputed with Garfield++ for the selected gas mixture and operating field, rather than simulated microscopically inside each Geant4 event. For a detector hit with energy \(E\), the process converts the hit into an effective number of primary electrons,

where \(W\) is the mean energy required to create one electron–ion pair in the gas. Depending on the configuration, the number of electrons may include Poisson or Fano fluctuations, and it may be capped for computational efficiency in high-energy events. Each electron is then displaced with Gaussian diffusion widths that scale with the square root of the drift distance \(z_{\mathrm {d}}\):

where \(D_{\mathrm {T}}\) and \(D_{\mathrm {L}}\) are the transverse and longitudinal diffusion coefficients expressed in the units used by the gas metadata. The transverse diffusion spreads charge between neighboring readout strips, while the longitudinal diffusion broadens the arrival-time distribution and therefore the reconstructed coordinate along the drift direction. The process also includes an optional attachment probability, allowing electrons to be lost during drift if an attachment model is enabled.

This response model is deliberately intermediate in complexity. It is more realistic than simply moving the full hit energy to the readout without broadening, because it produces drift-distance-dependent cloud sizes and finite statistical charge granularity. At the same time, it avoids the cost of a full microscopic electron-transport simulation for every event in a large background campaign. For the background model this is the appropriate compromise: the simulated X-ray-like observables remain tied to measured or Garfield-derived gas properties, while the same reconstruction chain can still be applied to millions of source-specific Monte Carlo events and to experimental data.

The diffusion model does not, by itself, reproduce every contribution to the measured detector resolution. Residual effects such as gain non-uniformity, avalanche fluctuations, electronics noise, imperfect calibration, and channel-to-channel response variations can broaden the reconstructed energy and hit distributions beyond the Garfield-derived diffusion expectation. For this reason the response chain also includes TRestDetectorHitsSmearingProcess. This process applies an empirical smearing to detector hits before digitization, with separate settings for the TPC and veto subsystems when required. Its role is not to replace the physical diffusion model, but to absorb the remaining resolution needed to match calibration data, in particular the width and shape of the reconstructed \(\ce {^{55}Fe}\) peak. In practice, the diffusion parameters fix the gas-transport scale, while the smearing parameters provide a controlled detector-response tuning step when calibration runs show that diffusion alone gives an overly narrow or otherwise idealized response.

The conversion from detector hits to raw waveforms is central to the realism of the method. It uses separate sampling and shaping parameters for the TPC and the veto system, a fixed waveform length of 512 bins, and trigger delays chosen to reproduce the position of the signal within the acquisition window. This step also applies the calibration factors that place simulated signals on the same ADC scale as experimental data. For the Micromegas readout, the response is anchored with the \(\ce {^{55}Fe}\) calibration peak: the conversion from deposited energy to shaped waveform amplitude is tuned so that the reconstructed \(5.9\,\mathrm {keV}\) peak appears at the same position in simulation and data, after the same raw-signal reconstruction is applied. For the veto system, the corresponding reference is the through-going muon response. Each scintillator panel is allowed to have its own effective calibration factor because the measured muon peak is not universal: it depends on panel length, light-collection geometry, orientation, optical quality, coupling, and the individual readout channel response. The veto calibration therefore aligns the simulated and measured muon-peak positions module by module, rather than imposing a single global scintillator scale. In other words, the simulated raw signals are not simply proportional to the total deposited energy; they are calibrated and time-structured waveforms that can be processed in the same way as measured data.

This transformation also depends on the detector readout metadata described in the software chapter. That metadata provides the mapping between DAQ identifiers and physical detector elements, including the Micromegas strip geometry and the veto-panel aliases. This layer makes it possible to interpret simulated and measured waveforms in the same detector-centered coordinate system rather than as anonymous channel numbers.

Once the raw waveform representation has been reached, the process chain reproduces the standard experimental pre-processing. It attaches the readout metadata, removes masked channels, applies baseline and common-noise corrections, computes channel-level observables, and searches for TPC and veto peaks. The veto peak finder is particularly important because it extracts the timing, multiplicity, amplitude, and channel information used later for veto selections. The subsequent reconstruction recovers detector signals and spatial hits from the waveform representation, after which hit and track analyses provide the topological observables used for X-ray–background discrimination.

The final observables employed in the background model are therefore reconstructed quantities rather than ideal transport quantities. This distinction is important because many backgrounds are rejected not only by their total deposited energy, but also by their temporal and topological signatures: channel multiplicity, hit dispersion, track topology, veto coincidences, and delayed signals. Treating these effects at the waveform and reconstruction level provides a more realistic estimate of the residual background than a simple energy-in-sensitive-volume approach.

The observables generated along this chain are stored in the TRestAnalysisTree, which becomes the common input for selection optimization, control plots, and source-by-source background estimates. This provides an important practical advantage of the framework: once the reconstruction chain has been executed, threshold scans, topology studies, or veto-timing optimizations can be performed directly on the stored observables without re-deriving the low-level quantities from the event containers. In this sense, the common analysis configuration defines not only the reconstruction logic, but also the common observable space in which the different background sources can be compared and combined.

6.1.6 Reference samples for cuts and normalization

In addition to source-specific background simulations, dedicated reference samples were used to characterize the response to X-ray-like events and to validate the analysis cuts. These samples are conceptually different from the background source productions. Their purpose is not to estimate a physical source rate, but to define the signal acceptance of the reconstruction and to provide a controlled reference against which background events can be selected or rejected. They therefore occupy a central position between the detector-response model and the final source-normalized background table.

Two classes of signal-like simulation samples were used for this purpose. The first class consists of \(\ce {^{55}Fe}\)-like calibration simulations. The dominant manganese \(K_{\alpha }\) line at \(5.9\,\mathrm {keV}\) lies inside the axion-search energy interval and produces compact photoelectric conversions in the gas. This sample is used to validate the response near the standard calibration energy and to compare the simulated reconstructed spectrum with measured calibration data, as discussed in Section 3.6.1. The same sample also provides useful examples of topologies that are X-ray-like in energy but not in spatial structure. One such event is shown in Fig. 6.8. The simulated \(\ce {^{55}Fe}\) photon undergoes photoelectric absorption, but the atomic relaxation produces an argon fluorescence photon that travels several millimetres before being reabsorbed. The result is a two-site charge topology, rather than a single compact conversion. REST reconstructs this as two separated charge clusters in both strip projections, so the event is rejected by observables that test whether most of the energy is concentrated in a single dominant track. This example illustrates why track observables provide a particularly powerful route for rejecting background-like events while preserving genuinely point-like X-ray candidates.

The second class consists of uniform low-energy gamma simulations, in which primary photons are generated over a flat 0–12 keV energy range. This sample is used to map the cut efficiency across the full low-energy region rather than only at the \(\ce {^{55}Fe}\) line. The remaining reference samples in Table 6.5 provide the corresponding background rejection and accidental-veto information.

The production campaign keeps the calibration and background samples gas-matched. For the final cosmic-ray comparison presented below, the \(\ce {^{55}Fe}\), muon, and neutron samples were reconstructed with the same argon–isobutane detector-response settings used by the IAXO-D1 simulation chain. Equivalent \(\mathrm {Xe}\)-\(\mathrm {Ne}\)-\(\mathrm {iC}_{4}\mathrm {H}_{10}\) calibration productions are also part of the broader BabyIAXO program, but they are combined only with background samples reconstructed with the same gas, pressure, drift field, and readout configuration. Keeping the reconstruction stage identical is essential: the efficiencies must be expressed in terms of the same observables that are later applied to the background components. In practice, the most relevant reconstructed quantities are the fiducial or readout-plane energy, the number of reconstructed hits, the spread of the charge cloud in the readout plane, the balance between the two strip directions, and the track observables produced after hit clustering.

The X-ray-like selection can be written schematically as a sequence of cuts,

where \(C_{E}\) selects the reconstructed energy region of interest, \(C_{\mathrm {fid}}\) removes events outside the active or well-reconstructed detector region, and \(C_{\mathrm {topo}}\) rejects events with extended or track-like topology. The uniform X-ray sample is the natural dataset for measuring the corresponding signal efficiency,

This definition can be used either to produce reconstructed-energy efficiency curves or, after applying the appropriate event weights, to estimate the efficiency for an assumed axion signal spectrum. The \(\ce {^{55}Fe}\) sample provides a complementary check at the calibration energy: it tests whether the Monte Carlo response produces the same compact event population, reconstructed peak position, and peak width observed in measured calibration data.

Machine-learning definition of the X-ray-like topology cut

The refined X-ray-like topology selection used in this thesis is based on a boosted decision tree (BDT) trained on reconstructed TRestAnalysisTree observables. The purpose of the BDT is not to replace the physical interpretation of the Micromegas cuts, but to implement a multivariate version of the same idea: an axion-induced X-ray candidate should be a compact, localized event in the gas, while many background candidates contain extended charge, multiple fragments, asymmetric strip projections, or veto-correlated activity. The classifier is therefore treated as an analysis cut defined in observable space, not as a truth-level background tagger.

All events first pass the reference energy requirement

which is the energy interval used for the final analysis in this work. The reconstructed energy is then removed from the classifier inputs. This prevents the BDT from learning a source-specific energy spectrum and forces it to use topological information within the analysis window. The signal-like training population is defined by \(\ce {^{55}Fe}\) calibration events or gas-matched \(\ce {^{55}Fe}\) simulations processed with the same reconstruction chain. For the current cosmic-ray cut flow, the background-like training population is the reconstructed neutron-control sample, which provides the difficult compact residuals that most closely mimic low-energy X-ray events after the energy preselection. During development, additional selectors were trained against measured background samples, muon samples, and combined control mixtures to understand the available rejection power. Those comparisons are used as validation and robustness checks, while the table below uses the current \(\ce {^{55}Fe}\)-versus-neutron topology working point. The source identity, particle type, Geant4 history, event origin, run label, and any simulation-only classification variable are excluded from the input feature list. They are used only for weighting, bookkeeping, and post-selection interpretation.

The BDT score is computed with the HistGradientBoostingClassifier implementation in scikit-learn [138]. For a reconstructed event with observable vector \(\mathbf {x}\), the score is

as returned by the classifier probability estimator. With this convention the score is bounded between zero and one; larger values indicate a more X-ray-like topology. The score is nevertheless not interpreted as an absolute physical probability, because it depends on the training mixture, class weights, and finite simulation statistics. Only the ordering of events and the selected operating threshold are used in the final cut.

The topology cut is

During the selector development, \(s_{0}\) was scanned with the expected sensitivity figure of merit in the \(2\)–\(7~\mathrm {keV}\) window,

where \(S(s_{0})\) is the number of signal-like calibration or simulated X-ray events surviving the threshold and \(B(s_{0})\) is the weighted number of background-mixture events surviving it. For the current background-model cut flow the working point is fixed instead at the \(80\%\) \(\ce {^{55}Fe}\) reference efficiency. This choice gives a stable and interpretable calibration-anchored selection while the high-statistics cosmic productions are still being accumulated. The optimized \(S/\sqrt {B}\) point is retained as a cross-check of the same selector, but it is not the operating point used for the preliminary cosmic-ray table below.

The present production selector uses scalar observables exported to the TRestAnalysisTree after the standard REST-for-Physics detector-response chain. The reconstructed energy cut is made with the readoutEnergyInFiducial observable from hitsReadoutAnalysisAfter. This observable is produced by TRestDetectorHitsReadoutAnalysisProcess after raw-signal reconstruction, using a \(30~\mathrm {mm}\)-diameter fiducial circle centered on the Micromegas readout. The diameter corresponds to the Mylar entrance-window region through which the focused axion-induced X-ray signal is expected to enter the detector, and it is therefore the natural signal area for this comparison. The energy cut is applied to the reconstructed energy inside that fiducial readout region, but the scalar energy variable alone is not used as proof that the reconstructed topology is fully contained. For the final X-ray-like rows, an additional containment check requires the reconstructed X and Y hit or track locus to remain inside the same \(15~\mathrm {mm}\)-radius circle.

The BDT inputs are the reconstructed hit multiplicities, charge-cloud widths, and projection-balance quantities computed after the signal-to-hit reconstruction, readout-hit analysis, Gaussian-hit analysis, and two-dimensional track-analysis stages. In the analysis RML these correspond to the signalToHits, hitsReadoutAnalysisAfter, hitsAnaAfter, hitsAnaGauss, and tckAna2D process outputs. The current topology vector can be summarized as

These observables are directly tied to the physical difference between an X-ray conversion and a background residual event. A \(\ce {^{55}Fe}\) event is expected to be compact, to involve both strip projections, and to have comparable reconstructed size and energy in the X and Y views. Cosmic-ray, neutron-induced, radon-related, or material-radioactivity events can fall in the same reconstructed energy window, but they more often contain extended charge, multiple fragments, or an uneven distribution between the two projections. The hit multiplicities and widths therefore provide the main separation, while the balance variables act as consistency checks against partial, asymmetric, or poorly matched reconstructions.

The BDT was evaluated against two transparent reference methods. The first is a binned log-odds classifier built from the same observables, which approximates the product of one-dimensional signal-to-background likelihood ratios. The second is a greedy interval-cut procedure that sequentially chooses one-dimensional rectangular intervals using \(S/\sqrt {B}\) as the optimization criterion. Each step searches an allowed interval in a single observable, applies the interval that gives the best figure of merit, and then repeats on the remaining observables. A single decision tree and an extra-trees ensemble were also tested as interpretability checks. The single tree produced readable nested rules but was less competitive as a final selector, while the extra-trees ensemble performed close to the gradient-boosted classifier. These methods are less flexible or less stable than the BDT, but they provide useful cross-checks and help identify which observables carry most of the rejection power.

Table 6.7 shows the behavior that motivated the adoption of a multivariate topology selector. On measured calibration and background optimization data, the \(S/\sqrt {B}\)-scanned BDT keeps nearly the same calibration efficiency as the historical \(80\%\) working point while reducing the number of validation background events by roughly a factor of two relative to the manual sequential cuts. At a fixed \(80\%\) calibration efficiency, the BDT and binned log-odds selectors perform similarly, whereas the adaptive interval cuts are less effective because a sequence of one-dimensional rectangles cannot reproduce the useful correlations between observables. On the neutron simulation comparison, the BDT provides stronger rejection than the log-odds and simple X-ray-like cuts. The gain is important because neutron-induced residuals that survive the energy preselection are already the difficult, compact tail of the neutron population. The BDT is therefore used as the common topology selector, while the log-odds, manual cuts, and adaptive rectangular cuts are retained as transparent robustness checks. Figure 6.9 gives the same operating point in confusion-matrix form, emphasizing that the relevant off-diagonal entry is the small background leakage into the X-ray-like sample rather than the overall classification accuracy. Figure 6.10 makes the corresponding observable-space behavior visible: most of the separation is already organized by widths, hit multiplicities, and projection balance, but the BDT boundary can follow their correlations more naturally than rectangular cuts.

The same selection definition is also applicable to experimental data. This is an important conceptual point rather than a technical afterthought. The BDT is built on scalar observables stored in the TRestAnalysisTree, not on Monte Carlo truth quantities. Experimental calibration and background runs processed through the corresponding REST-for-Physics chain therefore produce the same type of energy, hit, balance, and track variables as the simulated samples. During this thesis, the experimental work consisted mainly of analyzing existing IAXO-D0 prototype data rather than performing new laboratory campaigns. Those data were nevertheless essential: the \(\ce {^{55}Fe}\) calibration runs provide the experimental analogue of the signal-like population, background runs test the behavior of the selectors on real surface data, and calibration-triggered events provide the empirical veto-noise sample used in the accidental-coincidence studies. In this sense, the final BDT selection is a simulation-trained, calibration-anchored, and data-applicable selector. It can be applied to both simulated and measured REST-for-Physics analysis trees, provided that the gas, readout, calibration, and reconstruction configuration are matched. Figure 6.11 shows the corresponding detector-response check for an IAXO-D0 \(\ce {^{55}Fe}\) calibration run and a gas-matched \(\ce {^{55}Fe}\) simulation processed through the same reconstruction chain. The comparison uses the track-level observables that enter the fiducial and topology selections: reconstructed track energy, radial containment, projection track multiplicity, charge-cloud widths, hit-count balance, and energy balance between the X and Y strip views. The shaded intervals mark the fiducial cuts applied before the multivariate topology cut, namely the \(2\)–\(7~\mathrm {keV}\) calibration window, the \(r<10~\mathrm {mm}\) central region, and the single-track requirement in both strip projections. The figure illustrates why a calibration-anchored validation is needed even when the simulation uses the same gas and readout settings. After the final \(\ce {^{55}Fe}\) response snapshot, the measured and simulated samples agree well in the energy scale, radial containment, dominant one-track population, mean transverse width, and hit-count balance. The largest residual differences are in the longitudinal width and projection-energy balance, where the simulation remains somewhat narrower than the experimental data. Those differences are treated as detector-response systematics rather than as background-composition effects, and they motivate deriving the final topology working point independently on measured calibration data and on simulated calibration data.

At this stage of the analysis, no veto observables enter the BDT. The experimental-data application shown in this section should therefore be interpreted as a Micromegas-only topology comparison: the published IAXO-D0 surface analysis selected the \(2\)–\(7~\mathrm {keV}\) focal-spot sample with conventional Micromegas cuts before applying the prompt and delayed veto selections [69], while the BDT provides an alternative topology selector built from the reconstructed Micromegas observables alone. The appropriate comparison with the published result is thus a pre-veto cut-flow comparison: number of events and \(\ce {^{55}Fe}\) calibration efficiency after the published Micromegas cuts versus after the BDT topology selection, evaluated on the same experimental background and calibration data set. The extension to veto information is a separate analysis layer. It is introduced in the shielding and veto chapter, where prompt, delayed, multiplicity, and veto-pattern observables can be compared directly with the published prompt-muon and advanced-veto reductions.

The active veto introduces a second selection, denoted here as \(C_{\mathrm {veto}}\). For cosmic muons and many neutron-induced events, veto activity is a real physical part of the event, produced by prompt charged particles, electromagnetic secondaries, moderation, or neutron capture products. For genuine X-ray signal events, however, the external veto is not physically correlated with the X-ray conversion in the gas. Any signal rejection caused by the veto must therefore be interpreted as an accidental-coincidence loss. This distinction is important enough that signal and background samples must be treated differently.

For signal-like X-ray simulations, the veto branches are not left in an unrealistically empty state when veto cuts are studied. Instead, the simulated X-ray event is overlaid with veto activity sampled from experimental calibration events. Calibration events provide an empirical measurement of random veto peaks, channel occupancy, multiplicity, and timing structure in the detector environment. After this overlay, the veto survival probability for signal-like events is

where \(P_{\mathrm {acc}}(C_{\mathrm {veto}})\) is the accidental probability that unrelated veto noise satisfies the veto rejection condition. This is the correct quantity to apply to an axion-like X-ray signal. It is also the quantity that determines the dead-time-like cost of using a given veto selection.

For background components with physical veto correlations, the treatment is different. The veto decision is applied to the reconstructed veto response produced by the same detector simulation. If appropriate, calibration-like veto noise can be added on top of the simulated veto response in order to reproduce the accidental component present in the experimental data. This is particularly relevant for comparisons with measured background runs, where the observed veto pattern is the superposition of true particle-induced activity, electronic noise, random coincidences, and the effect of missing or unstable channels. In the current cosmic cut flow, the veto classifier uses the reconstructed rawPeaksVETO observables produced by TRestRawPeaksFinderProcess after light attenuation, quenching, shaping, digitization, baseline correction, and the \(300\)-ADC peak threshold. Its inputs are deliberately compact: total reconstructed veto visible energy, number of peaks, number of hit veto channels, number of good veto signals, and the threshold-integral observable. The prompt muon cuts and delayed neutron-sensitive observables discussed in the shielding and veto chapter therefore enter the background model as reconstructed veto selections, not as truth-level labels.

The final source contribution is obtained by combining the raw source normalization with the event-level survival of the X-ray-like and veto selections. For a source \(i\), the most general expression is a weighted sum over reconstructed events,

where \(w_{ij}\) contains the source normalization and any geometrical, spectral, live-time, activity, surface, or phase-space weight assigned to event \(j\), and \(I_j\) is one when the event passes the X-ray-like selection and is not rejected by the veto. For an unweighted sample generated directly from the physical source distribution, Eq. 6.17 reduces to the familiar expression \(R_i^{\mathrm {raw}}N_i(C_{\mathrm {x}}\cap \overline {C}_{\mathrm {veto}})/N_i^{\mathrm {generated}}\). Depending on the source class, the raw normalization is derived from a material activity, a measured environmental flux, a cosmic-ray flux model, or an experimental live-time normalization.

The total predicted background rate in the region of interest is then

with analogous sums before cuts and after X-ray-like cuts alone. This three-stage presentation is useful because it separates the physics source model from the detector selection:

1. the raw rate before analysis cuts tests the source normalization and geometry;
2. the rate after X-ray-like cuts tests whether the component can mimic a compact low-energy Micromegas event;
3. the rate after X-ray-like plus veto cuts tests the residual background after the active-shielding strategy is applied.

The final background tables are therefore organized, for each source class, around the number of simulated events, the number of analyzed events, the efficiency of the X-ray-like selection, the veto survival fraction, the raw normalized rate, and the residual rate after all cuts. This structure makes it possible to update the rate budget without changing the conceptual organization of the chapter: new simulations or improved source normalizations modify only the source-specific entries in the sum, while the definitions of the X-ray-like and veto selections remain common.

Monte Carlo statistical uncertainties are propagated with Poisson counting statistics after applying the event weights used for the source normalization, following the standard counting-experiment treatment summarized by the Particle Data Group [139]. When no simulated event survives a selection, the corresponding table entry is quoted as a one-sided 90% confidence-level upper bound. The convention used in this thesis is the standard zero-count Poisson bound, \(N_{90}=-\ln (0.1)=2.30\) equivalent selected events, corresponding to the \(n=0\) case of the exact Poisson confidence-interval construction of Garwood [140]. This equivalent-event limit is converted into a background level with the same activity, exposure, energy-window, and fiducial-area normalization as the nominal rate. For a source built from several independently generated subgroups, the upper-bound contributions are normalized subgroup by subgroup and then summed.

6.2 Measurement Inputs and Normalization Strategy

The measurements used in this chapter do not constitute a single background data set. They enter the model in three distinct ways. Material-screening measurements provide activity normalizations for intrinsic radioactivity. Environmental and cosmic-field measurements define source terms for particles entering the detector from outside. Detector background data provide validation samples and operational constraints for the reconstruction, veto response, radon handling, and residual event interpretation. This separation is important because a measured activity, a measured external flux, and a measured detector rate constrain different parts of the calculation.

6.2.1 Material Screening and Radiopurity Inputs

Radiopurity screening provides the activity normalization for the intrinsic-background part of the model. The measurements summarized here are collaboration inputs, principally from the Zaragoza detector and radiopurity teams and from work performed at the Canfranc Underground Laboratory (LSC); they are not claimed here as an original contribution of this thesis. They are nevertheless essential to the simulation chain, because every activity limit or measured contamination level must ultimately be translated into an expected event rate in the Micromegas region of interest.

The screening strategy follows the low-background Micromegas program developed for CAST, TREX-DM, and the IAXO prototypes [83, 141, 142]. Material samples are measured mainly with ultra-low-background high-purity germanium (HPGe) detectors at LSC, where the underground overburden suppresses the cosmic-ray component of the counting background. The relevant gamma-emitting isotopes and decay-chain segments include \(\ce {^{40}K}\), \(\ce {^{60}Co}\), the \(\ce {^{232}Th}\) chain, and the \(\ce {^{238}U}\)/\(\ce {^{235}U}\) chains. For the background model, the outcome of these measurements is a set of specific activities, or upper limits, assigned to detector volumes such as the Micromegas readout, field cage, cathode, chamber, shielding, calibration hardware, cables, and electronics. Upper limits are retained explicitly because many selected materials are sufficiently clean that no statistically significant peak is observed in the screening spectrum.

Recent collaboration-meeting updates clarify how these inputs enter the current IAXO-D1 background model. In the 23rd IAXO Collaboration Meeting report on the IAXO-D1 Micromegas setups, M. Jimenez Puyuelo presented the status of the intrinsic-radioactivity model used for the LSC detector studies [143]. The normalization of most detector materials was taken from the TREX-DM and Micromegas material-screening campaigns, with many entries still treated as upper limits. The report also identified the few components that were not merely limits in the current model, notably \(\ce {^{39}Ar}\) in the gas, \(\ce {^{210}Pb}\) associated with the lead shielding, and \(\ce {^{40}K}\) in the readout. This distinction is important: a simulated component normalized to an upper limit should be interpreted as a conservative bound on the corresponding background contribution, not as a measured central value.

The radiopure-electronics program is another collaboration input that affects the material inventory close to the detector. E. Picatoste reported the status of the Micromegas radiopure electronics at the 21st IAXO Collaboration Meeting, including the production and testing of front-end flex circuits, limandes, and FEC/BEC interconnect elements intended to reduce the amount of non-radiopure material inside the shielded volume [144]. This work is relevant for the background model because the electronics are geometrically close to the gas volume and can therefore contribute through compact low-energy deposits or through secondary radiation produced in nearby materials. For this reason, the final detector model must distinguish between material located inside the radiopure boundary and services or back-end electronics that are farther away or shielded differently.

Radiopurity measurements alone do not determine the low-energy background, because the detector response depends on where the isotope is located, on the geometry between the source and the gas volume, and on the subsequent reconstruction cuts. The procedure used in the model is therefore to simulate each relevant isotope–volume pair with Geant4, process the surviving events with the same analysis chain used for experimental data, and only then scale the accepted rate by the measured activity or upper limit. The corresponding intrinsic-contamination simulations are described in Section 6.3 as part of the full production inventory.

6.2.2 Environmental and Cosmic Source Measurements

External source terms are constrained by measurements and generators in a different way from material screening. For surface cosmic-ray backgrounds, CRY, analytic muon parameterizations, EXPACS, and HENSA measurements define the incident particle spectra used in the detector simulations. For laboratory environmental radiation, NaI and HENSA measurements provide local gamma and neutron fields that can be propagated through the detector geometry. These inputs are source terms, not detector backgrounds by themselves: they become a predicted Micromegas rate only after transport, detector response, reconstruction, and the X-ray-like selection.

The Zaragoza laboratory measurements and HENSA-based neutron spectra are therefore used as source-term anchors for the simulations discussed in Section 6.4. They are especially useful for testing the response of the shielding and veto system to realistic neutron fields. However, the corresponding absolute rates remain site dependent. A future DESY-specific characterization of the gamma field, floor and hall materials, local structures, and neutron environment is needed before the same catalogue can be converted into a final BabyIAXO site prediction.

6.2.3 Detector Background Data and Operational Constraints

Detector data are used primarily to validate the reconstruction and to constrain operational background mechanisms. The surface-veto validation uses the published IAXO-D0 prototype data set [69]; the HENSA-driven simulations are used to study the neutron response of the final multilayer veto geometry; and environmental gamma or material-produced neutron studies are retained as source-specific checks until their DESY normalization is fixed. This separation avoids mixing measured detector performance, simulated source transport, and site-dependent absolute fluxes into one number before the final master rate table is available.

The LSC IAXO-D1 data sets also show why the material model must be complemented by operational background studies. The detector was operated inside a 20 cm lead shield with a calibration source, nitrogen or radon-free-air flushing inside the shielding, and evolving gas recirculation and buffer configurations [143, 145, 146]. Those measurements showed that changes in gas handling and radon suppression can affect the alpha and low-energy backgrounds substantially, even when the solid materials have been selected for radiopurity. Consequently, the background model separates intrinsic material radioactivity from radon-related and surface-contamination components, rather than absorbing all observed low-energy events into a single material-activity term.

6.3 Intrinsic Background

6.3.1 Gas-Borne and Radon-Related Contamination

The IAXO Micromegas detector is designed to operate with either an argon-based gas mixture or a xenon–neon-based gas mixture. Because the active gas is the interaction medium, its isotopic composition and any gas-borne radioactive contaminants must be treated separately from the solid detector materials. Common gas impurities such as oxygen and water affect electron attachment, gain stability, and energy calibration, but their concentrations and natural isotopic composition do not make them relevant radioactive-background sources. The radiological gas model is therefore dominated by two classes: intrinsic radioisotopes in the gas itself and radon-related activity introduced by emanation, leaks, or recirculation.

For argon mixtures, the relevant intrinsic isotope is \(\ce {^{39}Ar}\), a beta emitter with \(Q_{\beta }=565~\mathrm {keV}\) and \(T_{1/2}=269~\mathrm {y}\). Natural atmospheric argon has a measured \(\ce {^{39}Ar}\) specific activity of \(1.01\pm 0.08~\mathrm {Bq}\,\mathrm {kg}^{-1}\) of natural argon [85]. The absolute rate therefore scales with the gas inventory and with the choice of atmospheric or underground argon; low-radioactivity underground argon has been measured to suppress \(\ce {^{39}Ar}\) by a factor \((1.4\pm 0.2)\times 10^{3}\) relative to atmospheric argon [147]. In the topology model, \(\ce {^{39}Ar}\) beta decays generally produce extended ionization tracks rather than compact few-keV X-ray-like clusters, so this component is expected to be strongly reduced by the Micromegas topology selection.

\(\ce {^{85}Kr}\) provides a second gas-borne beta-decay scenario for argon-based operation when krypton traces remain in gas distilled from air. Its half-life is \(10.7~\mathrm {y}\), with \(Q_{\beta }=687~\mathrm {keV}\), and its activity can vary strongly between gas batches and handling histories. The GERDA collaboration measured a \(\ce {^{85}Kr}\) specific activity of \((0.36\pm 0.03)~\mathrm {mBq}\,\mathrm {kg}^{-1}\) in an atmospheric liquid-argon batch, while also noting the broader atmospheric and experiment-dependent variability of this isotope [148]. The \(\ce {^{85}Kr}\) simulation is therefore treated as a scenario component normalized by an assumed gas activity, not as a fixed property of the detector materials.

Radon must be handled differently from ordinary material-chain activity. As a noble gas, \(\ce {^{222}Rn}\) can escape from surrounding materials or gas-system components and break secular equilibrium with the parent uranium chain. Its concentration in the detector volume is consequently an operational quantity, set by emanation, leaks, flushing, recirculation, and gas purification rather than by the bulk activity of a single detector material. The most relevant isotope for this model is \(\ce {^{222}Rn}\), with \(T_{1/2}=3.82~\mathrm {d}\). It acts first as a uniform gas source, but its daughters can become surface sources after ion drift or plate-out.

The separation between the radon components is important because each component has a different normalization. \(\ce {^{218}Po}\), the first short-lived daughter of \(\ce {^{222}Rn}\), is often positively charged after production and can drift toward the cathode under the detector field. Long-lived \(\ce {^{210}Pb}\), with \(T_{1/2}=22.3~\mathrm {y}\), can then remain on detector surfaces and is not generally in equilibrium with the instantaneous radon activity. For this reason, and following the surface-contamination concern motivating dedicated \(\ce {^{210}Pb}\) screening with Micromegas detectors [149], the model treats gas \(\ce {^{222}Rn}\), cathode \(\ce {^{218}Po}\), cathode \(\ce {^{210}Pb}\), and vessel or surface \(\ce {^{210}Pb}\) as separate source hypotheses. The source taxonomy is summarized in Table 6.9.