4 Shielding and Veto System

Introduction

Surface operation exposes the BabyIAXO detectors to cosmic-ray particles and their secondaries as well as to environmental radioactivity. Lead shielding attenuates environmental photons, but energetic neutrons can interact in the lead and produce additional neutrons, photons, and charged fragments. The active veto must detect activity associated with a low-energy Micromegas event, including showers whose primary particle never crosses the gas. This requires both prompt muon tagging and sensitivity to the later scintillator signals produced after neutron moderation and capture.

We studied a three-layer veto of plastic scintillator and cadmium surrounding the lead shield and compared its reconstructed response with measurements from the IAXO-D0 surface prototype. The chapter develops the shielding and geometry choices, explains the adopted prompt-plus-neutron selection, and assesses its experimental controls. We also compare passive-shielding alternatives for a future detector iteration, using the calibrated $2\text{–}7\text{keV}$ background ${𝐵}^{𝐸}$ as the main comparison and the TPC baseline as a separate check. The classifier studies test whether timing and segmentation add useful rejection and whether the gain remains stable across calibration runs.

Veto rejection is evaluated for a specified event population and compared at a specified calibration-control acceptance. For the background prediction, the veto is applied to the same X-ray-like time projection chamber (TPC) candidates selected in Section 3.5.3; the published prototype comparison retains its original selection. Section 5 relates the surviving counts to source activities or incident fluxes and treats radioactive decays outside the coincidence window separately. The simulation and reconstruction methods use REST-for-Physics and restG4, described in Section 3 [86–89].

4.1 Surface backgrounds and detector requirements

4.1.1 Detector configurations and requirements

The design must preserve X-ray-like Micromegas events in the keV region while rejecting surface backgrounds. It must remain compatible with the X-ray beam path, services, mechanical clearances, available scintillator modules, and the synchronized AGET-based readout. The beam pipe prevents perfectly hermetic passive shielding, whereas the neutron-capture timescale requires a readout window long enough to retain post-trigger activity without accepting an excessive number of random coincidences. These constraints make geometry, timing, and analysis inseparable parts of the veto design.

The design studies, prototype measurements, and BabyIAXO projection refer to distinct detector configurations, summarized in Table 4.1. The transport geometry, the prototype readout, and the operating channels have different panel inventories. The illustrated three-layer IAXO-D1 design contains 59 scintillator panels, while a separate geometry snapshot captured in September 2026 contains 60. The readout extracted from the original IAXO-D0 data defines 59 panel positions, of which 57 provided operational signals. Matching the number of positions does not establish equal panel dimensions or channel states, and neither geometry revision is assigned retrospectively to every historical simulation campaign. A background prediction for BabyIAXO at DESY requires finalized detector, source, and response specifications; the Zaragoza prototype result cannot simply be rescaled to obtain it.

4.1.2 Surface source inputs

The selected design studies use source-specific inputs rather than one generic “cosmic” sample. We simulated cosmic muons with the correlated sea-level parameterization of Guan et al., implemented in the CosmicMuons generator [99]. The neutron layer scans use the archived HENSA outdoor-spectrum input in the $1\text{MeV}$–$10\text{GeV}$ interval [117]. In the layer and inclination scans, the sampled zenith-angle distribution was proportional to $sin𝜃cos𝜃$, instead of the intended $sin𝜃{cos}^2𝜃$. Transferring these results to the intended distribution requires angle-dependent event weights or new simulations. The source normalization and angular-distribution audit are documented in Section 5. The layer and inclination scans used the same HENSA input and sampled angular distribution. Earlier passive-shielding scans and cross-checks used CRY, while EXPACS provides an independent spectral comparison [91, 96, 97]. The fixed-volume alternatives in Section 4.2.5 instead use the full outdoor HENSA spectrum, extended down to $1\text{meV}$, with the corrected downward ${cos}^2𝜃$ angular distribution.

The HENSA input describes the outdoor neutron field, including atmospheric neutrons and neutrons produced or modified by the surroundings. The shielding comparisons use this field over the stated generation range. The background model instead approximates cosmic neutrons as predominantly downward and environmental neutrons as approximately isotropic, with some unquantified overlap (Section 5.3.2). The generators are described in Section 3.3.1.

4.2 Limits of passive shielding

4.2.1 Material roles

Lead remains essential because it strongly attenuates environmental photons. Its role for fast neutrons is different. In an elastic collision with a nucleus of mass number $𝐴$, the maximum transferable fraction of neutron kinetic energy is $4𝐴/(1+𝐴{)}^2$, which is unity for hydrogen but only about $0.019$ for lead. Consequently, lead is a poor moderator, while inelastic and neutron-emission channels produce a secondary shower once the incident energy reaches the MeV range.

Hydrogen-rich plastic scintillator complements the lead by slowing secondary neutrons and converting recoil-proton and charged-particle energy into light. Cadmium sheets between the scintillator stages capture neutrons after they have slowed, producing a gamma cascade near an active panel. The nuclear de-excitation is prompt relative to the capture, but moderation can place the capture and its scintillator response well after the Micromegas trigger. The Micromegas gas remains sensitive to compact secondary photons and electrons as well as to nuclear recoils, so the veto must tag the surrounding history rather than identify the primary particle from the Micromegas deposit alone.

Section 4.3.5 tests the transport models supporting this mechanism.

4.2.2 Comparison observables for shielding studies

Shielding optimization requires comparing many combinations of material, thickness, and position. The complete TPC baseline of Section 3.5.3 gives the event population used for the background prediction, but only a small fraction of generated particles produces an accepted event. At the available simulated exposure, the resulting statistical uncertainty can obscure differences between configurations. We therefore use earlier selection stages to compare broad shielding trends and evaluate promising arrangements with the complete baseline.

The closed-layer neutron scan of Section 4.2.4.1 illustrates this limitation. The Pb-only reference contains $8653$ valid reconstructed events, of which 26 pass the complete TPC baseline. The configuration with the lowest observed valid-event yield contains $2169$ valid events and six baseline events. For independent rare-event counts, the approximate relative statistical uncertainty scales as $1/\sqrt{𝑛}$. The baseline counts therefore have counting uncertainties of about $20\%$ and $41\%$, whereas the valid-event counts have uncertainties of approximately $1\%$ and $2\%$. Distributing the available computing resources among many configurations makes a precise baseline comparison substantially more demanding.

The first comparison observable is the yield of valid reconstructed TPC events, before the energy, track-multiplicity, and fiducial requirements. For configuration $𝑖$, its yield relative to a reference configuration is

where ${𝑉}_{𝑖}$ counts valid events and ${𝑁}_{𝑖}$ includes all generated particles, including those producing no saved detector event. For the same physical source and generation normalization, the common source rate cancels. This ratio measures how the shielding changes the production of reconstructable TPC activity. It does not itself select the X-ray energy region.

The relationship to the baseline background depends on the remaining selection. Let ${𝜖}_{𝑖}={𝑁}_{𝑖}^{\text{baseline}}/{𝑉}_{𝑖}$ be the fraction of valid events satisfying the energy, track-multiplicity, and fiducial requirements. For the same baseline area and energy interval in every configuration,

The valid-event ratio approximates the baseline-background ratio when the remaining-selection efficiencies are sufficiently similar. A reduction in valid-event yield then implies a comparable reduction in baseline background. If the efficiencies change appreciably, the two ratios can differ.

The second observable retains an energy requirement while omitting the more restrictive track-multiplicity and fiducial requirements. The corresponding mean differential background-level approximation is

where ${𝑁}_{𝑖}^{𝐸}$ is the accepted count, ${𝑇}_{𝑖}$ is the equivalent simulated exposure including all generated particles, $\mathrm{\Delta }𝐸$ is the energy-window width, and ${𝐴}_{𝐸}$ is the area over which these events are counted. Its units are $\text{counts}{\text{keV}}^{-1}{\text{cm}}^{-2}{\mathrm{s}}^{-1}$. Restricting the energy interval makes this comparison more closely related to the analysis region and retains sensitivity to spectral changes that the unrestricted valid-event yield would conceal. It also retains fewer events. The energy-selected observable is therefore preferable when its statistical precision is sufficient for the comparison.

Each study must specify the energy definition and counting area. The lead-thickness and closed-layer comparisons below select calibrated maximum-track energies in $2\text{–}7\text{keV}$ after detector response and valid reconstruction. Earlier comparisons used sensitive-gas deposits in $0.1\text{–}10\text{keV}$, without detector-response broadening. An estimate averaged over the full readout area also cannot be assigned to the smaller fiducial region without an additional assumption about the spatial distribution. The normalization in Equation (4.3) preserves these distinctions; it does not supply the missing selection efficiency.

These approximations are physically motivated when the shielding mainly changes the number of particles producing TPC activity while leaving the relevant energy, track-multiplicity, and position distributions approximately unchanged. Keeping the chamber, gas, and detector response fixed makes this plausible, but does not establish it. Moderator placement can alter the neutron spectrum, capture-photon contribution, and relative importance of electromagnetic deposits and nuclear recoils, changing the remaining-selection efficiency. The available spectra and selection efficiencies provide checks of this assumption; complete-baseline calculations for representative configurations are needed to test the inferred background reduction. Compatibility within broad statistical intervals cannot establish equal efficiencies. The earlier-stage observables guide the choice of configurations for further study, while final background predictions require the complete selection. Neither observable includes additional TPC classification or active-veto rejection unless those stages are evaluated explicitly.

4.2.3 Lead thickness and penetrations

We repeated the lead-thickness scan with complete detector response and the energy-selected observable ${𝐵}^{𝐸}$ defined in Equation (4.3). The lead thickness ranges from zero to $250\text{mm}$, around an $18\text{cm}$ cubic cavity. Both configurations retain the copper chamber and detector internals, without veto assemblies. The capped-pipe configuration also includes the copper X-ray pipe and its $5\text{mm}$ end cap. Photon energies follow the tabulated atmospheric CRY spectrum [91], sampled over its full stored range. Neutrons use the full outdoor HENSA spectrum and source convention of Section 4.2.5; its distinction from the environmental model follows Section 4.1.2.

The comparison selects valid reconstructed events with calibrated maximum-track energy in $2\text{–}7\text{keV}$, before track-multiplicity, fiducial, classification, or active-veto requirements. We normalize each count to the $5\text{keV}$ window, the full $36{\text{cm}}^2$ readout area, and the equivalent exposure obtained from all completed generated primaries and the geometry-specific source rate. Completed blocks with no accepted event contribute to the exposure; failed blocks and incomplete transfers are excluded. These rates describe energy-selected TPC activity and do not predict the background after the complete baseline selection.

The photon-induced response falls strongly with increasing lead thickness, while the capped-pipe configuration retains a larger contribution at large thicknesses. This difference demonstrates the importance of penetrations, although the scan does not separate transmission through the pipe from scattering around it. The thickest closed-shield photon configurations have few accepted events, so their upper limits remain relevant to the comparison.

The neutron-induced response rises at intermediate thicknesses and then decreases, with much weaker suppression than for photons. This behavior is consistent with competing attenuation and secondary production in lead; the scan alone does not identify the dominant interaction channels. It supports combining passive photon shielding with an active neutron-sensitive veto, without establishing $200\text{mm}$ as an optimum. The statistical intervals exclude source and detector systematic uncertainties, and the snapshot can favor faster-finishing jobs while production continues.

4.2.4 Passive neutron moderation

We studied whether borated polyethylene (BPE) could reduce neutron-induced TPC activity while retaining the full $20\text{cm}$ of lead required for photon attenuation. Hydrogen slows neutrons, while boron captures part of the moderated population; capture photons can also contribute to the detector response. The material ordering therefore matters as well as the total moderator thickness.

The closed-geometry study in Figure 4.2 and Figure 4.3 compares BPE thickness, position, and layer count under this constraint. It concerns a future shielding iteration; the adopted detector design retains the full lead shield.

4.2.4.1 Moderator position and multiple layers

We compared closed cubic arrangements to study moderator placement with a fixed $20\text{cm}$ total lead thickness on every face. The additional borated polyethylene (BPE) thickness, $𝑀$, takes values of 2.5 cm, 5 cm, 7.5 cm, & 10 cm. The modeled BPE contains $5\%$ natural boron by mass, with density $1.04\mathrm{g}{\text{cm}}^{-3}$. The detector occupies the same $18\text{cm}$ cubic cavity in each arrangement. These idealized geometries omit the beam-pipe opening, electronics, and scintillator veto assemblies; they therefore test passive material ordering rather than the response of the complete detector installation.

We varied the lead thickness between the cavity and the first BPE layer, $𝑝$, from $0\text{cm}$ to $20\text{cm}$ in $5\text{cm}$ steps. The BPE is divided into $𝑛=1$, 2, or 3 equal layers, each followed by a lead layer. For $𝑝<20\text{cm}$, the remaining lead thickness is divided equally among these $𝑛$ layers. At $𝑝=20\text{cm}$, a single BPE layer lies outside the full lead thickness. The comparison contains 52 BPE arrangements, 52 air controls with the same lead positions and outer dimensions, and a closed Pb-only shield.

Figure 4.2 illustrates the three-layer arrangement with $𝑀=10\text{cm}$ and $𝑝=5\text{cm}$.

4.2.4.2 Energy-selected background

We compare the energy-selected background ${𝐵}^{𝐸}$, defined in Equation (4.3), relative to the Pb-only configuration. The selection retains valid events with calibrated maximum-track energies in $2\text{–}7\text{keV}$ over the full $36{\text{cm}}^2$ readout, before the track-multiplicity and fiducial requirements.

The simulations use the full outdoor HENSA spectrum from $1\text{meV}$ to $10\text{GeV}$ and a downward ${cos}^2𝜃$ neutron field [100], with the same source surface and detector-response settings for all configurations. The cosmic trajectories are generated with the Probability Distribution Projection method described in Section 3.3.1. The combined sample contains approximately $3.55\times {10}^9$ generated neutrons, $45502$ energy-selected events, and 524 events passing the complete TPC baseline. The two productions use independent random seeds, and no neutron contributes more than one energy-selected event in the accepted blocks. The exposure includes all generated neutrons in completed blocks, including those without a saved TPC event. Neither the TPC BDT nor active-veto rejection is applied.

The common source rate, energy interval, and counting area cancel in ${𝐵}^{𝐸}/{𝐵}_{\text{Pb}}^{𝐸}$, while the normalization accounts for the different generated exposures. Central 68.27% Clopper–Pearson intervals and one-sided 90% binomial limits are divided by the observed Pb acceptance; the reference uncertainty is shown separately. These pointwise intervals exclude model uncertainty and simultaneous coverage for the lowest observed result across the scan. The Pb-only control is therefore at 1.0 in Figure 4.3.

The lowest observed central yield occurs for $𝑀=10\text{cm}$, $𝑝=5\text{cm}$, and $𝑛=1$: approximately $963$ energy-selected events per ${10}^8$ generated neutrons, compared with $1384$ for Pb only. This places a single $10\text{cm}$ BPE layer between $5\text{cm}$ of inner lead and $15\text{cm}$ of outer lead. The ratio ${𝐵}^{𝐸}/{𝐵}_{\text{Pb}}^{𝐸}=0.696$ corresponds to a $30.4\%$ reduction after energy selection. Placing all BPE outside the lead, $𝑝=20\text{cm}$, gives little reduction at the largest moderator thickness. Dividing the BPE into several layers does not consistently lower the energy-selected background; the preferred ordering depends on the total thickness. At $𝑀=10\text{cm}$ and $𝑝=5\text{cm}$, two and three BPE layers give ratios of 0.771 and 0.778, respectively.

Replacing the BPE in the lowest-yield arrangement with air gives approximately $1221$ energy-selected events per ${10}^8$ neutrons, or 0.882 relative to Pb. The matched-air control has a higher central yield than BPE, with broader statistical intervals because of its smaller sample.

The remaining-selection efficiencies are compatible within the limited baseline statistics, which cannot establish their independence from shielding geometry. The ${𝐵}^{𝐸}$ comparison therefore identifies promising arrangements without predicting a background level after the complete selection.

4.2.4.3 Lithium-containing capture layers

Capture on ${}^6\text{Li}$ produces an alpha particle and a triton [118], motivating an absorbing layer beside the moderator. We tested four BPE arrangements: $𝑀=10\text{cm}$ with $𝑛=1$, 2, or 3, and $𝑀=7.5\text{cm}$ with $𝑛=1$. Each retains $20\text{cm}$ total Pb, $𝑝=5\text{cm}$ inner Pb, and the original cavity and outer dimensions.

The composite contains equal LiF and poly(methyl methacrylate) (PMMA) mass fractions, $95\%$ ${}^6\text{Li}$ abundance in the lithium, and density $1.62\mathrm{g}{\text{cm}}^{-3}$, as in Section 4.2.5. This assumed composition is not a characterization of a procured component. Only its passive effect on transported particles is included.

Composite layers of thickness 1 mm, 2 mm, & 5 mm replace BPE on the detector-facing surface of either the innermost BPE layer or every BPE layer. Here $𝑀$ denotes the initial BPE thickness, and the thickness $𝑡$ applies to each treated interface. Treating $𝑚$ interfaces leaves $𝑀-𝑚𝑡$ of BPE, with $𝑚=1$ or $𝑚=𝑛$. The placements coincide for $𝑛=1$, giving 18 distinct composite arrangements, four BPE controls, and a Pb-only control.

Preserving the envelope does not preserve the material mass or the amount of BPE. Outer interfaces cover larger surfaces: for $𝑛=3$ and $𝑡=5\text{mm}$, treating every interface requires about $20.0\mathrm{L}$ of composite, compared with $2.44\mathrm{L}$ for the innermost interface alone. The corresponding composite masses are approximately $32.5\text{kg}$ and $4.0\text{kg}$. The two placements therefore compare different quantities and distributions of absorbing material while displacing different amounts of BPE.

We used the same neutron source and TPC response as in the preceding scan. The current comparison contains $1468800000$ generated neutrons, with $15705$ events passing energy selection and 199 passing the full TPC baseline. Figure 4.4 compares ${𝐵}^{𝐸}$, defined in Equation (4.3), relative to the Pb control from the same sample. Each configuration contains between $63600000$ and $64000000$ generated neutrons; the normalization accounts for these different exposures.

The lowest central value occurs for the BPE-only arrangement with $𝑀=10\text{cm}$ and $𝑛=1$: ${𝐵}^{𝐸}/{𝐵}_{\text{Pb}}^{𝐸}=0.767$. Replacing $1\text{mm}$ of its BPE with composite gives 0.779. Across the composite arrangements, central values relative to the corresponding BPE controls range from about 0.88 to 1.07, without a monotonic improvement with thickness. The comparison does not establish an advantage from lithium over the lowest-background BPE arrangement. After selecting energy, the remaining TPC criteria may reject different fractions of events in the BPE and LiF/PMMA configurations. Too few events survive the complete selection to determine whether the small differences in ${𝐵}^{𝐸}$ persist.

4.2.4.4 Implications for a future shielding iteration

These closed-geometry results concern a future shielding iteration. The adopted design retains the full lead shield, and any proposed moderator arrangement requires further study with the beam opening, services, and veto materials restored. The treatment of thermal scattering in hydrogen bound in polyethylene also remains to be validated. The separate study below replaces part of the lead while preserving the outer dimensions, and therefore also requires a comparison of photon attenuation.

4.2.5 Fixed-volume shielding alternatives

The moderator scan described above retained the full $200\text{mm}$ of lead and required additional space. For a future detector iteration, we also investigated whether part of the lead could be replaced by neutron-moderating and absorbing materials while preserving the outer dimensions of the shield. This comparison addresses a different design constraint: the material substitution reduces the lead thickness, so an improvement in the neutron response must eventually be assessed together with the change in photon attenuation. The adopted detector design retains the full lead shield.

We compared three configurations with the same $600\text{mm}$ by $600\text{mm}$ by $550\text{mm}$ outer envelope. The Pb-only control contains $200\text{mm}$ of lead. The Pb + BPE configuration replaces the innermost $50\text{mm}$ with borated polyethylene (BPE), leaving $150\text{mm}$ of lead on the exterior. The Pb + BPE + LiF/PMMA configuration uses $49\text{mm}$ of BPE followed by a $1\text{mm}$ lithium-fluoride/poly(methyl methacrylate) composite (LiF/PMMA) on the detector side. Both replacement configurations retain $150\text{mm}$ of effective lead at the front collar; the existing $200\text{mm}$ by $200\text{mm}$ aperture in the lead remains an exception to the nominal lead thickness. Figure 4.5 shows three orthogonal sections of the Pb + BPE + LiF/PMMA configuration and an enlarged view of the thin capture layer beside the copper. The drawing omits chamber internals, electronics, the beam pipe, and veto assemblies.

The BPE model contains $5\%$ natural boron by mass and $95\%$ polyethylene, with density $1.04\mathrm{g}{\text{cm}}^{-3}$. The LiF/PMMA model contains equal LiF and PMMA mass fractions, a ${}^6\text{Li}$ isotopic abundance of $95\%$ in the lithium, and density $1.62194\mathrm{g}{\text{cm}}^{-3}$. These assumed compositions define the simulated materials; they are not measured properties of procured shielding components. The copper shield, beam pipe, and plastic-scintillator veto panels with their cadmium layers are unchanged. The veto material therefore participates in neutron transport and moderation even when its signals are not used to reject events.

4.2.5.1 Common source and TPC selection

We used the full outdoor HENSA neutron spectrum from $1\text{meV}$ to $10\text{GeV}$, with an assumed downward ${cos}^2𝜃$ angular distribution [100]. This energy range extends below the $1\text{MeV}$ threshold used for the archived HENSA layer and inclination comparisons. The source is treated as one outdoor neutron field; it is not added to a separate HENSA-derived environmental-neutron contribution. Each generated primary is one physical neutron, and all configurations use the same source normalization and detector-response settings.

The comparison applies the TPC baseline defined in Section 3.5.3 in the $2\text{–}7\text{keV}$ region: valid reconstruction, one reconstructed track in each projection, and the $10\text{mm}$ radial fiducial requirement. Neither the TPC boosted decision tree nor active-veto rejection is applied. The neutron-induced background after this selection is denoted ${𝐵}^{\text{TPC}}$.

We converted the fraction of accepted events into a rate using the nominal neutron-generation rate of $1336.87{\mathrm{s}}^{-1}$. Dividing this rate by the $5\text{keV}$ energy-window width and the fiducial area of $𝜋{\text{cm}}^2$ gives the mean differential background level. The simulated exposure includes every neutron in the completed, reconstructed simulation blocks, including those that produce no saved detector event.

We also calculate ${𝐵}^{𝐸}$ using Equation (4.3), retaining valid events with calibrated maximum-track energies in $2\text{–}7\text{keV}$ before the track-multiplicity and fiducial requirements. This estimate averages over the full $36{\text{cm}}^2$ readout rather than the baseline fiducial area. Both selections use the same generated sample and equivalent exposure.

The figure shows the background estimate with a central $68.27\%$ statistical interval and a separate one-sided $90\%$ upper limit. The interval summarizes the statistical precision of the estimate; the upper limit provides a one-sided bound under the adopted statistical model. Both quantify simulation statistics with the nominal source flux, geometry, material composition, and detector response held fixed. For $𝑘$ selected events among $𝑁$ generated neutrons, we scale the central 68.27% Garwood interval and the one-sided 90% Poisson count limit by the same factor $𝜆/(𝑁𝐴\mathrm{\Delta }𝐸)$, with source rate $𝜆$ and the area of the stated selection. This conditional Poisson model excludes uncertainty from source and response assumptions and does not establish coverage under the computing-time stopping rule or exclusion of failed blocks.

4.2.5.2 Preliminary comparison

Figure 4.5(e,f) compares the three shielding configurations at both selection stages. The Pb-only control gives the highest estimated neutron background. Replacing its inner lead with BPE lowers the central estimate, and adding the detector-facing LiF/PMMA layer gives the lowest estimate in this sample. The intervals show the statistical precision of these preliminary predictions; the individual upper limits do not establish the significance of the differences between configurations. The energy-selected estimates also decrease with the substitutions, but their relative changes are smaller than those after the complete baseline.

4.2.5.3 Implications for a future design

The lower central estimates motivate further simulation of both replacement layers. The present comparison does not establish an additional benefit from LiF/PMMA over BPE alone. As the samples increase, the incident-neutron energies and capture locations can help explain the differences between the configurations. The treatment of thermal scattering in hydrogen bound in polyethylene remains to be validated; increasing the sample size cannot resolve that model uncertainty.

Reducing the lead thickness can change the photon contribution and material-induced backgrounds even if the neutron response improves. A design recommendation therefore requires the corresponding photon and muon calculations, material radiopurity information, and a comparison after the final TPC and veto selections. These neutron-only results describe a possible future shielding iteration and are not inserted into the adopted full-lead background budget.

4.3 Neutron-sensitive active veto concept

The limits of passive shielding motivate a veto sensitive to the secondary shower surrounding a TPC event. We first identify the incident neutron energies that produce reconstructable activity and examine the neutrons generated in the lead. We then follow moderation and capture through scintillator deposits to reconstructed veto peaks, establishing the physical basis for the multilayer comparison in Section 4.4.

4.3.1 From surface primaries to taggable secondaries

The integral surface-neutron field does not directly describe the neutrons that produce reconstructable TPC activity. Figure 4.6 compares the CRY and HENSA outdoor primary spectra with the populations surviving the TPC validity requirement ${𝐶}_{𝑉}$ of Section 3.5.3. This comparison precedes the energy, track-multiplicity, fiducial, classifier, and veto selections. The HENSA diagnostic uses the full input spectrum, including incident energies below $1\text{MeV}$, unlike the historical layer scans described in Section 4.1.2. The rates use the respective incident fluences and all generated primaries; bands show 68% statistical intervals.

The abundant low-energy source population is strongly suppressed after shielding and valid reconstruction. For CRY, the narrowest logarithmic interval containing 95% of valid events extends from approximately $20.7\text{MeV}$ to $16.9\text{GeV}$. This interval is determined from the full-spectrum sample and identifies the primary energies that dominate reconstructable activity, rather than the energies of the resulting gas deposits.

The energy dependence also guides the allocation of simulation time. Figure 4.7 compares the valid-event yield per launched neutron and per transport CPU-hour. The CRY and HENSA samples are combined within each half-decade energy bin, so the result describes their sampled energy and angular mixture. Independent timing samples measure neutron generation and transport, including event recording; detector reconstruction, process startup, and finalization are excluded. The yield per primary rises with energy, whereas the yield per CPU-hour has a broad maximum around a few GeV because higher-energy showers cost more to simulate.

Additional CRY simulations restricted to energy intervals above $10\text{GeV}$ extend this conditional-yield study to the input-spectrum endpoint, $8.17\times {10}^6\text{MeV}$. They do not enter the full-spectrum normalization or its 95% population interval. The sparse highest-energy results remain preliminary: failed simulations are excluded and may bias the completed sample. The CPU-yield axis starts at one event per CPU-hour; uncertainty intervals may extend below the frame.

4.3.2 Neutron multiplication in lead

Inelastic neutron collisions in lead leave excited residual nuclei that can emit additional neutrons through statistical evaporation [119]. Their characteristic energies reflect a nuclear temperature of order MeV, producing a broad low-energy component alongside faster cascade particles [120, 121]. The MeV component in Figure 4.8 is consistent with this mechanism, although the inclusive spectrum does not isolate evaporation. Its apparent peak shifts upward in logarithmic bins, which weight $𝑑𝑁/𝑑𝐸$ by an additional factor $𝐸$.

We follow monoenergetic neutrons to their first nuclear interaction in natural lead, without a TPC selection. The prompt outgoing multiplicity, ${𝜈}_{\text{out}}$, includes any surviving incident neutron, and its mean includes zero-neutron outcomes; the local change is $\mathrm{\Delta }𝑛={𝜈}_{\text{out}}-1$. At $1\text{GeV}$, the mean is approximately 7.9 outgoing neutrons per interaction. GeV-scale structure overlaps transitions between the hadronic models and requires model comparisons before assigning a physical origin. The following spectra and maps describe subsequent transport through the complete shield.

Secondary-neutron energies provide a complementary description of the cascade within the shield. The recorded birth spectrum in Figure 4.9 is concentrated around the MeV scale, where moderation in hydrogen-rich scintillator and subsequent capture become effective. The three-layer simulation uses HENSA outdoor primaries from $1\text{MeV}$ to $10\text{GeV}$; first lead exits include neutrons from all birth volumes. The birth and exit spectra describe different populations, so their ratio does not give an escape probability. The next recorded volume after the first lead exit defines the copper-box and world fractions, which do not measure TPC acceptance. This diagnostic precedes the reconstructed TPC selection and describes recorded activity rather than complete secondary-neutron production.

Figure 4.10 locates the recorded lead-born neutrons in two central slices. The maps and their projections describe the spatial distribution of this activity, without correcting for the local lead volume. Births extend through the lead around the cavity, so neutron production cannot be represented by a single interaction point next to the TPC. This distributed origin motivates surrounding the shield with active material; the maps alone do not determine its optimum placement or thickness.

4.3.3 Tagging the secondary shower

The distributed cascade provides two complementary signatures: prompt charged-particle scintillation and gamma emission after moderated neutrons capture in cadmium near an active panel. Figure 4.11 connects their origin to their timing relative to the TPC trigger. Neutron line width qualitatively indicates kinetic energy; the local material section and signal times are schematic.

Figure 4.12 compares the physical origin of HENSA outdoor neutron events after TPC validity, the additional $2\text{–}7\text{keV}$ energy requirement, and the complete TPC selection with the fixed BDT of Section 5.1.7.1. Each event is classified by following the ancestry of its largest depositing track within the gas back to the incoming energy carrier. Photons, electrons, and positrons form the electromagnetic class, while the neutron class includes local recoil energy and explicitly transported descendants. Protons and nuclei entering from surrounding material are separated from recoils produced by neutrons inside the gas. Other contains the remaining carriers, such as charged mesons and muons, and any histories that cannot be assigned uniquely. The valid and energy-selected populations contain 847 and 172 events, respectively. The BDT comparison uses a wider independently checked archived sample with only 13 survivors. The plotted fractions describe the composition of each selected population; they do not give category-by-category selection efficiencies between these different samples. Statistical intervals resample complete neutron histories; independent BDT events use Wilson intervals.

Electromagnetic carriers account for approximately two-thirds of both the valid and energy-selected events. An incident neutron can therefore produce low-energy TPC activity through photons and electrons generated elsewhere in its shower. Tagging the surrounding activity remains necessary even when the gas signal resembles an electromagnetic event. The class fractions after the complete TPC selection remain preliminary because of the small surviving sample.

We used simplified slab comparisons to examine how the position of lead changes the scintillator response (Figure 4.13). The BC408 slab is $10\text{cm}$ thick; the three lead-coupled arrangements each contain $20\text{cm}$ of lead, placed before, after, or on both sides of the active material. A bare slab provides the control. The configured source samples neutron energies uniformly in $ln𝐸$ from $1\text{MeV}$ to $100\text{GeV}$. Each point gives the fraction of saved scan entries whose total scintillator-energy proxy exceeds the stated threshold, without a TPC selection, acquisition gate, or reconstructed-peak requirement.

Electron-equivalent energy, denoted ${\text{keV}}_{\text{ee}}$ or ${\text{MeV}}_{\text{ee}}$, expresses scintillation response on the electron calibration scale. The scan uses a nominal $500{\text{keV}}_{\text{ee}}$ threshold to compare arrangements before light collection and waveform reconstruction; it is not the reconstructed veto operating point. Section 4.6.1 explains the detector light-response model and its sensitivity checks.

The effect of lead depends on the incident neutron energy and the layer order. For $1\text{–}10\text{MeV}$ primaries, the fraction above threshold is 36.4% in the bare slab and 11.9% with upstream lead. For $0.1\text{–}1\text{GeV}$ primaries, the corresponding fractions are 12.8% and 64.0%. The increased response at higher energy is consistent with detecting the secondary cascade produced in lead. These controls support coupling active material to the passive shield, while the complete geometry and reconstructed response are needed to assess veto coverage and background rejection.

4.3.4 Moderation and capture in the veto

The capture signature develops as neutrons from the shielding shower lose energy and move through the surrounding materials. Repeated elastic collisions with hydrogen in the plastic scintillator can transfer a large fraction of their kinetic energy to recoil protons. These protons produce quenched scintillation, while the slower neutrons continue to scatter, escape, or be absorbed. Moderation and capture are therefore separate processes: slowing a neutron does not guarantee its absorption in cadmium, and captures can also occur in the scintillator, shielding, and detector materials.

Natural cadmium has a large, energy-dependent absorption cross section for slow neutrons. At thermal energies, ${}^{113}\text{Cd}$ provides the dominant contribution. Consequently, a $1\text{mm}$ sheet can absorb thermal neutrons efficiently even though it provides little shielding against fast neutrons. The radiative reaction forms an excited compound nucleus, illustrated schematically by

Slow-neutron capture releases approximately $9\text{MeV}$ of nuclear binding energy, distinct from the initiating surface neutron’s kinetic energy. The nucleus generally emits several photons while returning to lower excitation states [122]. The cascade is prompt relative to the capture; moderation and transport determine when that capture occurs relative to the TPC trigger.

The cadmium sheets place this radiation close to active scintillator. Capture photons can Compton scatter, be absorbed, or produce electron–positron pairs in the surrounding materials, and their charged secondaries generate scintillation. Photons may escape or deposit energy in several panels, so the emitted cascade energy differs from the energy deposited in any panel or in all active material. Quenching then determines visible energy, and light collection and electronics determine reconstructed amplitude. Finite thresholds and the recorded time interval can leave a physical capture without a reconstructed peak. The effective $46.9\text{μs}$ capture-tail timescale discussed in Section 4.3.9 consequently describes the selected geometry and gas-deposit trigger proxy, rather than the lifetime of the nuclear de-excitation.

4.3.5 Neutron transport and capture modeling

We calculate neutron collisions and the correlated secondary particles with Geant4, then convert scintillator deposits into reconstructed veto signals. The transport configuration of the optical-response study combines Livermore electromagnetic physics, the QGSP_BIC_HP hadronic component, high-precision (HP) neutron elastic scattering, and radioactive decay, with PhotonEvaporation enabled for capture de-excitation. Below approximately $20\text{MeV}$, HP models use evaluated neutron cross sections and scattering final states; higher-energy hadronic models supply the energetic shower [123]. An accurate absorption cross section alone does not determine how the excitation energy is partitioned among capture photons. Table 4.2 separates these stages from the detector response.

The supporting neutron-data validation used Geant4 11.0.3 with G4NDL4.6 [124]. At thermal energies, hydrogen is bound in the plastic, and its scattering law $𝑆(𝛼,𝛽)$ describes energy and momentum transfer to bound atoms. Agreement of constituent-weighted cross sections does not validate this treatment, which is not established by the archived high-precision settings and material mapping. The moderation-time distribution therefore remains incompletely validated. Section 4.6 distinguishes the historical scintillator response from the explicit optical and waveform study.

We checked two transport steps independently. A thin-target benchmark of outgoing neutrons from natural lead at $14.1\text{MeV}$ was compared with EXFOR data in the measured energy and angular acceptance. The four tested high-precision reference lists lie $8$–$9\%$ below the experimental integral and differ from one another by less than 1%. This comparison supports the secondary-shower interpretation but does not validate the full GeV-scale neutron response.

For capture de-excitation, the earlier default and strict-isotope ParticleHP treatments and PhotonEvaporation were replayed through the same detector-response and peak-finding chain. The evaluated capture final state samples available photon distributions, whereas PhotonEvaporation generates the compound nucleus’s de-excitation through nuclear transitions, including internal conversion. Different partitions of the cascade energy among photons change threshold-dependent response even when total emitted energies are similar. The probability of reconstructing any veto peak remains between 0.719 and 0.742, whereas the fraction of the processed response sample above the $10\text{MeV}$-equivalent operating point changes from 0.314 to 0.383. The any-peak response is therefore more stable than rejection at a fixed reconstructed-energy threshold. For PhotonEvaporation, selected gamma-line yields differ from evaluated values by up to approximately a factor of five, limiting the accuracy of individual spectral lines. This model spread is not a confidence interval on the true response; its incomplete propagation to the adopted classifier is discussed in Section 4.8. Capture histories provide the physical interpretation of timing; the adopted classifier receives reconstructed veto observables rather than capture-truth labels.

4.3.6 Capture multiplicity and initiating energy

A source neutron can initiate a shower containing several secondary neutrons, each of which may capture. We count captures in $3864$ saved histories of the 60-panel, three-layer optical-response study described in Section 4.6, retaining 26 histories without captures. This population is conditional on the simulation saving the event; final TPC and veto selections are not applied.

The $101091$ captures give a mean of 26.2 per history and a median of 14; the mean in cadmium is 20.6. Figure 4.14 shows the mean increasing from 1.0 capture at $1\text{–}10\text{MeV}$ to 58.1 at $1\text{–}10\text{GeV}$. The initiating energy is distinct from the neutron energy at capture and the binding energy released. The increase reflects multiple capture opportunities within the shower; these captures remain correlated descendants of one incident neutron. We resample complete histories to retain correlations among captures from the same shower.

4.3.7 Capture materials, faces, and layers

Capture locations determine which scintillator panels can intercept the emitted radiation. Figure 4.15 groups the volumes where captures occur, distinguishing cadmium sheets, active plastic, shielding, and other detector components. Cadmium sheets account for 78.8% of the $101091$ capture endpoints, and active plastic for 13.7%. The saved volume names assign cadmium captures to detector faces and native layer indices, ordered from the shielding outward. Layers 1, 2, and 3 contain 62.7%, 29.3%, and 8.0% of cadmium captures, respectively; captures reach all three in 55.0% of stored histories. These are successive layers within a single design. Most captures occur in the inner stage, but the response extends across the surrounding layers, motivating a comparison of their additional reconstructed tagging contribution.

Each capture contributes to the material and position distributions, so a history with many captures carries more weight than one with a single capture. Source direction, geometry, and stored-event selection influence these fractions, which lack face-area or incident-exposure normalization. They describe the absorbed-neutron population, rather than capture efficiency for an incident neutron. Section 4.3.8 tests how capture location translates into scintillator deposits.

4.3.8 Capture photons and scintillator deposits

We sum the direct photon energies, ${𝐸}_{\text{emitted}}^{(𝛾)}$, for each cadmium capture and trace their electromagnetic descendants into the plastic. Direct conversion electrons and subsequent nuclear or radioactive-decay branches are excluded. The attributed plastic energy, ${𝐸}_{\mathrm{v}\mathrm{i}\mathrm{s},\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}}^{(𝛾)}$, already includes the saved quenching. We compare these energies through

The median ${𝑅}_{𝛾}$ over $79645$ captures is 18.1%; the ratio of total visible to total emitted energy is 25.2%. A capture reaches a median of four panels (Figure 4.16); 2.68% give no attributed plastic deposit. For nonzero responses, the largest panel carries a median 64.5% of the attributed plastic visible energy. These deposit counts use all saved times, without an acquisition gate or DAQ threshold. The complement $1-{𝑅}_{𝛾}$ includes photon energy deposited outside plastic, quenching, escape, and omitted descendant branches; it does not measure escape alone. The partial and shared deposits explain why a large capture probability does not translate directly into a large signal in one panel. Panel thresholds and the combination of signals across channels therefore enter the reconstructed response studied next.

4.3.9 Prompt and post-trigger signatures

Here, prompt and post-trigger refer to time relative to the Micromegas trigger, not to the duration of the nuclear de-excitation. To test how physical captures translate into observed signals, we use the separate $2706$-entry processed three-layer sample in Figure 4.17. No additional TPC selection is applied. Here a late peak has reconstructed time $𝑡\ge 10\text{μs}$; peaks before this boundary include the $5\text{–}10\text{μs}$ interval as well as prompt and near-trigger activity. These peak times use the reconstruction alignment and are distinct from the truth-level gas-deposit time used below.

In this response sample, 98.3% of analysis entries contain a cadmium-sheet capture. At event level, however, 23.8% contain a cadmium capture but no reconstructed veto peak. Another 24.6% contain a cadmium capture and peaks only before $10\text{μs}$, while 49.9% contain a cadmium capture and a late reconstructed peak. Finite light collection, thresholds, timing, and reconstruction therefore prevent a one-to-one mapping between capture and observed veto signature.

The cadmium capture history in the three-layer neutron simulation provides the characteristic post-trigger timescale relative to the first simulated gas deposit, which is used as a trigger proxy and is distinct from both the physical capture time and the reconstructed veto-peak time. A truncated-exponential fit over $10\text{–}300\text{μs}$ gives $𝜏=46.9\text{μs}$. The cumulative retention uses captures with positive gas-relative delays below $2000\text{μs}$; it counts captures, not independently weighted events. Of these captures, 79.7% occur by $70\text{μs}$ and 88.8% by $100\text{μs}$. This is a simulation-derived capture-retention study, not a complete acquisition-window optimization: reconstructed thresholds, accidental activity, and dead time are not included in the fitted curve. The prototype record spans approximately $[-30,+70]𝜇\mathrm{s}$ relative to its hardware trigger; relating that trigger to the first-gas-deposit proxy requires a separate response mapping.

Late-window activity alone is not neutron-specific because calibration data contain electronic noise and unrelated environmental coincidences throughout the waveform. The useful observable combines prompt or near-trigger activity with post-trigger energy, peak multiplicity, signal quality, and segmentation. An event-mixing study quantifies the timing information: a late peak alone accepts approximately 52% of the neutron sample and 56% of a neutron-derived time-scrambled control, whereas requiring both prompt and late activity accepts approximately 46% and 14%, respectively. The scrambled control preserves neutron-like peak multiplicity and amplitude while removing alignment to the trigger; it does not measure the apparatus’s accidental-coincidence rate. Section 4.6.6 examines this timing information with reconstructed observables. In this chapter, post-trigger or late-window activity always refers to peaks inside the recorded waveform. The term delayed activation is reserved for radioactive-decay descendants occurring beyond the coincidence window, as defined in Section 5.2.2. No standalone $𝑚\ge 3$ peak-multiplicity requirement is adopted as an operating point in this thesis. Multiplicity enters the structured and multivariate selectors together with energy, timing, channel occupancy, and signal quality; the final threshold is fixed by calibration-like control acceptance.

Together, these studies connect neutron multiplication in lead to spatially distributed prompt and post-trigger activity in the veto. Only part of the capture radiation appears as visible scintillator energy, and thresholds and timing determine which signals are retained. Section 4.4 therefore compares the reconstructed response of multilayer designs. Section 5 evaluates absolute background levels using the corresponding source normalization and TPC selection.

4.4 Multilayer design comparison

We compared the reconstructed tagging gained by adding active panel stages around the lead shield. The scan includes one-, two-, three-, and four-layer cadmium configurations, together with three-layer gadolinium and stainless-steel variants. It uses the historical HENSA outdoor input from $1\text{MeV}$ to $10\text{GeV}$, with the common angular setting described in Section 4.1.2. The detector-response chain includes quenching, light attenuation, waveform formation, and veto-peak reconstruction.

Figure 4.19 illustrates the repeated-stage concept using the panel construction in the preserved September 2026 reference geometry. A layer denotes an active panel stage; the reference construction has cadmium on both broad faces of the scintillator, so the stage count differs from the number of capture foils. Repeating the stages adds moderator and active volume in which recoil and capture-induced energy deposits can be detected. The schematic omits detector-wide panel segmentation and services and does not specify the full historical scan layouts. Section 4.5 describes the prototype geometry and readout separately.

The scan exporter retains every entry in each processed AnalysisTree; it applies no additional one-track, $2\text{–}7\text{keV}$, fiducial, or X-ray-topology selection. The neutron-tagging fractions below are conditional on that processed response population. The nominal reconstructed-energy proxy is the sum of the exported veto-peak energies over an entry; its threshold is applied to that sum, rather than separately to each panel. It is distinct from the simulated scintillator-energy proxy used in the slab comparison of Figure 4.13.

The any-tag fraction increases from $0.465$ for one layer to $0.675$, $0.741$, and $0.771$ for two, three, and four cadmium stages, respectively. At a nominal $10{\text{MeV}}_{\text{ee}}$ threshold, the corresponding conditional rejection fractions are $0.150$, $0.292$, $0.376$, and $0.425$. Thus the third layer provides a substantial improvement, whereas the fourth adds $0.030$ in any-tag probability and $0.049$ in threshold rejection, at the cost of another active layer and its associated readout channels. The gadolinium variant gives results similar to cadmium for these aggregate observables, whereas stainless steel provides substantially weaker tagging. The statistical intervals resample complete simulation files, treating files as independent and retaining correlations among entries within each file; they exclude source and detector-response systematic uncertainties.

Table 4.3 places these conditional tagging measures alongside the historical classifier rejection and the absolute background levels evaluated in Section 5, with their respective populations and treatments.

Normalizing the processed analysis-entry count to the number of generated primaries gives a probability of approximately $2.2\times {10}^{-5}$ for each of the one- through four-layer cadmium samples. The processed-entry probability is similar across these samples, so the principal gain shown here is in conditional tagging.

Each additional layer also adds channels that can contribute accidental activity. An illustrative overlay model samples the measured calibration-triggered veto activity. At relative accidental level $𝛼$, an $𝑛$-stage configuration receives an average of $𝛼𝑛/3$ independent calibration-template entries. Thus $𝛼=1$ assigns one complete template entry to the three-layer reference, with fewer or more accidental opportunities for the other layer counts. The scalar addition assumes a common nominal energy scale for simulation and the calibration-derived template; this model does not validate that correspondence or the acquisition-window response.

Over the scanned accidental range, the four-layer configuration retains the largest sensitivity proxy. At $𝛼=1$, $𝑄$ is $1.274$ for four layers and $1.232$ for three layers, while the corresponding noise-only acceptances are $0.860$ and $0.897$. These curves show a frozen realization of the scalar-overlay model, without a full uncertainty band for the detector response or accidental population. Three layers are an engineering and channel-count compromise made after most of the conditional tagging gain has been obtained; this model does not establish a statistical optimum. The small separation between the three- and four-layer sensitivity proxies should be compared with the response and cascade-model variations before assigning a preferred physics operating point. For an expected background of only a few counts, an expected Poisson-likelihood limit with signal and live-time losses is more appropriate than $𝑆/\sqrt{𝐵}$. The following section describes the three-layer prototype and its synchronized readout.

4.5 Prototype geometry and synchronized readout

4.5.1 Geometry and prototype construction

The three-stage veto surrounds the lead shield with Top, Bottom, Left, Right, Front, and Back panel groups. Layer 1 is closest to the shield, and layer 3 is outermost. The front group accommodates the X-ray beam pipe.

The prototype reused NE-110 plastic scintillator bars from a former time-of-flight spectrometer [125]. The bars were cut to $150\text{cm}$ and $65\text{cm}$, with a $20\times 5{\text{cm}}^2$ cross-section, and coupled to photomultiplier tubes (PMTs) through light guides. Cadmium sheets of $1\text{mm}$ thickness were placed between neighboring panels to capture moderated neutrons close to active material [17]. The preserved transport references use BC408 scintillator and $80\text{cm}$ short bars; their paired cadmium foils and wrapping are illustrated in Figure 4.19.

Atmospheric muons provided the gain-equalization reference. For muons crossing $5\text{cm}$ of plastic, the most probable energy loss is approximately $10\text{MeV}$ [17]. Measurements on the long bars showed that the collected light at the far end can be reduced by approximately a factor of two [17]. The reconstructed panel energy therefore depends on attenuation and calibration. This single-panel reference is distinct from the sum of reconstructed veto-peak energies used as the nominal threshold proxy in Section 4.4.

Figure 4.21 shows the spatial arrangement and group–layer–panel naming convention of the selected 59-panel IAXO-D1 design. The dimensions and spacings in the expanded drawing are schematic.

The archived prototype readout defines 59 panel positions, including two inactive channels, while the publication reports 57 installed panels [17]. Table 4.4 summarizes the resulting 57 operational channels. The readout map alone does not establish an installed-bar inventory; the transport and prototype configurations remain distinct (Table 4.1).

4.5.2 Electronics and timing

The Micromegas and veto branches each use four AGET application-specific integrated circuits, with 64 channels per chip and a 512-sample circular buffer [17, 83]. Separate field-programmable gate arrays (FPGAs) permit different readout settings for the two branches, while a common module supplies the trigger and clock reference. The Micromegas electronics trigger readout of all veto channels. The TPC record was set between $10\text{μs}$ and $30\text{μs}$ to contain the drifting charge, while the nominal veto record lasts $100\text{μs}$ with the trigger $30\text{μs}$ after its start [17].

Figure 4.23 relates the acquisition branches to the veto time coordinate. The veto record spans approximately $[-30,+70]𝜇\mathrm{s}$ relative to the Micromegas hardware trigger. Activity near zero supplies the prompt tag, while later capture-related peaks contribute to the post-trigger tag if they arrive before the waveform ends. This hardware trigger differs from the first simulated gas deposit used as the time origin in Figure 4.18.

The long veto record makes prompt muon and shower activity and a substantial part of the capture-related tail available for analysis. A wider accepted coincidence interval also increases the probability of accidental vetoes; its effect on acquisition live time depends on the trigger and readout settings. The following section describes how the recorded signals are reconstructed into the observables used for event selection.

4.6 Veto response and event selection

The recorded veto signals described in Section 4.5.2 depend on the light produced by each deposit, its collection along the bar, and the waveform reconstruction. We follow these stages to construct veto observables, test prompt tagging with experimental TPC tracks, and define the selection used for the background model. The nominal response uses an effective attenuation law; a separate optical-photon study tests response assumptions with measured activity added before waveform reconstruction. The adopted prompt-plus-residual-BDT selection is presented before the historical classifier comparisons that explain its choice.

4.6.1 Scintillation quenching for neutron-induced deposits

Neutrons produce scintillator light through the charged particles created in their interactions, including recoil protons and heavier nuclei such as carbon. These particles can deposit energy densely along short paths, reducing the light produced per unit deposited energy. The reduction depends on the particle and its energy, so neutron-induced deposits cannot be assigned one constant quenching factor. Capture photons produce light mainly through secondary electrons and positrons, whose response differs from that of nuclear recoils.

This treatment follows established simulation practice. Ros et al. used the same coefficient in Geant4 simulations of electron and proton response in polystyrene scintillator [128]. For thermal-neutron detection in boron-loaded plastic, Porosev and Savinov adopted Birks parameters from published work and examined the response dependence on step limits and secondary-production thresholds [129]. Their capture products and material differ from ours, so this comparison supports the modeling approach rather than a numerical transfer of light yield. Measurements by Pöschl et al. further show that quenching depends on the plastic composition [130].

The archived response introduces an additional approximation: local energy-loss density is estimated using distances between neighboring stored hits instead of the true charged-particle step. For energy deposited locally on a neutron track, that distance need not represent the stopping path of the unresolved recoil. This limits the physical accuracy of the light estimate, especially for short recoil tracks. The saved scintillator energies already include this historical Birks treatment and enter the optical response once; applying another quenching factor would suppress the same energy twice.

The neutron-veto predictions therefore remain conditional on the adopted light-response model. The separate optical-response study below tests the consequences of this approximation while keeping the muon gains fixed.

4.6.2 Veto readout geometry and light attenuation

The position of an energy deposit in a scintillator determines which veto channel receives its signal and how far the light travels before collection. These two operations must describe the same bar: an incorrect orientation can assign a deposit to the wrong channel or reverse its attenuation along the bar. We therefore extended the spatial readout description in REST-for-Physics and developed tools to construct the veto channel map from the simulated geometry [86].

In TRestDetectorReadout, each scintillator is represented by an independent readout plane, with one module and one channel covering its cross-section. The plane lies at the light-guide end of the bar, and its normal points along the bar toward the opposite end. Its sensitive depth is therefore the bar length, rather than its thickness. The generator obtains the bar center and light-guide position in global coordinates, derives the longitudinal direction from their separation, and places the plane at the corresponding bar end. Local transverse axes describe each panel’s cross-section in its own orientation.

For a deposit at position $𝐫$, the projection onto the local transverse axes determines whether it lies within the channel cross-section. The longitudinal coordinate is

where ${\widehat{𝐧}}_{𝑗}$ is the unit normal of panel $𝑗$. With a numerical guard $𝛿=1\text{mm}$, the readout origin ${𝐫}_{0,𝑗}$ lies $𝛿$ before the physical bar end and its sensitive depth is ${𝐷}_{𝑗}={𝐿}_{𝑗}+2𝛿$, where ${𝐿}_{𝑗}$ is the bar length. The transverse acceptance is also slightly enlarged to retain deposits on numerical boundaries. Panel spacing must keep these readout regions unambiguous. The panel alias records its face, layer, and position; a separate map supplies the acquisition-channel identifier.

The same longitudinal coordinate sets the effective light attenuation applied before waveform formation:

Here ${𝐸}_{\text{vis},𝑖}$ is the visible-energy proxy for deposit $𝑖$ after the scintillator quenching described in Section 4.6.1, and $𝑗$ is its assigned panel. The attenuated deposits are then summed in their channel at the sampled arrival times, retaining the position dependence of each contribution. The nominal response configuration uses ${𝜆}_{\text{att}}=215\text{cm}$, giving a factor $0.50$ over $150\text{cm}$, consistent with the approximate decrease measured along the long prototype bars [17]. This effective length describes the collected response, including optical losses and coupling; it is not the manufacturer’s bulk-material attenuation length. The attenuation process also adds a configurable propagation delay. Subsequent signal conversion and acquisition timing must be included when defining the final peak time.

The generation checks recover the expected channel identifiers at panel centers and require unique identifiers in the combined Micromegas–veto readout. During attenuation, a veto deposit must match exactly one veto plane; missing or multiple assignments stop processing. Figure 4.24 illustrates the geometry and distance calculation. It uses the preserved 60-panel IAXO-D1 transport reference. The archived IAXO-D0 prototype readout instead defines 59 positions and 57 operational channels, with different short-bar dimensions. Geometry and acquisition maps must consequently be selected together for each comparison. For each geometry, the readout links deposits to panel labels and acquisition channels; response calibration remains a separate requirement.

4.6.3 Detector response and reconstructed observables

The nominal detector-response simulation converts the quenched and attenuated deposits into channel signals, shapes and digitizes them, and applies the REST-for-Physics peak finder (Figure 4.25). Simulated and measured signals then have the same definitions of peak time, amplitude, multiplicity, and channel quality. This common reconstruction permits direct comparisons of observables, while agreement of the physical response must be tested separately.

A separate optical-response study follows $3864$ saved neutron histories, with separate development and checking files. Explicit photon transport replaces the effective attenuation law, and a muon-calibrated bipolar pulse model is combined with one joint measured waveform record before reconstruction. Only 37 common channels contribute rejection; their optical properties and geometry transfer remain assumptions. The checking population contains 170 valid reconstructed $2\text{–}7\text{keV}$ events, without the final TPC multiplicity or fiducial requirements. At a selection fixed with a 1% development-sideband activity budget, net additional tagging is 32.4% (95% whole-file bootstrap interval 26.3–38.3%). The same selection retains 468/473 and 1546/1560 actual-trigger ${}^{55}\text{Fe}$-enriched controls in two acquisitions, or 98.94% and 99.10%; these fractions are not pure signal efficiencies or measured dead time. Varying ${𝑘}_{\mathrm{B}}$ by $\pm 50\%$ with muon gains fixed changes net tagging to 28.2–35.3%, a model sensitivity rather than a confidence interval. These saved histories supply no generated-primary exposure, so this conditional check does not replace the adopted hybrid-veto background evaluation.

Muon-induced events are predominantly prompt, high-amplitude, and track-like across several panels. Neutron-induced events are more heterogeneous: they contain softer prompt activity, a broader distribution of later peaks, and less regular channel correlations. These differences motivate aggregate observables rather than a single opposite-panel coincidence.

4.6.4 Prompt tagging and the adopted hybrid veto

We selected extended, approximately straight TPC tracks from measured background runs to test prompt tagging independently of the veto response. The selection requires sufficient strip multiplicity and spatial extent, compatible charge-weighted line fits in XZ and YZ, and no flagged TPC saturation. It yields 351 candidates in four background runs. These events are muon-like, but the selection does not establish particle purity or represent muons that miss the TPC and produce low-energy secondaries. The subsequent veto comparisons informed the choice of the hybrid selection, so they are development controls rather than an independent test of the adopted rule.

The fixed prompt-amplitude reference tags 339/351 candidates, or 96.6% with an exact 90% statistical interval of 94.5–98.0%, while retaining 87.8% of the calibration controls from run 1347. The historical neutron level-1 boosted decision tree (BDT) tags 57.5%, and the revised neutron level-2 amplitude and counts/timing models tag 25.4% and 37.6%, respectively. The muon-trained amplitude model tags 77.8%. These conditional experimental fractions demonstrate that the high simulated muon rejection cannot be transferred directly to measured tracks. A broader response comparison applies matching TPC requirements on strip multiplicity, spatial extent, and valid charge, without the straight-track refinement, and includes all experimental TPC saturation states. The data have larger median peak amplitudes and a substantially stronger high-multiplicity veto tail than simulation; full signal-distribution agreement is not established.

The nominal 88% calibration-retention target defines the adopted level-2 amplitude-aware hybrid for the background evaluation. It retains the fixed prompt-amplitude tag and applies a residual neutron BDT to prompt survivors, with its threshold set exclusively on calibration run 1345. Table 4.5 compares the hybrid with the fixed 500-ADC prompt reference and a 455-ADC prompt threshold set to the same nominal retention target.

Relative to the fixed 500-ADC reference, the hybrid adds 280 simulated neutron tags while preserving all 339 prompt-tagged experimental tracks. The gain is 6.94 percentage points, with a central 90% paired-bootstrap interval of 6.29–7.61 percentage points. At comparable calibration retention, the net gain over the 455-ADC reference is 215 neutron tags, or 5.33 percentage points, with a 90% interval of 4.73–5.92 percentage points; the hybrid tags one fewer experimental track. These paired intervals hold the models, thresholds, and activity donors fixed and exclude detector-response and run uncertainties. These results support the hybrid in this control comparison; they do not establish experimental neutron efficiency or agreement of the full detector response. At the lower 85% retention target, the hybrid tags 340/351 tracks, rejects 77.3% of simulated neutrons, and retains 84.7% of calibration controls. Mixed-particle BDTs, including a monotonic model and a development-derived timing correction, do not reproduce prompt-level experimental tagging.

The rejection rule is

where ${𝐴}_{𝑖}$ is the nonnegative reconstructed peak amplitude in ADC counts, ${𝑏}_{𝑖}$ is its stored or aligned sample index, and ${𝑠}_{\text{res}}$ is the residual neutron-BDT score. The fixed threshold is ${𝑠}_{\text{thr}}\simeq 0.9382$; the archived model preserves the full precision, feature order and separate simulated and measured channel maps. Figure 4.28 shows the two rejection paths.

The residual BDT must distinguish neutron-induced scintillator activity from unrelated activity that survives the prompt veto. Its 163 inputs describe peak amplitudes, timing, and their distribution among panels. Table 4.6 groups these inputs using the same partition as the permutation analysis. TPC observables and the inconsistent total-energy scalar used in the earlier hierarchy are excluded.

4.6.4.0.1 Reading a ROC curve and its area.

A classifier assigns a score to each event; a threshold determines which events the veto tags. For simulated neutrons and calibration controls, the tagged fractions are

where TPR and FPR denote the true-positive and false-positive rates of this two-class comparison. Calibration retention is $1-\text{FPR}$, used as the horizontal coordinate in the subsequent comparison plots. Lowering the score threshold generally increases both fractions. The receiver operating characteristic (ROC) traces this tradeoff over all thresholds, as illustrated in Figure 4.29. Its area under the curve (AUC) measures score ordering: an AUC of 0.5 corresponds to random ordering and 1 to perfect separation. Equivalently, AUC is the probability that a randomly selected neutron entry receives a higher score than a calibration entry, with tied scores contributing one half. Rejection at a chosen threshold is read from one point on the curve; AUC summarizes the complete ordering.

To identify the information used by the frozen model, we shuffled individual inputs or complete families across events and measured the resulting decrease in ROC AUC. Figure 4.30 compares the two tests. The model and thresholds remain fixed, and this diagnostic reuses the existing held-out data, including calibration controls from run 1347.

Maximum peak amplitude is the most important individual input in this AUC diagnostic: its permutation decreases AUC by approximately $0.048$, compared with $0.014$ for prompt amplitude in the inner layer. Jointly shuffling the amplitude-derived family gives a decrease of approximately $0.294$. This family includes amplitudes resolved by time window, face, and layer, their fractions and entropies, and amplitude-weighted timing. Its dominance therefore does not separate amplitude information from timing or spatial patterns. This reliance makes the unresolved amplitude and saturation differences between measured and simulated tracks relevant to transferring the adopted veto response.

Correlated inputs can substitute for one another, so individual and grouped losses are not additive contributions. These dimensionless AUC decreases measure model reliance in the stated sample, not experimental neutron efficiency or importance for rejection at the frozen nominal 88% retention operating point. At the frozen threshold, joint permutation of the amplitude-derived family lowers neutron rejection by 6.44 percentage points and control retention by 0.95 points on average. This comparison keeps the prompt decisions fixed; shuffle variability and activity-donor sampling have different uncertainties.

4.6.4.1 Timing and spatial information in the residual classifier

The small timing and spatial losses in Figure 4.30 require interpretation because moderation, capture, and the multilayer geometry motivate precisely these correlations. The permutation groups classify input formulas, rather than independent physical mechanisms. Of the 68 amplitude-derived inputs, only one is the maximum amplitude; 50 are sums resolved by window, face, or layer, 15 are fractions or entropies, and two are amplitude-weighted times. Consequently, this group retains information about when and where activity occurs. The separate spatial inputs describe coarse occupancies and spread, rather than a reconstructed neutron trajectory. Moreover, the prompt rule already rejects $2462$ of $4035$ neutron entries, leaving the harder residual comparison.

We first compared the existing full model with an archived 95-input model trained without amplitude-derived quantities. Both models use the same amplitude-based prompt selection. Figure 4.31 shows that permuting timing, spatial, and spatiotemporal summaries has a larger effect in the latter model. Its AUC is 0.690 on the complete post-prompt population, compared with 0.772 for the full model. These results establish predictive information in unweighted timing and occupancy summaries, while their usefulness to a fitted classifier depends on its other inputs.

To test additional information directly, we trained four models with the same records, run partitions, and fitting settings. Table 4.7 defines the three input blocks and the four model combinations. Both $𝑁$ and $𝐴$ retain timing and position information; $𝐴$ also describes how the measured amplitude is distributed.

The full refit reproduces the adopted scores and threshold to numerical precision. Each threshold uses run 1345 alone at nominal 88% total control retention; achieved run-1347 retention spans 87.51%–87.67%. The prompt rule alone retains 87.80% in that run, bounding every residual selection.

Adding $𝑁$ to $𝐺$ gains 92 neutron tags, or 2.28 percentage points in total rejection (central 90% paired resampling range: 1.76–2.79 points). Adding $𝑁$ after $𝐴$ changes the net count by $-2$, or $-0.05$ points ($-0.24$ to $+0.15$), consistent with no resolved additional rejection at this operating point. Block $𝐴$ contains both additional amplitude-scale information and timing and spatial structure; this comparison does not isolate those physical effects. The results support overlapping information as an explanation of the small separate permutation losses. Their ranges exclude training, threshold, run, and detector-response uncertainties. The physical motivation for timing and segmentation remains, while their incremental classification gain depends on prompt selection, representation, and the measured waveform response.

4.6.4.1.1 Time conventions and acquisition response.

The fixed prompt interval is defined in stored or aligned sample indices. Table 4.8 distinguishes this interval from the published hardware window and the empirical coordinate used in the historical capture-delay diagnostic.

The archived application requires a response-specific timing check. An audit completed on 2 October 2026 found that the legacy veto conversion expected acquisition bin 262, while both independent-electron files and the processing logs covering all 29 independent neutron TPC-BDT survivors used bin 234. The difference is 28 samples, or $5.6\text{μs}$, and can change whether physical scintillator activity enters the prompt interval. A separate reference-window replay of the two electron baseline events preserved their TPC decisions and generated exposure but changed the diagnostic selection sequence from $2\to 1\to 1\to 1$ to $2\to 1\to 0\to 0$. The corresponding neutron replay was incomplete at that audit. Waveform-edge and peak-finding effects require reconstruction of the veto response; shifting exported peak times alone is insufficient. This response diagnostic qualifies the archived application without replacing the reported source yields or establishing experimental neutron efficiency.

The threshold is fixed; the 85% and 80% settings remain comparison points. Background predictions use the actual joint TPC-plus-veto event decisions wherever the necessary response and exposure are available, rather than multiplying by the control-sample rejection fraction. Section 4.6.5 explains the separation of development and evaluation samples and the interpretation of the joint acceptance.

4.6.5 From veto development to a background prediction

The background model requires the count surviving the complete TPC and veto selection. The TPC selects low-energy, X-ray-like candidates, which differ from the general neutron and muon populations used to develop the veto. We therefore follow each simulated candidate through the common TPC baseline, the TPC topology BDT, the prompt veto, and the residual neutron BDT. Reporting the two veto stages separately shows the additional rejection after prompt tagging. The surviving count is obtained from these event decisions rather than from a control-sample efficiency factor.

4.6.5.0.1 Separate learning, threshold setting, and evaluation.

Training samples determine the BDT response; the adopted veto threshold is set only on calibration run 1345 at a nominal 88% retention target. The cosmic evaluation uses separate primary histories after the TPC and veto models and their thresholds have been fixed, with all descendants of a primary kept together. Calibration run 1347 is separate from the veto-model training runs 1335, 1339, and 1342 and from threshold setting, but its controls informed the hybrid development comparisons and its records are reused for the activity overlay. The cosmic yield therefore tests independent particle histories using this previously studied activity population.

The earlier independent neutron evaluation, with 141 baseline candidates, is preserved in the technical companion; its larger development inventory is excluded from that exposure. The updated source estimates in Section 5.4.2 use separately qualified samples and retain each sample’s generated-primary exposure.

4.6.5.0.2 More statistics without changing the selection.

Additional independent primary histories can increase the evaluation statistics without changing the adopted response or selection. Compatible productions combine selected physical-parent contributions and generated-primary exposures, including primaries that produce no stored detector event. Production blocks are defined before their results are inspected; missing reconstruction is recorded as incomplete processing, not as rejection.

Grouped cross-validation can instead assess the selection procedure using models trained without the group being tested. Because it evaluates several fitted models, it remains distinct from an independent test of the single adopted model.

4.6.5.0.3 Signal retention and accidental veto activity.

The 80% TPC-BDT target and the 88% veto target refer to different reference populations. Their product is not a measured acceptance of the joint selection. That acceptance requires following calibration events through the complete chain and measuring veto retention among the TPC-selected survivors. Each simulated parent receives one complete measured veto record from run 1347, retaining the donor’s channel, timing, and amplitude correlations. Repeating this overlay tests sensitivity to the activity realization without adding independent neutron exposure. For a later radioactive-decay acquisition, scintillator activity from the original production interaction is not credited as a veto tag.

4.6.5.0.4 Acquisition timing.

The acquisition-response audit accompanying Table 4.8 limits the archived evaluation preserved in the technical companion. The updated calculation in Section 5.4.2 uses the native TPC acquisition and grants veto rejection only when physical coincidence is established. Both veto stages act on the same independent TPC candidates; unresolved timing receives no rejection credit.

4.6.6 Classifier-development comparisons

Capture timing and detector segmentation can distinguish neutron activity from isolated veto pulses, but added model complexity is useful only if it also preserves control-sample stability. We tested this information in a historical hierarchy, from aggregate observables to a panel–time neural model. These comparisons use the original aligned response at nominal 90% calibration-control acceptance. The historical level-1 benchmark and the level-3 neural hybrid are distinct from the adopted prompt-plus-residual-BDT rule, whose residual threshold is fixed at the nominal 88% target.

The hierarchy uses $20274$ aligned simulated neutron events and $139454$ experimental calibration events. Each neutron peak train receives one independently sampled calibration train, preserving correlations within the measured activity but omitting pulse merging, saturation, and baseline shifts before peak finding. Separate calibration runs define training, threshold setting, and held-out evaluation; overlaid neutrons follow their activity donor’s partition, preventing reuse of its measured activity across partitions. The control class is calibration-triggered activity, so the scores are ordering statistics rather than neutron probabilities.

Level 1 uses six aggregates: total reconstructed veto-energy proxy, peak count, unique panel count, active face count, active layer count, and maximum peak amplitude. Level 2 adds waveform-window summaries and detector segmentation; level 3 combines a panel–time tensor with the six aggregates. No level uses Micromegas energy or topology. The total-energy scalar differs between experimental and simulated flattened inputs and is not a common calorimetric measurement; the adopted residual BDT excludes it. The historical input also retains simulated activity at two prototype-inactive panel positions.

Historical aligned response; nominal $90\%$ control acceptance.

Full level 2 gains 0.47 percentage points over level 1 in held-out rejection (central 90% paired-bootstrap interval: 0.07–0.82 percentage points), with an AUC difference consistent with zero. Across five calibration runs, acceptance spans 88.2%–90.9% for level 1 and 84.4%–90.5% for the full model: additional features increase one run’s acceptance shift for a small rejection gain. Total energy dominates the historical classification; its removal retains 79.1% rejection, but the remaining amplitude and multiplicity inputs prevent this comparison from isolating timing or position. The acquisition time range and energy calibration remain unresolved, so these conditional results do not establish an absolute neutron-veto efficiency. These historical results retain endpoint clipping of out-of-record peaks; the adopted hybrid instead discards them.

4.6.6.1 Capture-delay signature

The cadmium-capture timescale in Figure 4.18 motivates a prompt–delayed sequence, rather than a tag based on any late peak. Those truth times are measured from the first simulated gas deposit and never enter a classifier.

Bins 0–511 span $[-46.2,+56.0]𝜇\mathrm{s}$, but physical simulated peaks in the inspected flat neutron input end at $+41.6\text{μs}$; calibration overlay can populate the remaining bins. The diagnostic prompt and capture-like intervals are $-10\text{–}5\text{μs}$ and $10\text{–}50\text{μs}$. Their $5\text{–}10\text{μs}$ gap does not bound pulse tails or peak-finding leakage. These intervals differ from the broad hierarchy’s stored-bin windows: its legacy “capture” bins 240–280 map to $1.8\text{–}9.8\text{μs}$, rather than $10\text{–}50\text{μs}$. Neither historical scheme calibrates the relation to the hardware window or replaces the adopted stored-bin prompt rule.

The seven timing features describe delayed-peak times, their spread, and the presence of prompt and delayed activity. The full 18-variable signature adds multiplicities, amplitudes, detector occupancies, delayed fractions, and panels active only after the prompt interval.

Figure 4.33 illustrates the sequence and segmentation in a representative prompt-plus-delayed event.

We tested the sequence with 879 neutron events and 250 time-scrambled realizations. Circularly shifting complete neutron peak trains preserves their amplitudes, multiplicities, and spatial correlations while removing their alignment with the Micromegas trigger. This constructed control tests trigger-correlated timing; it does not measure the experimental accidental rate. A late peak alone accepts 52.4% of neutron events and 56.3% of the mixed control on average, whereas requiring prompt followed by late activity gives 46.4% and 14.3%, respectively. Figure 4.34 shows the additional segmentation and delayed-energy requirements.

The seven timing features reject 49.8% of held-out neutrons, and the full capture signature rejects 74.1%. Adding the signature to the six level-1 aggregates raises rejection from 83.69% to 84.19%: 20 additional neutrons among $4035$, or 0.50 percentage points (central 90% paired-bootstrap interval: 0.20–0.82), with an AUC difference compatible with zero. The net gain comprises 40 newly rejected events and 20 lost level-1 tags. Minimum control acceptance across five runs falls from 88.20% to 86.33%. The sequence supplies a small additional rejection gain with poorer run stability; some captures produce no reconstructed veto peak, and calibration data also contain late activity.

4.6.6.2 Level-3 spatiotemporal neural model

The level-3 study tests whether a $59\times 512\times 2$ panel–time tensor can recover useful structure without engineered summaries. Tensor-only temporal and tensor-plus-graph models reject 71.2% and 72.6% of held-out neutrons, respectively; adding the six aggregates gives a neural hybrid with 84.1% rejection. Its gain over historical level 1 is 0.42 percentage points (central 90% paired-bootstrap interval: 0.10–0.74), with an AUC difference compatible with zero. Control acceptance falls to 83.4% in run 1339, below the full level-2 and level-1 minima of 84.4% and 88.2%, failing the predeclared run-stability criterion.

These studies establish useful timing signatures without demonstrating a more stable replacement for the aggregate benchmark in the historical response. For background evaluation, we use the adopted prompt tag plus residual BDT at the nominal 88% target, excluding the inconsistent total-energy scalar. Section 4.7 tests the experimental basis of this approach: whether the prototype selection reproduces the measured background rejection and whether the broader late-window population is described by the simulated neutron signatures.

4.7 Experimental validation with IAXO-D0

The prototype data test two different aspects of the veto response. The published X-ray selection measures background rejection in a defined exposure; applying our residual BDT to the same candidates tests its transfer to that population. A separate, broader sample tests whether simulated neutron signatures describe late activity in the measured waveforms. We keep these populations separate because their gas mixtures, event selections, and response conditions differ.

4.7.1 Published surface selection sequence

The commissioned prototype was operated with IAXO-D0 at surface level in Zaragoza for an effective exposure of $52.1\mathrm{d}$, with 57 operational veto channels [17]. Its readout has 59 positions and 57 operating channels (Table 4.4). The gas mixture was Xe–Ne–isobutane (48.85%–48.85%–2.3%) at $1050\text{mbar}$, rather than the argon-based reference used for the background model. The published selection uses a $2\text{–}7\text{keV}$ region of interest and a $9\text{mm}$-radius focal region. This differs from the $10\text{mm}$ fiducial radius in the final common TPC baseline of Section 3.5.3. We recovered the archived Micromegas-selected candidates and repeated both veto stages using the original gain-calibrated panel maxima and fixed thresholds. The resulting sequence, $257\to 56\to 49$, reproduces the published veto decisions on the same historical events; it is a reconstruction of the reported result rather than a second measurement. This common candidate population permits the BDT comparison below.

Background level in ${10}^{-7}\text{counts}{\text{keV}}^{-1}{\text{cm}}^{-2}{\mathrm{s}}^{-1}$

The prompt selection removes $201/257=78.2\%$ of the Micromegas-selected events and provides the largest reduction in the surface-background sample. The advanced selection removes $7/56=12.5\%$ of the post-prompt sample; the exact two-sided 90% binomial interval is $6.0\%$–$22.2\%$. The publication reports approximately 97% calibration retention for the advanced selection; cumulative efficiency is 79.4%, compared with 81.9% after the Micromegas selection. Together, the two veto stages remove $208/257=80.9\%$ of the X-ray-like background candidates, a reduction by a factor of 5.24. The final background level is the published $8.56\times {10}^{-7}\text{counts}{\text{keV}}^{-1}{\text{cm}}^{-2}{\mathrm{s}}^{-1}$. Table 4.10 uses 90% confidence intervals, while Ref. [17] quotes a statistical uncertainty of $1.22\times {10}^{-7}$ at one standard deviation.

The prompt veto rejects a candidate when a panel signal exceeds $5\text{MeV}$ in a $16\text{μs}$ interval around the Micromegas trigger. The advanced selection requires fewer than 13 panel signals over the full record, a summed energy below $7034\text{keV}$ in the record interval $23\text{–}53\text{μs}$, and fewer than 12 signals in $35\text{–}68\text{μs}$. The trigger is at $30\text{μs}$, so the latter intervals extend from $-7\text{μs}$ to $23\text{μs}$ and from $5\text{μs}$ to $38\text{μs}$ relative to it. The published multiplicity counts at most one reconstructed signal per panel; it differs from a count of all peaks in a waveform. Figure 4.35 shows the resulting selection sequence.

Prompt activity provides the largest background reduction; the long record adds rejection through multiplicity and activity extending beyond the trigger. The seven additional removals demonstrate background discrimination in the post-prompt X-ray sample. Without identifying those events as neutrons, their number cannot determine neutron efficiency or the neutron fraction of the residual background.

4.7.2 BDT comparison on the published candidates

To compare the BDT with the published additional rejection, we applied the frozen residual classifier to the same 56 candidates surviving the original prompt veto. We recovered multi-peak records for 19 events from the archived reconstruction and reconstructed the remaining 37 from their original acquisition files. The classifier retains its 163 veto features, channel map, and fitted weights; the original Micromegas selection and prompt-veto decisions define the common candidate population.

At the adopted score threshold, $𝑠\ge 0.9382$, the residual BDT rejects three candidates, all among the seven removed by the published advanced veto. The additional prompt-amplitude requirement of 500 ADC counts removes four candidates, two of which also exceed the BDT threshold. Their union removes five events; after that additional prompt requirement, the BDT adds only one rejection among 52 survivors. The adopted BDT gives less additional rejection and retains 99.90% of the first-period evaluation controls from runs 1696 and 1698 after the original Micromegas, energy-region, and prompt selections. This retention excludes the additional 500-ADC criterion and exceeds the approximately 97% reported for the published advanced selection.

To test the dependence on the operating point, we fixed a second threshold using only the original post-Micromegas, post-prompt calibration population in runs 1663 and 1666, with a nominal 97% retention target. The threshold $𝑠\ge 0.7545$ retains $7524/7756=97.01\%$ of these controls and $8175/8344=97.97\%$ in the independent runs 1696 and 1698. It rejects $7/56=12.5\%$ of the background candidates without using their scores or published advanced-veto labels to choose the threshold. Four rejected events coincide with the published selection and three differ; the rejected fraction is reproduced, while the event classification changes. Figure 4.36 compares the additional rejection and calibration retention at the two fixed thresholds.

Calibration retention varies between runs, including within the first period: the adjusted threshold retains 99.02% in run 1696 and 96.92% in run 1698. It retains 94.8% in run 1748 and 95.4% in run 1830. Separate 97% thresholds derived within the second and third periods retain only 94.0% and 93.8% in their reserved evaluation runs. The BDT therefore provides additional discrimination on the published candidates, but matching the seven removals does not establish the same event selection or a uniform calibration cost. These background candidates are not individually identified neutrons, so the comparison does not measure neutron efficiency. The adopted threshold and independent simulated-background yields remain those of Section 4.6.5.

The original score selects $3877$ measured events, or 0.50% of the full input and 5.88% of the clean subset. Removing the Micromegas-energy factor reduces the selected clean-background fraction to 4.78% and the neutron-template fraction from 17.76% to 10.74%. The population therefore depends appreciably on that factor, but the veto-only variant does not resolve the response mismatch: its selected data and neutron template have median all-peak counts of 85 and 10, or 12 and 6 for peaks above 200 ADC counts. These ${𝑆}_5$ populations differ from the original ${𝑆}_6$ selection examined below. Additional channel correlations, event rasters, and Micromegas projections are preserved in the independent veto-validation document.

4.7.4 Template agreement and control stability

For the original ${𝑆}_6$ selection, Figure 4.37 compares $3877$ measured events with $1722$ neutron-plus-noise events. Their median all-peak counts are 47 and 9, falling to 10 and 5 above 200 ADC counts. At that threshold, the median numbers of distinct channels are 4 and 5, while late-window peak counts are 7 and 4; multiple peaks can occur in one channel. Late-window amplitude-sum medians decrease from $6822$ and $2707$ ADC counts for all peaks to $2772$ and $2241.5$ ADC counts above threshold. Weak peaks account for much of the discrepancy, but the samples still differ in gain, noise, Micromegas energy, hit multiplicity, and topology. The amplitude sums are not calibrated deposited energies, and these unmatched population medians do not measure veto rejection in the published X-ray selection.

The calibration controls also depend on acquisition run (Figure 4.38). Over the full input, run 1339 has a median of 19 peaks, compared with 4–5 in the other four runs, while all runs have a median of one peak above 200 ADC counts. After prompt and burst removal, ${𝑆}_6$ selects 2.35% of run 1339 and 0.62%–0.74% of the others, despite the pooled 1% target. Removing Micromegas energy does not eliminate this dependence. When each run is omitted from the ${𝑆}_5$ calibration histogram and threshold calculation, the selected fraction in the omitted run is 2.66% for run 1339 and 0.57%–0.70% for the others. The simulated templates retain their pooled calibration-activity overlays, which may include donors from the omitted run, so this checks calibration-reference sensitivity rather than independently validating the full response.

The historical cosmic-neutron template predates the HENSA layer scan and lacks tagged-neutron calibration in the commissioned configuration. Its geometry and response differ from the prototype’s 59-position readout and 57 operational channels in panel dimensions, channel states, gaps, gains, and thresholds. Other showers, accidental activity, or correlated electronics signals can populate the late window; long-lived activation is a separate background channel from an in-waveform capture response. The neutron origin of the selected events therefore remains undetermined.

A quantitative comparison requires a common Micromegas selection, run-matched gains and channel states, and off-time or time-shifted controls, with test runs excluded from fitting, activity donors, and threshold setting. Together with competing particle templates and independent neutron-response constraints, these checks would support a neutron-fraction or rate inference. The present results instead establish the response and control-stability limits discussed next.

4.8 Response uncertainties and limitations

The inspected electron files and neutron-survivor processing used acquisition bin 234, whereas the veto conversion expected bin 262 (Table 4.8). This $5.6\text{μs}$ difference can change prompt rejection, so the affected archived yields remain conditional on the timing response. Testing its effect requires waveform reconstruction with the original TPC observables and generated exposure preserved; shifting exported peaks cannot recover waveform-edge or peak-finding effects.

Independent simulated histories do not imply independent measured activity: run 1347 informed hybrid development and supplies the nominal overlays. Peak-list overlays omit pulse overlap before reconstruction; the separate 37-channel optical-waveform study tests this response without supplying generated-primary exposure. Joint TPC-plus-veto retention must be measured on independent calibration events followed through both selections. Neither offline control acceptance nor the fixed-window cosmic-activity estimate in Section 5.4.3 establishes online live time.

The archived $-{25}^{\circ }$ to $+{25}^{\circ }$ inclination scan shows no resolved monotonic trend in processed entries per generated primary, but retains the historical neutron angular input. Its angular-measure discrepancy limits transfer to the final tracking exposure. Absolute background levels also require the source rate, complete generated exposure, and the selection’s energy interval and counting area; unresolved source rates permit only yields per generated primary.

4.9 Summary and outlook

Lead attenuates environmental photons but can generate secondary showers when energetic neutrons interact in it. Plastic scintillator and cadmium complement this shielding by detecting charged-particle activity and capture photons around the TPC. The simulations connect these processes to spatially distributed prompt and post-trigger signals, while showing that a physical capture need not produce a reconstructed veto peak.

The passive studies identify promising moderator arrangements for a future detector iteration. With $20\text{cm}$ of lead retained, the lowest observed energy-selected background is obtained with $10\text{cm}$ of BPE between $5\text{cm}$ of inner Pb and $15\text{cm}$ of outer Pb: ${𝐵}^{𝐸}/{𝐵}_{\text{Pb}}^{𝐸}=0.696$, a central reduction of 30.4%. This minimum was selected across the scan; its pointwise statistical intervals do not establish an optimal arrangement or the same reduction after the complete TPC selection. Within fixed outer dimensions, replacing the inner $5\text{cm}$ of lead with BPE gives a smaller central reduction in ${𝐵}^{𝐸}$, of approximately 9%; the additional LiF/PMMA layer has no established advantage over BPE alone. These neutron-only comparisons still require validation of thermal scattering and a joint assessment of photon attenuation and material backgrounds. The adopted geometry retains the full lead shield.

Adding active stages increases the probability of observing the surrounding neutron-induced shower. In the exported response population, three and four active stages with cadmium give any-tag fractions of 74.1% and 77.1%, respectively, without an additional X-ray-like TPC selection. The illustrative accidental-overlay model gives the larger sensitivity proxy to four layers, while three layers reduce the channel count and accidental opportunities after most of the conditional tagging gain has been obtained. Three layers are therefore an engineering compromise rather than a statistical optimum established by these simulations.

Measured TPC-track controls led us to preserve the fixed prompt-amplitude tag and add a residual neutron BDT, with its threshold set at a nominal 88% calibration-retention target. At comparable control retention, the hybrid gains 5.33 percentage points in simulated neutron tagging over the 455-ADC prompt reference (conditional 90% interval: 4.73–5.92), while tagging 339 rather than 340 of the 351 measured tracks. These development comparisons support the adopted rule without establishing experimental neutron efficiency or full agreement of the measured and simulated response. The documented $5.6\text{μs}$ acquisition-setting discrepancy can change veto decisions, so the affected archived background application remains conditional on its timing response.

The published IAXO-D0 surface measurement provides the experimental demonstration of background suppression: the selection reduces 257 Micromegas-selected candidates to 56 after the prompt veto and 49 after the advanced veto, for $52.1\mathrm{d}$ of exposure. The publication reports approximately 97% calibration retention for the advanced stage. On the same 56 candidates, the adopted residual BDT rejects three events; a comparison threshold set only on separate calibration data rejects seven, with different event membership and run-dependent calibration retention. This comparison establishes additional background discrimination, not neutron identification. The broader late-window study likewise finds activity distinct from calibration controls, but response differences and run dependence prevent an inference of neutron fraction or rate.

Further validation should reconstruct the affected veto response with the recorded acquisition settings and measure joint TPC-plus-veto retention on independent calibration data. Compact modules with wavelength-shifting fibers and silicon-photomultiplier (SiPM) readout offer a future design option [131], but comparison with the PMT prototype requires the response of the assembled system in a common mechanical envelope. Transfer to BabyIAXO also requires finalized geometry, channel states, and site-specific source inputs. Section 5 follows the adopted event decisions with generated-primary exposure accounting, reporting background levels where source normalization is validated and conditional yields otherwise, with radioactive decays outside the coincidence window treated separately.