5 Background Model

Introduction

In this chapter, we calculate how radioactive contamination and incident radiation produce low-energy background events in the IAXO-D1 Micromegas detector. We combine radiation transport, detector response, and event selection to obtain source-specific yields, which are converted into background levels where source activities or incident fluxes are established. The nominal calibration reference uses Ar–isobutane (1%) at $1.4\text{bar}$; source studies retaining different gas or response settings state those differences explicitly. These studies provide a basis for assessing background mechanisms and reduction measures; a BabyIAXO prediction additionally requires its xenon–neon response, optics, final veto configuration, and DESY source terms.

This study builds on the low-background Micromegas detector development for CAST [12]. Using the simulation and reconstruction methods of Section 3 and the veto selection of Section 4, we evaluate gas and surface contamination, radioactivity in detector and shielding materials, environmental radiation, and cosmic rays. Neutron-induced activities enter the radioactive-source model. The completed calculations provide a normalized radioactive-inventory subtotal and source-specific selection results. Together, these identify reduction priorities and the missing inputs needed to complete the model.

5.1 Simulation and analysis methodology

The background calculation follows each source from its activity or incident particle field to the events surviving the detector selection. We use REST-for-Physics [86] for radiation transport, detector response, and reconstruction, with the methods described in Section 3. Here, we specify how the source samples are compared and normalized.

5.1.1 Reference detector and normalization conventions

The nominal calibration reference is IAXO-D1 with Ar–isobutane (1%) at $1.4\text{bar}$. The source samples retain their recorded transport and response settings: several use 2% isobutane, and the conventional response can interpret pressure in atmospheres rather than bar. These differences are stated with the affected results; a common selection does not establish equal detector responses. Table 5.1 summarizes the reporting conventions.

5.1.1.1 Reading background estimates and upper limits

A background estimate gives the predicted contribution in the simulated sample; its Monte Carlo standard error describes sampling precision. A one-sided 90% upper limit bounds that contribution under a specified statistical model, including when no event survives. The superscript $†$ marks a conditional counting construction: Poisson for rare, effectively independent accepted events or a parent-correlated uncertainty calculation for populated decay chains.

The independent trial is a generated particle or complete decay history. One parent can produce several separated detector events, whose correlations are retained when estimating uncertainty. A bound on the probability of any accepted event is consequently not generally a bound on the mean accepted-event count. The generation stopping rule also enters the calculation: fixed-parent and target-saved-event samples have different sampling properties. A missing limit indicates an unresolved statistical construction; missing reconstruction or source normalization is identified separately.

For $𝑁$ generated histories, let ${𝐾}_{𝑗}$ count the selected descendants of parent $𝑗$, including ${𝐾}_{𝑗}=0$, and define $𝑆={\sum }_{𝑗}{𝐾}_{𝑗}$ and $𝑄={\sum }_{𝑗}{𝐾}_{𝑗}^2$. At fixed activity ${𝐴}_{𝑠}$, the estimate and its parent-correlated MC error are

For incident radiation, the generated-primary rate replaces ${𝐴}_{𝑠}$ and any sampling weights remain grouped by physical parent. In the Poisson working model, an observed count $𝑛$ has one-sided mean limit

The same source normalization converts this mean limit into a rate [52, 132]. Sparse material chains use the moment-matched count ${𝑛}_{\text{eff}}={𝑆}^2/𝑄$ and scale $𝑄/𝑆$; populated chains use a parent-correlated normal approximation [133]. Empty samples retain a positive rare-single-event limit; these working models do not constrain arbitrary unseen multiplicity tails. For joint radioactive-inventory bounds, source tail probabilities satisfy ${\sum }_{𝑖}{𝛼}_{𝑖}=0.1$ before the normalized bounds are added; individual 90% limits are not simply summed.

For environmental photons, we report an approximate one-sided 90% upper limit, marked $\ast$, from the estimated rate $\widehat{𝐵}$ and its physical-parent MC standard error ${𝜎}_{\text{MC}}$:

For the approximate shielding-plus-Pb sum, the independent MC errors are combined in quadrature before applying this expression. This Gaussian approximation describes the observed MC uncertainty; its 90% coverage has not been calibrated for finite weighted samples or unseen high-weight tails. It excludes source and model uncertainties and the unquantified bias from response-fit selection or data retention.

5.1.1.1.1 Common uncertainty convention.

Unless stated otherwise, intervals and limits hold the source activity or flux, geometry, nuclear data, detector response, and selection fixed. They exclude uncertainty in energy calibration, diffusion, noise, and transfer between gas or field conditions. More simulated events improve counting precision but do not resolve these response differences. This convention applies throughout the chapter; source-specific qualifications remain beside the affected results.

5.1.2 Workflow overview

Figure 5.1 connects source generation to the selected background. The restG4 transport supplies gas and scintillator deposits; restManager forms their respective charge and light signals and reconstructs the event observables. Measured waveforms enter at reconstruction. Separating these stages allows response settings to be tested without repeating transport when the required deposits and particle information have been saved.

Each source is followed through stored events, reconstruction, the TPC baseline, and any evaluated BDT and veto stages. Additional rejection is measured among survivors of the preceding stages, retaining their correlations. The final count is normalized with the generated exposure and the corresponding activity or incident-primary rate. Section 5.1.7 defines the adopted selection and its calibration checks. Delayed activation receives no veto credit from the earlier production pulse.

5.1.3 Source-specific simulations

Radioactive sources sample the specified material volume or contaminated surface. A mass-specific activity ${𝑎}_{𝑚}$ gives ${𝐴}_{𝑠}={𝑎}_{𝑚}𝑀$; a surface-specific activity ${𝑎}_{𝑆}$ gives ${𝐴}_{𝑠}={𝑎}_{𝑆}𝑆$. The simulated chain segment and any equilibrium assumption determine which decays that activity represents. Assumed gas and surface activities remain explicit scenarios.

External sources instead require energy and angular distributions and the rate of primaries crossing the generation surface. Environmental spectra come from measurements or auxiliary material-emission calculations. Cosmic inputs use particle-specific parameterizations or CRY spectra [91, 96]. The geometry-aware injection method developed in this work reduces transport of trajectories missing the apparatus [101]; its normalization is discussed with each field.

The gas is the sensitive target, with additional scintillator information where veto response is evaluated. Full-detector source calculations retain the shielding and veto; calibration-response studies can use a reduced chamber geometry, and the telescope study adds its entrance pipe. The source sections identify electromagnetic, radioactive-decay, and hadronic transport settings and their relevant limitations.

5.1.4 Background-model component inventory

Table 5.2 groups the sources by their physical normalization. Separate samples allow an activity, flux, or response assumption to be revised without changing unrelated components. Only non-overlapping, compatible contributions enter a subtotal.

5.1.5 Event types and detector-response chain

The selection uses reconstructed energy, tracks, and veto peaks, rather than ideal deposited energy or particle ancestry. Section 3 describes the conversion from deposits to waveforms and reconstructed observables. Truth information is used afterward to explain physical mechanisms and surviving candidates; it is excluded from the classifier inputs.

Figure 5.2 illustrates measured and simulated signals for two different muon events. The plotting procedure applies separate TPC and veto time offsets to each sample. Their displayed alignment therefore does not independently validate the hardware-trigger mapping or the quantitative timing response.

5.1.6 Analysis processes and observables

The conventional REST response includes gas diffusion and empirical broadening, scintillator quenching, effective light attenuation, and subsystem-specific electronics settings. The gas-recoil treatment is described in Section 2.1.3; Birks saturation affects highly ionizing scintillator deposits [126, 127]. The archived neutron diagnostic changes energy-weighted gas and scintillator signals by approximately 0.22% and 25.7%, respectively, under its recorded quenching settings. These averages do not determine selection efficiency.

The Micromegas energy scale uses the reconstructed $5.9\text{keV}$ ${}^{55}\text{Fe}$ peak; veto gains use through-going muons. Waveform reconstruction supplies energy, multiplicity, position, shape, and veto timing observables. The Garfield detector response is a separate comparison, not an additional selection stage.

5.1.7 X-ray selection and background-rejection strategy

The reference calculation selects compact, low-energy TPC candidates, applies the additional topology BDT, and evaluates the veto where a compatible response is available. Each source is followed through these stages before its surviving count is normalized. The resulting rates predict the response of the simulated detector; their transfer to laboratory data requires separate validation.

5.1.7.1 TPC baseline and adopted BDT

The baseline of Section 3.5.3 is common to data and simulation:

The full admitted readout is reconstructed before selection. An event must have usable native maximum-track observables, calibrated maximum-track energy in $2\text{–}7\text{keV}$, including both endpoints, exactly one track in each projection, and a maximum-track center at $𝑟<10\text{mm}$. No width, classifier, or veto requirement is included in the baseline. A surviving event is an X-ray candidate; its compact charge deposit does not identify the incident particle.

The additional selection is

The BDT combines the fifteen reconstructed shape variables in Table 5.3. Total energy, radius, track count, source identity, and transport truth are excluded. The archived model is retained, with ${𝑡}_{80}\simeq 0.694$ set using simulated ${}^{55}\text{Fe}$ candidates after the baseline; its full precision is preserved with the analysis configuration. Background counts do not determine this threshold.

For the conventional REST response, the calibration partition retains $12402/15502=80.00\%$; the separate original test partition retains $9224/11499=80.22\%$, with a 90% binomial interval of 79.59–80.83%. These are retrospective checks of historical samples. Missing or non-finite BDT inputs are rejected and remain in the baseline denominator; none occurs in these calibration or gas/cathode evaluations.

This 80% target is conditional on the calibration population. Figure 5.3 shows the fraction of baseline-selected test events that also pass the BDT in each reconstructed-energy bin, with the same threshold throughout. Acceptance is approximately 45–52% at reconstructed energies of $2\text{–}3.5\text{keV}$, compared with 81–83% at $5\text{–}7\text{keV}$. Energy is excluded as a direct BDT input, but the reconstructed shape variables can still depend on energy. The calibration-spectrum average therefore supplies neither an energy-independent signal efficiency nor a background survival factor. Every source supplies its actual post-BDT count, without division by 0.8. Gas and field differences retain their source-specific response-transfer qualifications. Cosmic evaluation excludes the production groups used to develop the classifier.

5.1.7.2 Veto selection and joint acceptance

The adopted veto is the fixed prompt-plus-neutron-BDT hybrid of Section 4.6.4, with a nominal 88% calibration-retention target. It follows the TPC BDT on the same candidates, as evaluated in Section 5.4.2. Source results without a compatible joint evaluation remain explicitly pre-veto.

The veto can reject correlated activity accompanying a prompt background, while unrelated particles or noise can also remove an X-ray. A later activation decay receives no coincidence credit from its production shower. The response, acquisition window, and activity controls must match the evaluated sample. The cosmic evaluation requires native acquisition coincidence and retains candidates whose physical timing cannot be established (Section 5.4.2).

The 80% TPC and 88% veto targets refer to different populations and are not multiplied. Joint signal retention must instead be measured among calibration events passing the preceding stages. Likewise, source-background survival is evaluated event by event, retaining TPC–veto correlations and the generated exposure.

5.1.7.3 Incident-photon signal efficiency

${}^{55}\text{Fe}$ calibrations test the response near $5.9\text{keV}$; uniform-energy photon simulations over $0\text{–}12\text{keV}$ provide a wider acceptance check. For the baseline, incident efficiency is

Non-interacting photons and reconstruction failures remain in the denominator. Acceptance among valid reconstructed events, such as Table 5.6, excludes these losses.

The historical uniform-photon selection, with its recorded response and calibration-like illumination, retains 24.49% over the $2\text{–}7\text{keV}$ true-energy interval. This historical efficiency awaits recomputation with the final baseline. It is neither a Garfield detector-response result nor a final axion efficiency, which also requires the appropriate gas, spectrum, optical illumination, and exposure and veto losses.

5.1.7.4 Response transfer and validation limits

Section 3 compares measured calibration with the REST and Garfield detector responses. Their remaining baseline-acceptance differences prevent treating improved spectral agreement as a validated background-rejection factor. The IAXO-D0 surface-veto measurements provide separate checks of the scintillator response and operating backgrounds [17], as discussed in Section 4. The background calculations retain their documented response versions. In the historical BDT transfer test, the simulation threshold retained only 13.85% of measured R02756 calibration events, against 80.22% in simulation. A measured-data or Garfield prediction therefore needs a matching calibration check and working point.

Separate width-based calibration illustrations and gas-matched response pilots remain auxiliary studies; their small or empty background populations do not establish a rejection factor.

5.1.7.5 Selection used in the source inventory

A further rejection claim requires fixing the response, model, and calibration thresholds before testing separate calibration and background events at their achieved signal acceptance. Previously inspected samples cannot become independent validation by being renamed. Muon-rich data constrain response but do not alone validate neutron rejection. The source tables therefore distinguish the adopted simulation prediction from laboratory validation and from results awaiting a compatible calculation.

5.2 Radioactive background

The radioactive-source inputs combine gas and surface inventories, material screening and neutron-induced activities. Screening measurements are collaboration inputs from the Zaragoza radiopurity teams and the Canfranc Underground Laboratory (LSC), mainly obtained with high-purity germanium detectors [16, 81, 134, 135]. Most supplied activities are upper-limit scenarios; the gas-isotope, inner-lead ${}^{210}\text{Pb}$ and readout ${}^{40}\mathrm{K}$ assumptions are stated with their source results.

5.2.1 Gas-borne and radon-related contamination

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

For argon mixtures, the relevant intrinsic isotope is ${}^{39}\text{Ar}$, a beta emitter with ${𝑄}_{𝛽}=565\text{keV}$ and ${𝑇}_{1/2}=269\mathrm{y}$. Natural atmospheric argon has a measured ${}^{39}\text{Ar}$ specific activity of $1.01\pm 0.08\text{Bq}{\text{kg}}^{-1}$ of natural argon [136]. The absolute rate therefore scales with the gas inventory and with the choice of atmospheric or underground argon; low-radioactivity underground argon has been measured to suppress ${}^{39}\text{Ar}$ by a factor $(1.4\pm 0.2)\times {10}^3$ relative to atmospheric argon [137]. ${}^{39}\text{Ar}$ beta decays generally produce extended ionization tracks rather than compact few-keV X-ray-like clusters. This motivates an additional topology selection, but its rejection must be evaluated on the reconstructed candidates rather than inferred from the true beta track.

${}^{85}\text{Kr}$ provides a second gas-borne beta-decay scenario for argon-based operation when krypton traces remain in gas distilled from air. Its half-life is $10.7\mathrm{y}$, with ${𝑄}_{𝛽}=687\text{keV}$, and its activity can vary strongly between gas batches and handling histories. GERDA measured $(0.36\pm 0.03)\text{mBq}{\text{kg}}^{-1}$ at the start of Phase II, whereas WARP reported an atmospheric-argon contamination corresponding to $(120\pm 90)\text{mBq}{\text{kg}}^{-1}$ [136, 138]. These are measurements of particular liquid-argon inventories, not interchangeable estimates of the activity in our gas. Distillation and subsequent handling can change the residual krypton content substantially; WARP also observed a commercial batch with three times its quoted contamination [136]. Without an assay of the actual batch, the background model adopts $300\text{mBq}{\text{kg}}^{-1}$ of argon as a conservative working scenario, obtained from the WARP central value plus twice its quoted uncertainty. This choice is not a confidence limit on an unknown gas batch, nor a guaranteed upper bound on commercial argon. For the simulated argon inventory it gives a post-BDT background of $(3.47\pm 0.59)\times {10}^{-9}$ counts keV${\begin{array}{}\end{array}}^{-1}$ cm${\begin{array}{}\end{array}}^{-2}$ s${\begin{array}{}\end{array}}^{-1}$, with the uncertainty here due to simulation statistics. The contribution is subdominant in the adopted background inventory, but it is not intrinsically negligible: its prediction scales linearly with the unknown activity. In particular, the reduction of ${}^{39}\text{Ar}$ in underground argon is not applied to ${}^{85}\text{Kr}$.

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

The radon components are separated because they have different normalizations. ${}^{218}\text{Po}$, the first short-lived daughter of ${}^{222}\text{Rn}$, is often positively charged after production and can drift toward the cathode under the detector field. This motivates a cathode-collection scenario: NEXT has measured radon-induced backgrounds from ${}^{214}\text{Bi}$ daughters deposited on the cathode of its gaseous TPC [139]. It does not establish complete collection in IAXO-D1, whose gas, field and geometry differ. Neutralization, gas motion and deposition on other surfaces can leave a different spatial distribution; the cathode-only case is therefore not assumed to be a conservative bound. Long-lived ${}^{210}\text{Pb}$, with ${𝑇}_{1/2}=22.3\mathrm{y}$, can then remain on detector surfaces and is not generally in equilibrium with the instantaneous radon activity. Its inventory can retain the history of radon exposure during fabrication, storage and assembly, including periods without an operating electric field. Radon-progeny deposition studies explicitly address this persistent surface contamination [140]. Thus Pb-210 on copper now hidden behind a PTFE liner can represent exposure before assembly; longevity does not itself redistribute the isotope over every surface. The model therefore treats gas ${}^{222}\text{Rn}$, cathode ${}^{218}\text{Po}$, cathode ${}^{210}\text{Pb}$, and vessel or surface ${}^{210}\text{Pb}$ as separate source hypotheses. Ion drift and plate-out are not dynamically simulated: their effect is represented by these distinct source locations and activity assumptions. The gas source contains the initial ${}^{222}\text{Rn}$ decay; the short-lived ${}^{218}\text{Po}$ samples follow the subsequent chain up to ${}^{210}\text{Pb}$, whose decays and descendants are simulated separately. This division permits different gas and surface activities without counting the same chain segment twice. The same concern about persistent surface contamination motivates dedicated ${}^{210}\text{Pb}$ screening with Micromegas detectors [141]. The source taxonomy is summarized in Table 5.4; Figure 5.4 shows exactly which decay-chain segments and source locations are simulated separately.

5.2.1.0.1 Testing the short-lived daughter location.

The cathode reference is supplemented by a matched three-location comparison: ${}^{218}\text{Po}$ starts either uniformly in the active gas, in the original cathode-window aluminum volume, or on the gas-facing cylindrical PTFE wall. The same short-chain stopping rule, transport physics, detector response and selection are used in all three cases. These are source-location scenarios, not three additional full radon activities. The wall case does not cover every endcap or electrode, and no field-driven ion migration between decays is implied.

Let ${𝑌}_{𝑗}$ be the accepted-event yield per generated short-chain parent for $𝑗\in \left\{\text{gas},\text{cathode},\text{wall}\right\}$. A mixture with one specified short-chain activity ${𝐴}_{\text{short}}$ is

The pure cases and their mixtures test sensitivity to the unknown location fractions without fitting them to the sparse background data. The largest pure-case yield bounds these mixtures only within this restricted model, not all possible daughter-migration histories. In a stationary model supplied solely by radon decaying in the active gas, ${𝐴}_{\text{short}}$ would be tied to that radon activity through retention and removal, rather than assigned a second independent inventory. The existing cathode surface benchmark is kept separate from this connected interpretation. Long-lived Pb-210 remains a distinct exposure-history hypothesis.

The completed comparison uses $4000$ generated parents per location. After the final baseline, $64$ cathode events, one gas event and no wall events remain; the unchanged BDT retains $12$, zero and zero, respectively. The cathode post-BDT response is $(1.91\pm 0.55)\times {10}^{-4}\text{counts}{\text{keV}}^{-1}{\text{cm}}^{-2}{\mathrm{s}}^{-1}{\text{Bq}}^{-1}$, where the error is the parent-cluster Monte Carlo standard error. This finite comparison supports the cathode as the more consequential of the three tested starting locations; the empty gas and wall selections do not establish zero response or exclude all other plate-out distributions. The boundary-recoil and gas-response limitations stated above remain. These matched alternatives are not added to the reference inventory below.

5.2.1.0.2 Application of the common analysis chain.

The gas and cathode samples have complete file coverage and use the final TPC baseline and frozen simulation BDT, without veto rejection. Transport uses argon–2% isobutane at $1.4\text{bar}$, while the calibration-tuned response uses 1% isobutane and nominal pressure 1.4 atm. The results remain conditional on this transfer between gas conditions. Equation (5.1) converts the selected counts to a response per becquerel using all generated parents and their correlated descendants. Table 5.5 gives the complete selection sequence, and Table 5.6 converts the selected counts into a response per unit source activity.

After the BDT, cathode ${}^{218}\text{Po}$ has 160 selected events from 159 parents and cathode ${}^{210}\text{Pb}$ has 1169 from 1168, requiring parent-correlated errors and limits. The 26 argon and 35 krypton events all have distinct parents; their limits use the Poisson working model. The radon single-event limit additionally accounts for its generation stopping rule; all samples retain daughter decays and secondary transport.

Absolute rates multiply these responses by the independently specified activities. The geometry and Ar2 mixture imply an argon mass of $0.519\mathrm{g}$. Table 5.7 gives an absolute background prediction for every activity scenario in Table 5.8. The cathode scenarios refer to one projected 15 mm-radius source disk, not the TPC fiducial area used to normalize the output rate. The atmospheric ${}^{39}\text{Ar}$ prediction includes the literature activity uncertainty [136]; the underground-argon alternative adopts a fixed reduction factor of 1400. The krypton reference and the radon and surface benchmarks are held fixed for their conditional statistical limits. These benchmark activities are not detector assays; the argon alternatives are not added together.

5.2.1.0.3 Cylindrical-wall contamination.

Wall activity is treated separately from the cathode source. Figure 5.5 distinguishes contamination on the gas-facing PTFE surface from contamination on the copper behind the 1 mm PTFE liner. Both models retain the full decay chain and secondary transport and use the same response, TPC baseline and additional simulation BDT as the other source components. They differ only in the specified source surface; neither includes endcaps or assumes a measured implantation-depth distribution. The completed fixed-parent production contains 500 000 parent decays per location. After the final baseline and BDT, 11 PTFE-surface events and one copper-surface event remain. For an explicitly illustrative surface activity of 1 mBq m${\begin{array}{}\end{array}}^{-2}$, the corresponding background estimates are $(1.32\pm 0.40)\times {10}^{-11}$ and $(1.22\pm 1.22)\times {10}^{-12}$ counts keV${\begin{array}{}\end{array}}^{-1}$ cm${\begin{array}{}\end{array}}^{-2}$ s${\begin{array}{}\end{array}}^{-1}$. These are alternative location benchmarks, not measured wall activities, and remain outside the known-inventory subtotals in Section 5.5.

Surface contamination requires an implantation-depth or plate-out distribution as well as an activity. Short-lived daughters need not remain at the original gas-decay position, and long-lived ${}^{210}\text{Pb}$ is not in equilibrium with the instantaneous radon concentration. Existing alpha and gas-handling controls can constrain these source classes without fitting each activity independently to the sparse X-ray background data. Changes in gas recirculation and radon suppression during IAXO-D1 operation at LSC affected the alpha and low-energy backgrounds [82, 142, 143].

5.2.2 Neutron-induced cobalt in copper

Neutron reactions in the copper components produce radioactive cobalt whose later decays can contribute to the detector background. We focus on ${}^{58}\text{Co}$ and ${}^{60}\text{Co}$: these two ground states account for every event passing the baseline and BDT in the reference calculation. The accepted background depends on both activity and the decay radiation reaching the gas.

The reference assumes continuous irradiation by the Zaragoza outdoor HENSA field above $1\text{MeV}$, with scalar fluence rate $6.920\times {10}^{-3}{\text{cm}}^{-2}{\mathrm{s}}^{-1}$. This is a proxy for sea-level DESY operation rather than a site measurement. Moderation and capture inside the geometry are included, but lower-energy incident neutrons are absent. The activity estimate assumes zero initial induced inventory, complete retention and fixed target composition, and follows radioactive daughter feeding. Table 5.9 gives the cobalt activities after five years and at formal equilibrium, including daughter feeding. Formal equilibrium assumes unlimited irradiation; the finite-time activities describe the buildup during operation. For a retained isotope produced at constant rate $𝑃$, without daughter feeding, $𝐴(𝑡)=𝑃(1-{𝑒}^{-𝜆𝑡})$ with $𝜆=ln2/{𝑇}_{1/2}$; the numerical activities include the feeding delays along each decay chain.

Surface activation has been observed in copper later assayed underground: the TREX-DM sample measured at Canfranc shared the vessel’s prior surface-exposure history [144]. For comparison with formal equilibrium, two independent controlled-exposure studies give central sea-level saturation activities of $0.60\text{–}0.80\text{mBq}{\text{kg}}^{-1}$ for ${}^{58}\text{Co}$ and $0.34\text{–}0.46\text{mBq}{\text{kg}}^{-1}$ for ${}^{60}\text{Co}$, after altitude and decay corrections [145, 146]. Our equilibrium activities averaged over approximately $69.6\text{kg}$ of copper in the reference geometry are $1.07\text{mBq}{\text{kg}}^{-1}$ and $0.873\text{mBq}{\text{kg}}^{-1}$, respectively. These comparisons establish the activity scale; the different incident fields and shielding prevent treating them as a validation of the production model.

The cobalt activities enter the same decay calculation used for screened contamination. For each cobalt state $𝑖$ and copper source volume $𝑣$, the activity ${𝐴}_{𝑖,𝑣}(𝑡)$ in Bq multiplies the selected response per Bq, ${𝑅}_{𝑖,𝑣}$:

where ${𝜖}_{𝑖,𝑣}$ is the mean selected count per generated decay, $\mathrm{\Delta }𝐸=5\text{keV}$ and ${𝐴}_{\text{fid}}=𝜋{\text{cm}}^2$. The decay response uses the common baseline and fixed TPC BDT; the source state, physical placement, geometry and detector response must match before a response is reused. Activity already included in screening inputs, particularly ${}^{60}\text{Co}$, must be reconciled before adding an induced contribution.

The modeled equilibrium contribution from cobalt in copper is $2.31\times {10}^{-10}$ counts keV${\begin{array}{}\end{array}}^{-1}$ cm${\begin{array}{}\end{array}}^{-2}$ s${\begin{array}{}\end{array}}^{-1}$, adopted in the final summary. The later decays lose the production interaction’s scintillator coincidence, so no veto rejection is assigned. This remains a partial activation estimate: incomplete response coverage prevents establishing that the other radionuclides are negligible, and production and source-model uncertainties are unquantified. An independent response study also selects ${}^{62}\text{Cu}$ and ${}^{64}\text{Cu}$, which dominate its restricted complete-cell diagnostic, $(2.57\pm 1.81)\times {10}^{-9}$ in the same units at equilibrium. Other cells fail response qualification, so that diagnostic is neither a full rate nor a lower bound and does not establish an increase relative to the reference. Its nominal MC error excludes fit-selection bias and source/model uncertainties; the reference estimate remains adopted, without a main-budget upper limit.

5.2.3 Detector materials

Radioactive contaminants in nearby materials can produce low-energy deposits in the gas through their emitted particles and secondary radiation. We evaluate ten detector components, with decays distributed throughout each source volume. Their masses follow the transported geometry, including only the PET film of the aluminized entrance window; no separate aluminum-coating activity is supplied. Table 5.10 gives the adopted specific activities from the collaboration inventory [82]. Most are screening-limit scenarios, while readout ${}^{40}\mathrm{K}$ uses reference values; unspecified assay uncertainties and confidence levels prevent treating this inventory as a set of measured central activities. Gas activity, surface plate-out, telescope contamination, electronics, and lead shielding are evaluated separately.

Neutron-induced activities from Section 5.2.2 enter the same decay-response calculation as screened activities. Each activity is assigned to its physical source volume; reusing a response requires matching the isotope state, geometry and decay-chain treatment. The screened-material subtotal and the partial activation result are reported separately because existing ${}^{60}\text{Co}$ screening inputs can overlap the induced inventory and the response geometries differ.

The additional ${}^{235}\mathrm{U}$ inputs are $0.093\text{Bq}{\text{kg}}^{-1}$ for copper readout, $0.046\text{Bq}{\text{kg}}^{-1}$ for Kapton and $0.0029\text{Bq}{\text{kg}}^{-1}$ for PET. PET also uses $0.0059\text{Bq}{\text{kg}}^{-1}$ of ${}^{226}\text{Ra}$, $0.0036\text{Bq}{\text{kg}}^{-1}$ of ${}^{228}\text{Th}$ and $0.002\text{Bq}{\text{kg}}^{-1}$ of ${}^{137}\text{Cs}$; the first two are alternative full-chain hypotheses. Table 5.11 combines the supplied, non-overlapping activities with their simulated responses. For the adopted activities, the selected subtotal is $(2.33\pm 0.11)\times {10}^{-8}$, with a conditional one-sided 90% upper limit of $8.16\times {10}^{-8}$${\begin{array}{}\end{array}}^{†}$, in counts keV${\begin{array}{}\end{array}}^{-1}$ cm${\begin{array}{}\end{array}}^{-2}$ s${\begin{array}{}\end{array}}^{-1}$. The uncertainty on the estimate is the parent-correlated MC standard error. The copper readout, Kapton readout, and PET film supply 80.6%, 14.2%, and 4.7% of the central estimate, respectively; the BDT reduces the baseline subtotal by a factor of 4.68. These rankings apply to the supplied activity scenarios. The upper limits show the limited sensitivity of sparsely populated samples: zero selected events do not imply zero background.

The subtotal includes 35 non-overlapping sources from the 54 simulated component–isotope hypotheses. Full-chain ${}^{226}\text{Ra}$ and ${}^{228}\text{Th}$ hypotheses overlap with their ${}^{238}\mathrm{U}$ and ${}^{232}\text{Th}$ parent chains and remain alternatives; missing activities are excluded, not set to zero. The assumed chain activities and daughter retention do not establish equilibrium in the installed detector. All generated parents enter the exposure, with their decay subevents grouped for uncertainty calculations. The common baseline and fixed BDT are applied to each reconstructed event with no veto rejection. The REST response and calibration threshold are transferred to the transported argon–2% isobutane mixture; their nominal calibration acceptance is not independently validated for these gas and field conditions. The subtotal and its statistical limit are conditional on those activity and response assumptions and do not bound unassayed contaminants or the complete detector background.

5.2.4 Telescope and X-ray optics contamination

Radioactive decays near the X-ray optics can emit photons along the bore and into the detector through its magnet-facing aperture. We evaluate this separate source using a thin emission disc at the far end of the telescope pipe (Figure 5.6).

The telescope study uses the BabyIAXO mechanical geometry, which includes the telescope-side pipe. The source disc has radius $275\text{mm}$, thickness $0.1\text{mm}$, and its center is at $𝑧=5512.15\text{mm}$ relative to the chamber origin. It represents the emission positions in vacuum, without modeling the optics material or self-absorption. For uniform projected activity, ${𝐴}_{𝑖}={𝑚}_{\text{optics}}{𝑎}_{𝑖}$, where ${𝑎}_{𝑖}$ is the isotope-specific activity per unit mass.

The chamber, detector pipe, electronics box and passive shielding match the IAXO-D1 material definitions and placements; the veto arrangement differs. The BabyIAXO name here selects the mechanical layout: the active gas remains argon–isobutane $2\%$ at $1.4\text{bar}$. These shared detector components do not establish equal telescope-background rates, because scattering and angular acceptance depend on the surrounding geometry.

Photons from ${}^{238}\mathrm{U}$, ${}^{232}\text{Th}$ and ${}^{40}\mathrm{K}$ are sampled within a ${15}^{\circ }$ cone towards the detector to improve sampling efficiency. Table 5.12 includes the isotropic-cone factor

and therefore reports only that cone’s contribution per becquerel of isotropic activity. Photons emitted outside the cone can scatter towards the detector; this complementary contribution remains unconstrained. The ${}^{40}\mathrm{K}$ sample uses a $1460.822\text{keV}$ photon with a yield of 0.1067 photons per decay. The selected photon spectra for ${}^{232}\text{Th}$ and ${}^{238}\mathrm{U}$ have yields of 2.69742 and 3.59079 photons per parent-chain decay, respectively, under the adopted chain-equilibrium convention.

The common TPC baseline and BDT use the fixed calibration response, transferred to these Ar2 conditions; the Ar1 calibration acceptance is not independently established for this mixture. The transport pressure of $1.4\text{bar}$ and response pressure of 1.4 atm retain the same transfer limitation. No veto rejection is applied because the IAXO-D1 readout map does not cover every BabyIAXO veto placement; the full veto geometry remains in transport.

The selected ${}^{40}\mathrm{K}$ sample contains nine independent photon histories, so its upper limit uses the sparse-count working model rather than the populated approximation used for uranium and thorium. Controls with source offsets of $-100$, $0$ and $+100$ mm, including IAXO-D1 with the same telescope added, retain only one baseline event from nine gas interactions. They cannot establish equivalent background rates or negligible incidence outside the cone. The telescope therefore remains outside the absolute budget: it requires optics masses and activities, compatible response validation and the angular complement.

5.2.5 Front-end electronics

The front-end electronics must be placed close to the Micromegas readout to preserve signal quality, but they contain materials that are harder to radiopurify than bulk copper, Kapton, or PTFE. Their background contribution was therefore treated separately from copper and readout-plane contamination. The analysis follows Section 5.1.2; the card-induced rate is evaluated after the final TPC baseline and then the BDT, retaining the baseline comparison and applying no veto rejection. The simulation described here corresponds to the four front-end cards represented in the IAXO-D1 detector model, without including the flat cables or other service elements. The activity model follows the component-level radiopurity study of the BabyIAXO electronics, used here as a collaboration input rather than as an original measurement of this thesis [81, 147].

The simulated source regions were the four electronics-card bodies located near the Micromegas readout. For each card and each isotope, radioactive decays were generated uniformly inside the corresponding card volume and transported with the same Geant4 physics configuration used for the rest of the intrinsic-background model. The isotopes included in the present production were ${}^{40}\mathrm{K}$, ${}^{60}\text{Co}$, ${}^{137}\text{Cs}$, the ${}^{232}\text{Th}$ chain, the ${}^{235}\mathrm{U}$ chain, and the ${}^{238}\mathrm{U}$ chain. The activities assigned to the four cards are summarized in Table 5.13. The optional contribution from the $10\mathrm{\Omega }$ resistors was not included in the nominal normalization because those components were not part of the original low-background board design considered in the reference electronics study.

The normalization was performed at the level of generated decays. For each isotope–card pair, the event weight was defined as

where ${𝐴}_{𝑖,𝑐}$ is the activity assigned to isotope $𝑖$ in card $𝑐$, and ${𝑁}_{𝑖,𝑐}^{\text{gen}}$ is the number of generated decays in that production. This choice is important because only a small fraction of the decays produce a stored detector event, and normalizing to saved or reconstructed entries would bias the rate estimate. Table 5.14 follows the six isotopes across the four cards through the cumulative baseline selection. Of the 121 baseline events, 37 pass the BDT; generated decays with no stored detector event remain in the normalization.

The response preserves the original argon–2% isobutane composition, but transfers the calibrated diffusion, shaping and energy-response parameters without fitting the background events. The transport pressure is $1.4\text{bar}$, while the retained response convention uses 1.4 atm; the $1.3\%$ difference is also part of this conditional transfer. The baseline definition is unchanged, whereas the absolute detector response and transfer of the Ar1-calibrated BDT threshold remain explicit modeling assumptions. The latter is not a demonstration of 80% calibration acceptance under the Ar2 conditions.

Applying the per-card activities to their verified generated-decay exposures gives the conditional baseline estimate

using the $2\text{–}7\text{keV}$ window and the $𝜋{\text{cm}}^2$ fiducial area. The uncertainty is the Monte Carlo standard error, with decay subevents grouped by their generated parent; it does not include activity or response-transfer uncertainties. The large ${}^{238}\mathrm{U}$ activity makes that chain the dominant contribution in this source scenario.

The actual BDT survivors give the conditional selected-background prediction

Table 5.15 gives the isotope contributions using the same per-card activities and generated-parent exposures. The quoted error is a parent-correlated MC standard error, not a 90% interval. The sparse-count treatment of Section 5.1.1.1 gives the card-only one-sided 90% working-model upper limit

The four cards have different simulated exposures, so their events are weighted separately before combining the predictions. The limit also includes card–isotope combinations with no selected event: a zero count does not establish a zero contribution. For the six-isotope subtotal, the statistical error budget is shared among all 24 card–isotope combinations, rather than adding six individual 90% limits and calling the sum a 90% limit. This deliberately conservative combination explains why the upper limit is much larger than the central estimate. All 37 selected events come from distinct generated parents; the $†$ still marks an assumed rare-event counting model, not evidence that multiple accepted descendants are impossible. This prediction is not corrected by dividing by the X-ray acceptance.

These results should be interpreted as the card-only electronics contribution for the current detector model and activity vector. They do not yet include flat cables, possible connector materials, or a detailed separation of the individual board components within each card volume. Those refinements are relevant for a future BabyIAXO background model because the activity is not uniformly distributed among components: the ${}^{238}\mathrm{U}$ activity is concentrated mainly in ceramic capacitors, while resistors, diodes, and chips contribute different isotope mixtures. The card-only result now uses the final selection, but the conditional response transfer and incomplete service-material geometry still prevent it from establishing that all front-end electronics are subdominant in the full background inventory. Within the adopted activity scenario, ${}^{238}\mathrm{U}$ supplies about 60% of the selected central estimate, followed by ${}^{232}\text{Th}$ at about 39%. The practical priority is therefore to constrain these activities and their locations in the cards, rather than treating the small unweighted event counts as evidence that the electronics can be neglected.

5.2.6 Shielding

The lead shield is the most massive passive component around the detector. Its radioactivity is therefore a background source as well as a means of suppressing external radiation. For photons and electrons, self-absorption makes the detector-facing lead particularly important. The calculation below applies the final TPC baseline and simulation BDT of Section 5.1.2; it does not credit any veto rejection.

The reference source is ${}^{210}\text{Pb}$, distributed uniformly through the innermost $10\text{mm}$ of lead. The adopted activity is

This is a lead-activity scenario, not a measurement of the installed shield. The copper liner and all transported decay products are retained. Because lead activity varies with material history, lower-activity inner lead scales this source term directly at fixed geometry.

The preserved ${}^{210}\text{Pb}$ transport uses the final, unmasked TPC reconstruction, baseline and BDT. Only reconciled exposure enters the normalization, including decays with no stored detector event. As for the other material sources, the Ar/2% isobutane response and BDT threshold use the explicitly conditional calibration transfer described in Section 5.1.7.1; the result is not an independent validation of this gas response.

The result is a prediction for the inner shell. Escape-particle diagnostics support a surface-dominated electromagnetic contribution, but do not establish convergence of the selected rate as deeper lead is included. A full-shield prediction therefore requires additional depth shells.

5.2.6.0.1 Copper liner and low-activity inner lead.

The lead and copper have complementary roles. Lead attenuates external radiation, but its own radioactive decays produce electrons and photons. The copper box provides a cleaner inner barrier: it stops escaping charged particles and attenuates lead fluorescence and low-energy bremsstrahlung. Copper can itself fluoresce near $8\text{keV}$, so its presence does not eliminate the need to model secondary radiation [16]. Its intrinsic radioactivity is included separately in the detector-material inventory.

The copper benefit is evaluated by comparing the nominal geometry with a control in which the box is replaced by air, leaving the lead source and all other detector components unchanged. Both samples use the common TPC baseline and simulation BDT, without veto rejection. After the baseline selection, the copper reduces this contribution by a factor of 3.0 (two-sided 90% interval: 1.3–6.3). This comparison includes the actual openings and unequal wall thicknesses, rather than treating copper as a uniform absorber.

After the BDT, the smaller air-control sample has no surviving events and gives an individual 90% upper limit of $\le 1.54\times {10}^{-8}{}^{†}$ $\text{counts}{\text{keV}}^{-1}{\text{cm}}^{-2}{\mathrm{s}}^{-1}$. The nominal copper result is $(6.02\pm 1.90)\times {10}^{-9}$ in the same units. The samples therefore demonstrate a benefit before the BDT, but do not resolve the reduction after it; the baseline factor must not be applied again to the final background budget.

The remaining lead contribution can also be reduced at its source. For a Roman-lead sample, Pattavina et al. report a ${}^{210}\text{Pb}$ activity below $0.715\text{mBq}{\text{kg}}^{-1}$ at 90% confidence [148]. Using that assay ceiling as a fixed design benchmark, rather than as a measurement of the proposed shield, Table 5.18 compares ordinary and archaeological lead in the same inner 10-mm shell. This changes the source activity, not the attenuation properties or event selection. It does not rescale the ordinary lead behind the replacement layer, or the independent U/Th/K contributions.

The useful thickness depends on how far into the lead the radiation reaching the detector originates. A complementary planar transport study varies the thickness and position of the low-activity layer, retaining ordinary lead elsewhere and the copper on the detector side. It compares a detector-facing layer with the same amount of low-activity lead buried deeper in the shield. The preferred ordering, from outside towards the TPC, is ordinary lead, low-activity lead, then copper: placing ordinary radioactive lead inside the clean layer would leave an unprotected nearby source. The thickness at which the remaining photon flux is reduced by 90% is about 8.6 mm for a 10-mm copper layer. Replacing the first 10, 20 and 30 mm of lead leaves, respectively, $7.5\pm 0.3$%, $1.7\pm 0.2$% and $0.5\pm 0.1$% of the ordinary-lead photon flux. These flux reductions guide the material choice, but are not substitutes for background rates after TPC selection.

On this basis, 1 cm of low-activity lead immediately outside the copper is a useful initial design benchmark; 2 cm provides further suppression where space and material availability permit. These are not demonstrated optima for the finite shield. Their benefit concerns lead-induced electromagnetic background, not a demonstrated reduction of the complete background budget or the neutron component. The reference budget therefore retains ordinary lead; the low-activity configuration is an alternative, not an additional contribution.

5.2.6.0.2 Other lead contaminants.

The reference specific activities are $3.3\times {10}^{-4}\text{Bq}{\text{kg}}^{-1}$ for ${}^{238}\mathrm{U}$, $1.0\times {10}^{-4}\text{Bq}{\text{kg}}^{-1}$ for ${}^{232}\text{Th}$, and $1.2\times {10}^{-3}\text{Bq}{\text{kg}}^{-1}$ for ${}^{40}\mathrm{K}$. For the same $38.8624\text{kg}$ shell these correspond to $12.8\text{mBq}$, $3.89\text{mBq}$, and $46.6\text{mBq}$, respectively. Their historical selected rates cannot be converted into final-chain results by changing the normalization area: the archived response used a different gas configuration and selection, and unfiltered source files were not located. Fixed-parent replacement productions retain the complete radioactive-decay physics and apply the same response and BDT as the ${}^{210}\text{Pb}$ calculation. Table 5.19 gives the results from $8\times {10}^7$ parents for each of ${}^{238}\mathrm{U}$ and ${}^{232}\text{Th}$, and $8\times {10}^8$ for ${}^{40}\mathrm{K}$. These contributions enter the radioactive-inventory subtotals in Section 5.5. Failed attempts are excluded; their complete replacements supply the corresponding exposure exactly once. No absolute ${}^{235}\mathrm{U}$ or ${}^{60}\text{Co}$ contribution is inferred without an adopted activity.

5.2.6.0.3 Neutrons produced within the shield.

Neutrons can reach the TPC from deeper lead, so their source model covers the full $2088.4\text{kg}$ shield rather than only its inner shell. The spontaneous-fission reference uses ${}^{238}\mathrm{U}$ specifically: $0.33\text{mBq}{\text{kg}}^{-1}$, or $689\text{mBq}$ in total. Its fission branch of $5.45\times {10}^{-7}$ [149] and mean multiplicity of $2.01$ neutrons [150] give ${𝑄}_{𝑛}=7.55\times {10}^{-7}{\mathrm{s}}^{-1}$.

The $(𝛼,𝑛)$ calculation includes the equilibrium ${}^{238}\mathrm{U}$ chain (with ${}^{234}\mathrm{U}$), ${}^{232}\text{Th}$ and natural-uranium ${}^{235}\mathrm{U}$. Direct reactions on natural lead are energetically closed for these alphas, but an escaping alpha can produce neutrons in copper or air. Evaluated decay data, stopping powers and reaction spectra define deliberately enlarged sources [151, 152]. Both fill the entire simulation box, even where their target material is absent, at the largest alpha exposure allowed by the uniform-lead slowing-down model. The ${}^{210}\text{Po}$ term assumes $80\text{Bq}{\text{kg}}^{-1}$ of equilibrium ${}^{210}\text{Pb}$ throughout the lead, explicitly a screening scenario rather than a measured outer-lead activity. Copper-liner bulk contamination is also included.

The completed $(𝛼,𝑛)$ production contains $1.2\times {10}^6$ source neutrons; none survives the final TPC baseline. Combining its three source limits with the independent fission reference gives ${𝐵}_{𝑛,\text{shield}}\le 2.81\times {10}^{-10}$ $\text{counts}{\text{keV}}^{-1}{\text{cm}}^{-2}{\mathrm{s}}^{-1}$ at the stated 90% level. This is a conservative, model-dependent upper bound, not evidence of zero neutron background or of additional BDT rejection.

The neutron sources use the same final reconstruction, baseline and simulation BDT as the other shielding terms, without veto rejection. The limits assume the stated composition, equilibrium and isotropic-neutron model; unknown impurities and unsupported surface contamination are not covered. This calculation is distinct from environmental neutrons and is not added again to inclusive decay-chain histories.

5.3 Environmental background

The environmental-photon model describes radioactivity in the surroundings, constrained by the NaI measurements. The environmental-neutron study approximates an isotropic field from the surroundings, including radiogenic emission and neutrons scattered or moderated by the ground. HENSA measures an inclusive neutron field containing terrestrial and atmospheric contributions [153]; its use here and in Section 5.4 does not establish disjoint environmental and cosmic populations. For BabyIAXO, the current working scenario is an outdoor, on-surface DESY location [15, 65]. The results in this section are detector-response estimates using the available laboratory source terms and are not a final DESY environmental-background budget.

The shielding and neutron calculations use the closed-pipe reference geometry; the photon study also compares two open-pipe geometries. All use $99\%$ argon–$1\%$ isobutane in transport and the conventional reference response. The transport material is defined at $1.4\text{bar}$, whereas REST interprets the response pressure as $1.4\text{atm}$; the resulting $1.325\%$ pressure difference remains a response-transfer limitation.

5.3.1 Environmental photons

5.3.1.1 Incident spectrum

We infer the incident spectrum from a joint fit to two NaI measurements, acquired for $92\mathrm{h}$ without lead and $240\mathrm{h}$ with lead bricks. A positive continuum over $0.25\text{–}2.6145\text{MeV}$ and nine independent gamma lines are folded through the simulated NaI response. The fit assumes no external photon contribution to the lead-shielded control and gives an isotropic scalar fluence of $2.47{\text{cm}}^{-2}{\mathrm{s}}^{-1}$, with a central 68.27% statistical interval of $2.459\text{–}2.489{\text{cm}}^{-2}{\mathrm{s}}^{-1}$. This normalization is conditional on the control assumption; it excludes calibration drift, incomplete lead coverage and source-model uncertainty.

Figure 5.9 shows the fitted source and its response against the lead-control-subtracted data; the fit itself uses the original counts from both measurements. The 6.7% root-mean-square fractional residual in the unshielded spectrum exceeds its statistical uncertainty. Alternative calibration and control choices give fitted fluences of $2.44\text{–}2.64{\text{cm}}^{-2}{\mathrm{s}}^{-1}$; this sensitivity is not included in the statistical interval.

5.3.1.2 Generation and transport

We treat photons incident on the shielding and around the entrance pipe separately, using the same incident spectrum and a local isotropic field inside the outer veto. For the pipe comparison, we remove the copper cap and sample only the four lateral faces of the surrounding virtual box, as shown in Figure 5.10. We compare air around the pipe with Pb filling this space between the shielding opening and the pipe end; the vacuum bore remains open in both cases.

Rays that would enter the lead before reaching the pipe boundary remain zero-yield trials, without resampling. Pipe photons undergo analog transport, including absorption, scattering and secondary production. The shielding calculation instead samples the exterior lead surface, excluding the entrance opening, and biases interaction rates to obtain sufficient rare transmission and gas interactions. Complete-history likelihood weights correct this sampling while preserving physical interaction final states and deposited energies. The two calculations do not establish complete coverage with a common first-entry assignment.

5.3.1.3 Detector response and results

Gas deposits pass through the conventional REST-for-Physics response and reconstruction, followed by the common TPC baseline and simulation-calibrated BDT. The baseline includes $2\text{–}7\text{keV}$ and the central $𝑟<1\text{cm}$ region. The BDT acceptance is already included in the selected counts.

Uniform surface positions and cosine-weighted inward directions give the generation rate for an isotropic scalar fluence $\mathrm{\Phi }$,

where $𝑆$ is the sampled area, equal to $1776.008{\text{cm}}^2$ for the four pipe faces. The background level is

where the sum runs over selected events, ${𝑁}_{\text{gen}}$ includes all generated primaries, including masked and non-interacting photons, $\mathrm{\Delta }𝐸=5\text{keV}$ and ${𝐴}_{\text{fid}}=𝜋{\text{cm}}^2$. The weights contain the NaI source correction and, for shielding, the transport likelihood. The original proposal rate is retained when reweighting to the fitted source, so each correction enters once. Monte Carlo errors retain correlations between events from the same physical primary. Table 5.21 compares the separate estimates before veto rejection.

The shielding estimate combines compatible samples normalized separately in each source region. It is conditional on excluding products with unresolved response-fit errors; the resulting selection bias has not been quantified. One photon history contributes 25.3% of the rate after BDT selection, so rare shielding histories still limit its precision.

Replacing air with Pb reduces the pipe point estimate after the BDT selection by about a factor of 19, although its statistical precision remains limited.

In the final background budget (Table 5.25), we approximate the photon contribution by adding Shielding and Pipe (four sides, Pb). These calculations use different geometries, and their sum omits front-opening incidence. Independent MC errors are combined in quadrature; they exclude uncertainty from the geometry approximation and the unquantified response-fit selection and retention bias.

The sampled pipe contribution is defined by first entry through the four lateral surfaces. The omitted incidence through the front surface facing the pipe opening, including oblique trajectories and subsequent scattering, could be studied in future with the full beamline geometry.

5.3.2 Environmental neutrons

5.3.2.1 Origin and incident spectrum

For the nominal outdoor location, we model cosmic neutrons as arriving predominantly from the sky and environmental neutrons as an approximately isotropic field from the surroundings. The environmental field includes neutrons produced by radioactivity in soil and nearby materials, together with cosmic neutrons scattered and moderated by the ground [97, 151, 154]. We approximate this diffuse contribution with thermal, epithermal and effective fast spectral components. This distinction is approximate, and some overlap between the two source descriptions is expected.

We derive the component fluences and fast scale from the outdoor Zaragoza HENSA measurement [100] and the CRY reference, following the normalization, subtraction and fit in Figure 5.11.

The thermal and epithermal templates follow the standard Maxwellian fluence $𝐸exp[-𝐸/({𝑘}_{\mathrm{B}}𝑇)]$ and $1/𝐸$ slowing-down forms [155, Chs. 8–9]. We adopt a temperature of $293\mathrm{K}$ and restrict the epithermal component to $0.1\text{eV}$–$0.1\text{MeV}$. For the effective fast component, we use the phenomenological template $\sqrt{𝐸}exp(-𝐸/{𝑇}_{𝑓})$, a Maxwellian form used to approximate fission spectra [156, Sec. 13.3], with ${𝑇}_{𝑓}=0.626\text{MeV}$ fitted to the excess. These overlapping components are sampled separately.

This is a working diffuse-field benchmark rather than a site-specific DESY measurement. The fit can also absorb discrepancies in the adopted cosmic reference.

5.3.2.2 Simulation method

Neutrons are generated on the enclosing surface shown in Figure 5.12, with uniform surface density and cosine-weighted inward directions. This represents approximately isotropic illumination; equal sky and ground contributions remain an assumption for the outdoor site.

Energy bins are sampled by integrated component fluence, with uniform energy inside each bin. Transport includes the closed lead, copper and pipe geometry, the complete veto and neutron-induced secondary particles. Within each source product that passes response validation, every generated neutron enters the normalization, including histories with no gas deposit.

5.3.2.3 Results

We apply the common TPC baseline and frozen BDT selection to each component. For ${𝑁}_{𝑘}$ generated neutrons and ${𝑌}_{𝑘}$ selected events, the background level is

where $𝑆$ is the source-box area, ${\mathrm{\Phi }}_{𝑘}$ the scalar fluence rate, $\mathrm{\Delta }𝐸=5\text{keV}$, and ${𝐴}_{\text{fid}}=𝜋{\text{cm}}^2$. Events from the same neutron remain correlated when evaluating the uncertainty. Products with unresolved response-fit errors and their generated exposure are excluded. The estimates and conditional limits assume representative retained histories; any resulting selection bias is unquantified and is not covered by the MC errors or counting limits. The baseline plus BDT selection retains $2$ events. Table 5.22 gives the estimates and conditional limits without active-veto rejection.

5.4 Cosmic-ray background

Cosmic particles can reach the gas directly or produce secondary radiation in the shielding. Electromagnetic descendants of neutrons, muons and protons can leave compact deposits resembling an X-ray. We therefore evaluate each incident component through the same TPC selection and then test its accompanying scintillator activity. The calculation uses independent evaluation samples, the corrected reference geometry and the fixed classifiers introduced in Section 3 and Section 4. The available validated samples provide partial source estimates; the incident-field inventory and the full response audit remain incomplete.

5.4.1 Sources and absolute normalization

Table 5.23 specifies the incident fields. The Guan parameterization supplies the total muon spectrum [99]; complementary, energy- and zenith-dependent charge fractions from CRY weight the separate positive- and negative-muon samples. Photons, electrons/positrons and protons use the complete populated support of their CRY spectra [91]. The electron/positron weights also correct the difference between the generated charge mixture and the scalar-fluence mixture. These are single-particle source models; correlated air showers and omitted hadron species are outside their coverage.

The CRY neutron field and the full outdoor HENSA spectrum are alternative source hypotheses. HENSA includes terrestrial and atmospheric neutrons [153]; its spectrum does not independently determine the assumed angular distribution. It is not added to the CRY neutron prediction or to the environmental residual of Section 5.3.2.

For source stratum $𝑗$, the selected background level is

where ${𝑁}_{𝑗}$ counts all generated physical parents with validated transport and original TPC response, ${𝐾}_{𝑗𝑝}$ counts their selected acquisitions, and ${𝑤}_{𝑗𝑝}$ is the incident-source weight. Parents producing no saved detector event remain in ${𝑁}_{𝑗}$. The incident-primary rate ${𝑄}_{𝑗}=𝜋{𝑅}^2{\mathrm{\Phi }}_{𝑗}$ uses the projected generation disk, with $𝑅=1.778\mathrm{m}$, and the scalar fluence ${\mathrm{\Phi }}_{𝑗}$ integrated over the generated phase space. It is distinct from the fiducial detector area. Statistical errors group all descendants of each physical parent before squaring their summed contribution.

5.4.2 TPC and veto results

Both muon charges remain unreported because no exposure has yet qualified in this evaluation; this does not indicate zero muon background. Photon and electron/positron samples have no selected candidate and retain positive upper limits. The neutron and proton estimates therefore do not establish a complete cosmic background or a joint limit.

Transport uses Ar–isobutane (2%) at $1.4\text{bar}$, while the calibrated REST response retains $155\mathrm{V}{\text{cm}}^{-1}$, $1.4\text{atm}$ and 1% isobutane. This gas and pressure transfer remains conditional, as discussed in Section 5.1.2. Veto signals are digitized with their own acquisition length and matched to the native TPC trigger. The prompt and neutron-BDT thresholds are fixed independently of these evaluation candidates. In the prompt-background evaluation, one complete measured calibration record supplies unrelated veto activity to each physical parent, preserving its channel and timing correlations.

Veto rejection is credited only when the complete gas and sensitive-scintillator histories establish physical coincidence in the acquisition. Radioactive branches with an unverified time reset prevent this credit even when the gas deposit is prompt. Unclassified candidates receive no rejection credit. The retained neutron histories also require an exact comparison with their archived TPC response; a failed auxiliary veto response preserves the original TPC candidates and exposure without rejection credit. Delayed radioactive decays are recorded separately and receive no credit from activity at the earlier production interaction. Unclassified candidates can contain unresolved activation and are not added to a separate activation estimate. These response and ancestry checks classify the selected events; particle identities are not classifier inputs.

The reported errors describe physical-parent Monte Carlo statistics at fixed source, response and nominal accidental-activity draw. They condition on the available qualified samples and do not quantify bias from incomplete delivery, processing time or response-fit selection. Conditional 90% limits use integer selected-parent counts under the declared rare-parent, single-selected-acquisition working model and the known source-weight bounds. An observed multiple acquisition from one parent invalidates that working-model limit. Source-model uncertainty, correlated showers, response transfer and unquantified fit-selection bias are outside these errors and limits. The 80% TPC and 88% veto calibration targets refer to different control populations; their product does not establish joint X-ray acceptance, and neither factor divides the background levels.

5.4.3 Radiation-induced veto activity and random coincidences

A separate earlier study of accidental veto activity combines cosmic muons, electrons and positrons, protons, neutrons, and photons with environmental gamma rays. Its source normalizations and detector response are independent of the partial source samples above. Identical active-panel and peak selections compare simulated and experimental calibration waveforms away from the Micromegas trigger.

Above the 300 ADC-count peak threshold, the simulation predicts approximately $2345$ peaks per second, compared with $7614$ in four stable calibration runs. Most of the difference lies below 1000 ADC counts. The model does not reproduce the complete measured activity, and this comparison does not identify the unexplained contribution.

A more selective comparison requires coincidences in at least three panels on two detector faces within $0.4\text{μs}$. Their rates are $278\pm 6$ groups per second in data and $286\pm 9$ in simulation, without a fitted normalization. About $93\%$ of the selected simulated groups originate from muon primaries. The experimental sample is consequently treated as muon-enriched, rather than pure muons. Errors are statistical; source and response uncertainties are excluded.

Despite the rate agreement, the simulated amplitude enhancement around 1300–1700 ADC counts is weaker in data (Figure 5.13). The high-end feature also differs and is affected by saturation and baseline treatment. This partial check does not validate the full response; measured-record overlays remain the input to the final background selection sequence.

5.5 Combined background budget and reduction priorities

Table 5.25 brings together the radioactive, environmental and cosmic results after all source models have been described. Background levels refer to the IAXO-D1 argon reference, the $2\text{–}7\text{keV}$ interval and $10\text{mm}$ fiducial radius, without correction for X-ray acceptance. The selection and source coverage are stated separately for each contribution.

Figure 5.14 compares the known radioactive inventory before and after the final TPC selection. The integral of the selected black curve, divided by the $5\text{keV}$ interval, reproduces the atmospheric-argon subtotal in Table 5.25. Environmental and cosmic contributions and sources without assigned activities remain outside this sum.

The pre-existing radioactive-inventory subtotal combines the adopted ${}^{39}\text{Ar}$ and ${}^{85}\text{Kr}$ gas activities, gas ${}^{222}\text{Rn}$, the independent cathode ${}^{218}\text{Po}$ and ${}^{210}\text{Pb}$ inventories, four front-end cards, non-overlapping detector-material contributions, and ${}^{210}\text{Pb}$ plus U/Th/K in the inner $10\text{mm}$ of lead. The source activities and responses remain in Section 5.2. The underground-argon alternative changes only ${}^{39}\text{Ar}$, using the fixed reduction factor of 1400; the krypton benchmark remains unchanged. Gas radon and cathode activities are independent parent inventories, without an assumed equilibrium or plate-out relation.

Alternative wall locations, nested chain hypotheses and the separate shield-neutron bound are excluded from these subtotals. Unassigned activities, environmental fields, cosmic sources and induced activation also remain outside these pre-existing subtotals. Its errors combine independent parent-history MC uncertainties and the stated argon activity uncertainty. The joint conditional 90% bounds use the common tail allocation of Section 5.1.1.1.

5.5.0.0.1 Contributions and reduction priorities.

Under the adopted activities, detector materials, atmospheric ${}^{39}\text{Ar}$ and inner-lead ${}^{210}\text{Pb}$ are leading terms in the quantified radioactive inventory. Underground argon suppresses ${}^{39}\text{Ar}$ while leaving the other terms in place. Gas selection, surface cleanliness, radiopure components and low-activity inner lead therefore address complementary sources. Their relative importance depends on the adopted activities and the evaluated source coverage.

5.5.0.0.2 Environmental fields and cosmic rejection.

The photon result resolves only part of the local field; remaining pipe incidence and rare weighted shielding histories limit the complete estimate. The diffuse-neutron estimate rests on two events surviving the baseline plus BDT selection and is reported with a conditional upper limit. These Zaragoza-based reference fields retain their spectral and angular assumptions, and the diffuse-neutron model can overlap the sky-dominated cosmic source. The available cosmic samples now have source-normalized partial estimates, including conservative veto accounting (Section 5.4.2). The CRY and inclusive HENSA neutron fields remain alternatives, and neither is added to the environmental residual. Missing muon exposure prevents a complete cosmic prediction.

5.5.0.0.3 Scope of the combined prediction.

Activation is evaluated as an instantaneous contribution at the stated irradiation time, separately from pre-existing contamination. We use the partial modeled contribution as the activation reference estimate at formal equilibrium. The broad conditional envelope remains a diagnostic of incomplete decay-response coverage under the retained HENSA irradiation assumptions, rather than a predicted physical background rate. Incomplete photon coverage, unknown activities, overlapping neutron fields, incomplete cosmic exposure and partial activation prevent establishing a complete detector total or demonstrating the target background level. Transfer to BabyIAXO requires its gas, optics and geometry together with the outdoor DESY fields; the statistical bounds quoted here do not include a complete source and detector-response uncertainty budget.