The CROSS experiment: detector construction, background projection, and sensitivity to $^{100}$Mo $0\nu2\beta$ decay

A. Drobizhev; A. Giuliani; A. Ianni; A. Ortiz de Sol\'orzano; A.S. Barabash; A. Zolotarova; B. Schmidt; C.A. Marrache-Kikuchi; C. Gotti; C. Nones

REVIEW 3 major objections 6 minor 67 references

The CROSS experiment: detector construction, background projection, and sensitivity to $^{100}$Mo $0\nu2\beta$ decay

T0 review · 3 major / 6 minor · reviewed 2026-07-30 · grok-4.5

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Pith's one-line read CROSS’s Monte Carlo background model predicts 3.2×10⁻³ counts/keV/kg/yr at the 100Mo Q-value, enough for a world-leading half-life limit near 4×10²⁴ yr in one year of running.

desk verdict Solid as-built construction + Geant4 forecast for the running CROSS array; the BI=3.2e-3 and one-year world-leading claim are projections that lean on transferred radiopurity and no surface term, but the authors already bound that with factor-3/10 scenarios. read the letter →

arxiv 2607.26732 v1 pith:SKJO77OY submitted 2026-07-29 physics.ins-det nucl-ex

D. Auguste , A.S. Barabash , G. Benato , V. Berest , L. Bergé , M. Buchynska , J.M. Calvo-Mozota , J. Cao

show 37 more authors

P. Carniti M. Chapellier D. Cintas I. Cojocari I. Dafinei F.A. Danevich M. De Deo A. Drobizhev L. Dumoulin F. Ferri A. Giuliani C. Gotti Ph. Gras A. Ianni V.V. Kobychev Yu. G. Kolomensky S.I. Konovalov P. Loaiza P. de Marcillac S. Marnieros C.A. Marrache-Kikuchi M. Martinez C. Nones E. Olivieri A. Ortiz de Solórzano M. Pageot Y. Peinaud G. Pessina D.V. Poda Ph. Rosier B. Schmidt R. Serino V.I. Tretyak V.I. Umatov M. Velazquez M. Zarytskyy A. Zolotarova

This is my paper

classification physics.ins-detnucl-ex PACS 29.40.Vj23.40.-s07.20.Mc95.55.Vj

keywords neutrinolessdouble-betadecay100MoscintillatingbolometerslithiummolybdatebackgroundindexGeant4cryogenicdetectorsCanfranc

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

CROSS has built and installed a 42-module array of scintillating cryogenic calorimeters holding 4.9 kg of 100Mo at Canfranc, and this paper reports the detector construction plus a full Geant4 projection of background in the neutrinoless double-beta region of interest. The simulations give a background index of 3.2(5)×10⁻³ counts/keV/kg/yr in a 100 keV window around 3034 keV. With the muon-veto dead time and ordinary facility duty cycle folded in, that level would let the experiment set a half-life limit around 4×10²⁴ yr after one year—competitive with or better than existing 100Mo bounds. Even if materials or detector performance push the background three- to ten-fold higher, two years of data would still remain competitive. The paper therefore establishes both that the hardware is in place and that the projected background supports a leading 100Mo search.

What carries the argument

A Geant4 geometry of crystals, light detectors, copper structure, cryostat screens, lead shielding and muon veto, with detector response (energy resolution, light-to-heat ratio, 1 ms integration, single-crystal and veto cuts) applied event-by-event to simulated U/Th chains, 100Mo 2ν2β pile-up and cosmic muons; the resulting spectra are integrated in the ROI to obtain the background index.

What would settle it

After one year of physics data, measure the actual event rate in the 100Mo ROI after the same single-crystal, light-band and muon-veto cuts; if it substantially exceeds ~3×10⁻³ cnts/keV/kg/yr the projected sensitivity fails.

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Extended reading notes

Core claim

Detailed Geant4 modeling of the installed CROSS array, cryostat, shielding and muon veto predicts a total background index of 3.2(5)×10⁻³ cnts/keV/kg/yr in a 100 keV interval centered on the 100Mo Q-value. Combined with 18 % muon-veto dead time, 90 % duty cycle, ~70 % total efficiency and 4.9 kg of 100Mo, this background yields a projected 90 % C.L. half-life sensitivity of order 4×10²⁴ yr in one year of elapsed time, still world-leading or competitive after two years even if the true background is several times worse.

Load-bearing premise

Crystal and copper-frame radioactivities are taken from an earlier experiment, surface contamination is left out of the geometry, and every detector is assigned the best prototype resolution and light yield.

Editorial extensions

If this is right

One year of CROSS data at the predicted background would set the strongest published limit on 100Mo 0ν2β decay.
A factor-of-three worse background still allows a world-best limit within roughly 1.5–2 years.
The same low-mass copper/PLA structure and NTL light detectors can be reused as a technology pathfinder for larger 100Mo arrays.
Muon-induced secondaries dominate the ROI, so further veto or shielding gains would directly improve sensitivity.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If surface α contamination proves higher than bulk assumptions, light-detector pulse-shape and NTL gain become the main remaining handles for recovering the projected BI.
The large muon contribution at Canfranc depth implies that any future ton-scale follow-on at the same site will need either deeper overburden or a higher-efficiency veto to stay background-free.
Successful operation of the uncoated LMO + NTL-LD configuration validates the fallback design chosen after surface-coating R&D underperformed on large crystals.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Punchline: this is the construction record and background/sensitivity forecast for the 42-module CROSS array that is already taking physics data at LSC. It is not a measured BI. What is new is the as-built inventory (32 enriched LMOs = 4.9 kg 100Mo, TeO and depleted/natural companions, NTL Ge/Si LDs, Cu/PLA holder at 6% Cu-to-crystal mass), the facility-specific muon-veto model with 18% dead time, and the end-to-end Geant4 number BI = 3.2(5)×10^{-3} ckky in a 100 keV window at 3034 keV, which under 90% duty cycle gives lim T1/2 ~ 4×10^{24} yr in one elapsed year.

They do the standard things carefully. Geometry includes crystals, LDs, frames, Kapton, cryostat screens, internal/external Pb, and a simplified veto. Response model uses 1 ms integration, resolution smearing from prototype fits (~6 keV FWHM at 2615 keV), LHR light summing, single-hit + LHR band + veto anti-coincidence + pile-up cuts. Activities are HPGe assays or CUPID-Mo numbers; muons use LSC flux/angular data; 2ν2β and pile-up use Decay0. Feldman–Cousins sensitivity arithmetic is transparent, and they plot conservative BI = 1×10^{-2} and 5×10^{-2} cases so a 2-year run still looks competitive or best-in-class for 100Mo.

Soft spot, in proportion: surface radioactivity is omitted by design, crystal/frame bulk 226Ra/228Th are transferred from CUPID-Mo, and every channel is given the best prototype resolution/LHR with no NTL gain and no spread. The text itself flags the 10 mK screen and frames as the most harmful near-ROI source (Fig. 11). Muons dominate the quoted total, so a realistic surface floor on nearest Cu could move the non-muon piece by the same factor 3–10 they already show. That is a modeling systematic, not a hidden contradiction; commissioning data (promised) will settle it.

Math, citations, and methods look solid for an instrumentation-and-projection paper. Self-cites are to their own prototypes, muon-veto paper, and CUPID-Mo background model—appropriate here. Who it is for: anyone running or designing cryogenic 100Mo arrays (CUPID, AMoRE, next CROSS stages). Bring it to reading group if the group does bolometers or underground background models; skip if you only care about final half-life limits. I would send it to peer review without hesitation and would cite the construction details and the BI breakdown when comparing projections. Engage.

Referee Report

3 major / 6 minor

Summary. The manuscript describes the construction and underground installation of the CROSS array of 42 dual-readout cryogenic calorimeters (32 100Mo-enriched Li2MoO4 crystals totaling 4.9 kg of 100Mo) at LSC, together with a Geant4-based background model and a projected sensitivity to 100Mo 0ν2β decay. Using assayed or sister-experiment activities, a detector-response model taken from CROSS prototypes, muon veto anti-coincidences, and standard selection cuts, the authors predict a background index of 3.2(5)×10−3 cnts/keV/kg/yr in a 100 keV window at Qββ=3034 keV. With 18% muon-veto dead time and 90% duty cycle this yields a projected 90% C.L. half-life limit ∼4×10^24 yr in one year of elapsed time, with conservative factor-3 and factor-10 worse BI scenarios still competitive after two years.

Significance. CROSS is a timely intermediate-scale 100Mo bolometric experiment that bridges CUPID-Mo/AMoRE-I and the forthcoming tonne-scale CUPID/AMoRE-II programs, while also serving as a technology demonstrator for NTL light detectors and a low-mass Cu/PLA holder. A documented as-built geometry, a full facility MC, and an explicit sensitivity projection with conservative BI envelopes are valuable to the community even before physics results appear. The construction narrative, cleaning protocols, wiring redesign, and muon-veto dead-time quantification are concrete contributions. The projection itself is falsifiable once commissioning data are released, which strengthens rather than weakens the paper.

major comments (3)

[Sect. 3.3, Fig. 11] Sect. 3.3 (and the explicit statement that “this simulation does not consider any special contribution to the radioactive components in the surface of the materials”): surface 226Ra/228Th on the copper frames and 10 mK screen is omitted entirely, yet the text and Fig. 11 identify precisely these facing surfaces as “the most harmful background” because degraded α/β events populate the β/γ band near Qββ. A bounding estimate (e.g., a surface activity scaled from CUPID-Mo or from the CROSS holder R&D) should be added so that the non-muon floor is not left unquantified; the factor-3/10 envelopes in Fig. 14 are not a substitute for a surface term in the baseline model.
[Table 1, Sect. 3.3.1] Table 1 and Sect. 3.3.1: bulk 226Ra/228Th activities of the LMO crystals and copper frames are taken equal to CUPID-Mo values rather than measured on the as-built CROSS parts. While the materials and producers are the same, the crystals underwent a different assembly/gluing campaign and the frames are a new low-mass design. The paper should either report (or cite) CROSS-specific HPGe/bolometric assays or propagate an explicit systematic on these two entries into the total BI uncertainty, instead of absorbing the risk only into the ad-hoc factor-3/10 scenarios.
[Sect. 3.2, Sect. 4] Sect. 3.2: every crystal and LD is assigned the single best prototype resolution and LHR of Ref. [48], with no performance spread and with NTL gain deliberately set to zero “worst case.” The sensitivity arithmetic in Sect. 4 then adopts a 17.1 keV ROI width taken from CUPID-Mo. Because energy resolution and light-yield uniformity directly set both the analysis ROI and the PSD/pile-up rejection efficiency, the baseline BI and the 70.2% total efficiency should be shown under at least one degraded-resolution scenario (e.g., FWHM scaled by the observed prototype spread), not only under a global BI rescaling.

minor comments (6)

[Abstract, Sect. 1] Abstract and Introduction state that physics data taking has been ongoing since mid-November 2025 / April 2026; the arXiv datestamp is 29 Jul 2026. Clarify the exact timeline (commissioning vs. physics) so that the reader knows whether any in-situ validation of the BI model is already available or still forthcoming.
[Sect. 3.2, Eq. (2)] Eq. (2): the numerical prefactors 30, 20, 5, 3 that convert crystal energy into LD scintillation are given without units or a clear derivation from the quoted 0.3 keV/MeV LHR; a one-sentence justification would help reproducibility.
[Sect. 3.5, Fig. 13] Fig. 13 error bars combine activity and MC statistical uncertainties, but the text does not state how the two are combined or whether activity upper limits (lead shielding) are treated as one-sided. A brief note would suffice.
[Sect. 3.3.4] The muon energy spectrum (Eqs. 3–5) is an above-ground approximation folded with a simple exponential overburden; a short comparison to the measured LSC muon spectrum (or a citation to the validation in Ref. [38]) would strengthen confidence that the dominant BI term is not biased.
Typographical / consistency items: “molibdate” → “molybdate” (Conclusions); “undeground” → “underground” (Introduction); Q-value is written both Q2β and Qββ; the abstract’s “mid-November 2025” vs. body “April 2026” start of physics running should be aligned.
[Sect. 3.3] Sect. 3.3 mentions that neutron-induced background is “not expected to represent a dominant contribution” on the basis of a ∼2 counts/day thermal-neutron rate, yet no MC estimate is given. A one-paragraph upper bound (or a clear deferral to a future note) would close the source list.

Circularity Check

1 steps flagged · score 1.0 of 10

Forward MC background projection with measured inputs; no derivation-by-construction circularity.

self citation load bearing [Sect. 3.3.1, Table 1; Sect. 3.2]
"Radiopurity of the enriched crystals and the copper frames is assumed to be the same as reported by the CUPID-Mo experiment [61]. ... All detectors of the same type (crystals and LD) were assumed to have exactly the same performance as reported in [48]"

Bulk 226Ra/228Th of crystals and Cu frames, and the uniform best-case resolution/LHR, are taken from prior papers with overlapping authorship rather than measured on the as-built CROSS parts. This is ordinary input transfer, not a definitional loop: the BI is still an independent MC integral over those fixed rates, not forced equal to a sensitivity target. Flagged only as minor self-citation of inputs.

full rationale

The paper’s central claim is a Geant4 forward projection of the background index (BI = 3.2(5)×10^{-3} cnts/keV/kg/yr in a 100 keV window at Qββ) and the resulting Feldman–Cousins half-life sensitivity. Activities are taken from HPGe assays or the published CUPID-Mo background model for the same crystal/Cu producers; muon flux and angular distribution are external LSC data; 2ν2β kinematics come from Decay0; detector resolution and LHR are fixed to prototype measurements. The sensitivity is then computed from that BI, live-time, efficiency, and number of 100Mo nuclei—none of these steps defines the output in terms of itself or renames a fit as a prediction. Self-citations (CROSS prototypes, CUPID-Mo BI model, muon-veto paper) supply numerical inputs but are not uniqueness theorems or load-bearing circular premises. Conservative factor-3/10 BI scenarios are shown explicitly. Score 1 only for ordinary reliance on overlapping-collaboration measurements as inputs; the derivation chain itself is non-circular.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central BI and sensitivity numbers rest on standard radiation-transport assumptions, measured or sister-experiment activities, prototype detector response, and several modeling choices (no surfaces, neutrons negligible, optimal resolution everywhere). No new physical entities are introduced. Free parameters are few and mostly resolution/LHR constants fixed from prior CROSS prototype data rather than tuned to the claimed sensitivity.

free parameters (5)

Crystal FWHM resolution coeffs a,b = a=0.94 keV, b=0.100 √keV
Gaussian smearing FWHM=a+b√E0 with a=0.94(18) keV, b=0.100(7)√keV taken from a fit to one CROSS prototype module and applied uniformly to all crystals.
LD FWHM resolution coeffs a,b = a=0.042 keV, b=0.31 √keV
Same functional form fitted on prototype LD data and applied to all light detectors without NTL gain.
Light-to-heat ratios (LHR) = 0.3 keV/MeV (top β/γ)
Fixed 0.3 keV/MeV (top) and 2/3 of that (bottom) for β/γ, with reduced α light yields, taken from prior structure tests and hard-coded in Eq. 2.
Pile-up irresolvable window = 1 ms
1 ms window chosen as worst-case LD rise-time scale to normalize 2ν2β–2ν2β pile-up rate; directly scales that background component.
ROI analysis width for sensitivity = 17.1 keV
17.1 keV ROI width adopted from CUPID-Mo performance rather than derived from this array’s data.

assumptions (6)

domain assumption Geant4 11.1 radioactive decay and electromagnetic physics accurately transport U/Th chains, 2ν2β electrons, and muon secondaries in the modeled geometry.
Entire BI forecast is a Geant4 integral; no data-driven closure test on the full CROSS geometry is shown yet.
domain assumption 226Ra and 228Th in crystals and copper frames equal CUPID-Mo bulk activities; contamination is purely bulk and homogeneous.
Table 1 and Sect. 3.3.1; surface terms are explicitly omitted and would populate the α and degraded-β bands near ROI.
domain assumption Neutron-induced γ background in the ROI is negligible relative to the quoted BI.
Sect. 3.3 argues from underground depth, shielding, and a ~2 counts/day thermal-neutron rate; no full neutron MC is included.
ad hoc to paper All 36 analysis LMOs and all LDs simultaneously achieve the prototype optimal resolution and LHR used in the response model.
Sect. 3.2 states this is the best-working-point assumption for every channel.
domain assumption Facility duty cycle is 90% and muon-veto anti-coincidence dead time is 18% over multi-year running.
Sect. 4; dead time from prior veto paper/simulations, duty cycle from previous CROSS cryogenic runs.
domain assumption Selection efficiency for 0ν2β is 90% (cuts) × 78% (full-energy single-crystal containment) = 70.2%.
Containment from this MC; cut efficiency assumed similar to CUPID design values, not yet measured on CROSS physics data.

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Cite this review

Pith. "Pith review of The CROSS experiment: detector construction, background projection, and sensitivity to $^{100}$Mo $0\nu2\beta$ decay." pith.science (2026). https://pith.science/paper/SKJO77OY

@misc{pith2026260726732,
  author       = {Pith},
  title        = {Pith review of: The CROSS experiment: detector construction, background projection, and sensitivity to $^100$Mo $0\nu2\beta$ decay},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SKJO77OY}},
  note         = {Machine review of arXiv:2607.26732}
}

abstract

The CROSS experiment to search for neutrinoless double-beta ($0\nu2\beta$) decay in $^{100}$Mo with the help of an array of scintillating cryogenic calorimeters, containing 4.9 kg of $^{100}$Mo, has been ongoing in a low-background setup at the Canfranc underground laboratory (Spain) since mid-November 2025. In this paper, we present the construction of the CROSS detector and the description of Geant4-based Monte Carlo simulations of expected background in the region of interest. The simulations predict the background index in a 100-keV-wide interval centered at the $Q$-value of $^{100}$Mo (3034 keV) on the level of 3.2(5) $\times$ 10$^{-3}$ cnts/keV/kg/yr. Taking into account an 18% deadtime induced by the muon veto cut and a typical 90% duty cycle of the facility, such background level would allow to reach the world-leading sensitivity to $^{100}$Mo $0\nu2\beta$ decay (lim $T_{1/2} \sim 4 \times 10^{24}$ yr) in 1 year of data taking. Considering conservatively a factor 3 (10) worse background index due to unpredictable radioactive contamination of construction materials and/or detector performance, a 2-yr-long operation of the CROSS array would be still compatible with the best (competitive) sensitivity to $0\nu2\beta$ decay in $^{100}$Mo.

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