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No sign of neutrinoless double electron capture in calcium-40

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2026-07-10 01:11 UTC pith:VHMGRWIS

load-bearing objection Solid, modest null-result paper from AMoRE on 40Ca 0ν2EC

arxiv 2607.08039 v1 pith:VHMGRWIS submitted 2026-07-09 nucl-ex hep-ex

A study of neutrinoless double electron capture in ⁴⁰Ca from the AMoRE experiment

AMoRE Collaboration: A. Agrawal , V.V. Alenkov , P. Aryal , J. Beyer , B. Bhandari , R.S. Boiko , K. Boonin , O. Buzanov
show 101 more authors
C.R. Byeon N. Chanthima M.K. Cheoun J.S. Choe Seonho Choi S. Choudhury J.S. Chung F.A. Danevich M. Djamal D. Drung C. Enss A. Fleischmann A.M. Gangapshev L. Gastaldo Y.M. Gavrilyuk A.M. Gezhaev O. Gileva V.D. Grigorieva V.I. Gurentsov C. Ha D.H. Ha E.J. Ha D.H. Hwang E.J. Jeon J.A. Jeon H.S. Jo J. Kaewkhao C.S. Kang W.G. Kang V.V. Kazalov S. Kempf A. Khan S. Khan D.Y. Kim G.W. Kim H.B. Kim Ho-Jong Kim H.J. Kim H.L. Kim H.S. Kim M.B. Kim S.C. Kim S.K. Kim S.R. Kim W.T. Kim Y.D. Kim Y.H. Kim K. Kirdsiri Y.J. Ko V.V. Kobychev V. Kornoukhov V.V. Kuzminov D.H. Kwon C.H. Lee DongYeup Lee E.K. Lee H.J. Lee H.S. Lee J. Lee J.Y. Lee K.B. Lee M.H. Lee M.K. Lee S.W. Lee Y.C. Lee D.S. Leonard H.S. Lim B. Mailyan E.P. Makarov P.B. Nyanda Y. Oh S.L. Olsen S.I. Panasenko H.K. Park H.S. Park K.S. Park S.Y. Park O.G. Polischuk H. Prihtiadi S. Ra S.S. Ratkevich G. Rooh E. Sala M.B. Sari J. Seo K.M. Seo B. Sharma K.A. Shin V.N. Shlegel K. Siyeon J. So N.V. Sokur J.K. Son J.W. Song N. Srisittipokakun V.I. Tretyak R. Wirawan K.R. Woo H.J. Yeon Y.S. Yoon Q. Yue
This is my paper
classification nucl-ex hep-ex PACS 23.40.Hc29.40.Vj
keywords experimentbetacapturedecaydetectorsdoubleelectronmathrm
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The AMoRE Collaboration searched for neutrinoless double electron capture (0ν2EC) in calcium-40 using cryogenic crystal detectors operated deep underground. This hypothetical decay, in which two atomic electrons are absorbed by the nucleus simultaneously with no neutrinos emitted, would violate lepton-number conservation and would imply that neutrinos are their own antiparticles (Majorana particles). The experiment used thirteen calcium molybdate crystals with a total exposure of 7.32 kg·yr, looking for a monoenergetic signal peak at 193.5 keV corresponding to the decay energy. No excess above background was found, allowing the collaboration to set a lower limit on the half-life of this process at greater than 1.7 × 10^22 years at 90% confidence, slightly improving the previous world limit set by the CRESST experiment. The result also demonstrates that calcium molybdate detectors, originally deployed to search for neutrinoless double beta decay of molybdenum-100, can simultaneously probe rare decays of calcium-40. A projected sensitivity of roughly 9 × 10^22 years is estimated for the upcoming AMoRE-II phase.

Core claim

The paper establishes that neutrinoless double electron capture in calcium-40 has a half-life exceeding 1.7 × 10^22 years at 90% confidence, based on 7.32 kg·yr of data from cryogenic calcium molybdate detectors. No signal excess was observed in the region of interest near 193.5 keV, and the limit slightly improves upon the previous best constraint of 1.4 × 10^22 years. The central mechanism carrying the experimental argument is the detection of a monoenergetic peak at the Q-value of the decay, arising from X-rays and Auger electrons emitted during atomic relaxation after two bound electrons are captured by the nucleus, combined with either an internal conversion electron or a real photon to

What carries the argument

The key experimental machinery is a set of thirteen CaMoO4 scintillating crystals operated at millikelvin temperatures with metallic magnetic calorimeters providing dual phonon-photon readout. The signal signature is a monoenergetic peak at 193.5 keV in the heat channel, produced by the combined energy deposition of atomic relaxation products (X-rays and Auger electrons) plus an internal conversion electron or photon. Background rejection relies on the dual-readout particle identification to suppress alpha events, anti-coincidence cuts to remove multi-site events, and a binned-extended likelihood fit that models the background as a linear component plus a small peak at 186 keV from radium-22

Load-bearing premise

The limit depends on the assumed branching ratio for real photon emission versus internal conversion in the KL capture channel. The authors conservatively assume all KL captures produce a photon, which has lower full-energy absorption efficiency than internal conversion, meaning the true detection efficiency could be higher and the true limit stronger. But the exact ratio is unknown, making this an unmeasured modeling input that directly affects the quantitative result.

What would settle it

A statistically significant excess of events at 193.5 keV above the modeled background in a dataset with comparable or greater exposure would indicate discovery of the process. Conversely, if the true KL photon-to-internal-conversion branching ratio differs substantially from the assumed value, the detection efficiency and hence the derived half-life limit would shift quantitatively.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If neutrinos are Majorana particles, 0ν2EC in calcium-40 must occur at some rate; pushing half-life limits eventually either discovers the process or constrains the Majorana neutrino mass scale and lepton-number-violating physics.
  • The demonstrated sensitivity of CaMoO4 crystals to calcium-40 rare decays means that experiments primarily designed for molybdenum-100 neutrinoless double beta decay can perform dual-isotope physics without additional detector hardware.
  • The projected fivefold improvement to ~9 × 10^22 yr sensitivity in AMoRE-II, driven primarily by background reduction rather than increased mass, underscores that background control at the 193.5 keV region of interest is the critical bottleneck for this search.
  • If the 2ν2K (two-neutrino double K-capture) process at 6.4 keV becomes accessible with improved low-energy thresholds in AMoRE-II, it would provide the first observation of a standard-model double electron capture process in calcium-40, calibrating the nuclear matrix elements relevant to the neutrinoless channel.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 7 minor

Summary. This manuscript reports a search for neutrinoless double electron capture (0ν2EC) in 40Ca using 7.32 kg·yr of exposure from thirteen 40Ca100MoO4 crystals in the AMoRE-I experiment. No significant excess is observed in the region of interest near Q2EC = 193.5 keV, and a 90% CL lower limit on the half-life of T_{1/2}^{0ν} > 1.7 × 10^22 yr is obtained, slightly improving the previous CRESST limit. The analysis uses a binned-extended likelihood fit with a background model comprising a linear component and a peak near 186 keV, with Gaussian constraints on peak shape parameters derived from calibration data. A projection for the upcoming AMoRE-II experiment is also provided.

Significance. The result represents a modest but meaningful improvement over the existing CRESST limit (1.4 × 10^22 yr) and demonstrates the capability of CaMoO4 detectors to probe rare decay processes beyond the primary 100Mo 0νββ program. The analysis is methodologically sound, with conservative assumptions clearly stated—most notably the choice of r_γ = 1 in Eq. (1), which minimizes the containment efficiency and thus yields a deliberately conservative (weaker) limit. The falsifiable AMoRE-II sensitivity projection (~9 × 10^22 yr) provides a concrete benchmark for future experiments. The dual-readout cryogenic calorimeter technique and the treatment of multiple capture channels (KK, KL) with GEANT4-based efficiency evaluation are strengths of the experimental approach.

minor comments (7)
  1. Section 2, Eq. (1): The statement 'We assumed r_γ = 1 to conservatively determine half-life' is correct and conservative, but a brief quantitative statement of the impact would strengthen the paper. For instance, noting that setting r_γ = 0 would raise ε_cont to approximately 0.99 (a ~7% change) would make the conservatism transparent to the reader.
  2. Table 1: The 'Total / Average' row lists ΔE_FWHM = 3.4 keV and b = 9.7 count/keV/kg/day, but it is unclear whether these are exposure-weighted averages or simple means. Given the wide variation in both resolution (2.5–6.5 keV) and background (5.3–54.7), specifying the averaging method would improve clarity.
  3. Section 2, paragraph on data-quality cuts: The single-hit requirement within a 3 ms window is stated to achieve ~99.8% efficiency, and the muon coincidence cut reduces efficiency by less than 0.1%. It would be helpful to state whether these efficiencies were measured from data (e.g., using randomly triggered events or calibration source runs) or estimated from simulation.
  4. Section 3, Eq. (3): The Gaussian constraint term uses θ′_i and Δθ′_i, but the text earlier refers to θ_i and Δθ_i. The relationship between the primed and unprimed parameter sets is not explicitly defined. A brief clarifying sentence would help.
  5. Figure 3: The caption mentions a 'green curve' for the 90% CL limit, but the visual distinction between the best-fit (red) and limit curves may be difficult to discern in print. Consider adding a brief textual description of what the green curve represents (e.g., the signal amplitude corresponding to the 90% CL upper limit).
  6. Section 4, sensitivity paragraph: The median exclusion sensitivity is quoted as T_{1/2}^{0ν} = 2.0^{+0.8}_{-0.6} × 10^22 yr. The observed limit (1.7 × 10^22 yr) is slightly weaker, which is consistent with the background-only hypothesis. A brief statement explicitly noting this consistency (e.g., 'The observed limit is consistent with the median sensitivity within 1σ') would be informative.
  7. Reference [24] is cited as 'in preparation.' Since this reference contains important details on the signal analysis and calibration framework, its availability is relevant for reproducibility. If possible, a preliminary version or additional supplementary material should be made available to referees.

Circularity Check

0 steps flagged

No circularity: the half-life limit is a direct experimental measurement from counting data, with no theoretical derivation chain that could reduce to its inputs.

full rationale

The paper's central result—T^{0ν}_{1/2} > 1.7×10^22 yr at 90% CL—is obtained through a standard binned-extended likelihood fit (Eq. 3) of signal-plus-background models to observed energy spectra in a ±12σ window around Q_{2EC} = 193.5 keV. The signal model (Eq. 2) depends on experimentally measured quantities (exposure m_i·t_i, detection efficiency ε_i, crystal mass) and a decay rate Γ that is the free parameter being constrained. The detection efficiency (ε ≈ 0.86–0.92) is computed from GEANT4 simulations with standard physics inputs (capture probabilities f_KK ≈ 85%, f_KL ≈ 14%, and a conservative r_γ = 1 assumption in Eq. 1). The background model consists of a linear function plus a 186 keV peak from 226Ra/235U, with shape parameters constrained by independent calibration data. The 90% CL upper limit on Γ is derived from the profile likelihood ratio (Eq. 5), which is a standard statistical procedure applied to the observed data. No step in this chain reduces to its own inputs by construction: the decay rate is not fitted to the data and then 'predicted' back; the efficiency is simulated independently; the background shape parameters are constrained by calibration, not by the signal region data. The self-citations present (Refs. [17, 22, 24] for experimental setup and analysis framework) describe methodology and are not load-bearing for the mathematical validity of the limit. The result is an experimental bound, not a theoretical derivation, and is externally falsifiable by any experiment with comparable or greater sensitivity. No circularity is present.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 0 invented entities

The analysis relies on standard nuclear and particle physics frameworks without introducing new theoretical entities. The free parameters are either fit to data (background shape) or conservatively assumed (r_γ). The signal shape parameters are derived from calibration data, not invented.

free parameters (3)
  • r_γ (KL photon emission branching fraction) = 1 (assumed)
    Set to 1 as a conservative assumption because the exact ratio between photon emission and internal conversion in the KL channel is undetermined. This directly affects the containment detection efficiency in Eq. 1.
  • Bukin function shape parameters (ξ, ρl, ρr, resolution) = Interpolated from calibration
    Peak shape parameters for the signal PDF are interpolated from calibration data using linear or exponential functions. These are constrained in the final fit.
  • Background model parameters (linear slope/intercept, 186 keV peak amplitude) = Fit to data
    The background is modeled as a linear function plus a peak at 186 keV. These parameters are determined by the fit to the data in the ROI.
axioms (3)
  • standard math The Standard Model weak interaction framework for electron capture is valid.
    The paper relies on standard nuclear physics for the description of electron capture and atomic relaxation processes.
  • domain assumption The 0ν2EC decay, if it occurs, produces a mono-energetic peak at the Q-value (193.5 keV) in the detector.
    This is the fundamental experimental signature assumed in the analysis. It follows from the fact that all decay products (X-rays, Auger electrons, IC electron/photon) deposit their energy locally in the crystal.
  • domain assumption The background in the ROI can be adequately modeled by a linear function plus a peak at 186 keV.
    This is the functional form used in the binned-extended likelihood fit (Eq. 4). It is justified by the known presence of 226Ra/235U backgrounds but is a modeling choice.

pith-pipeline@v1.1.0-glm · 14265 in / 2503 out tokens · 232173 ms · 2026-07-10T01:11:26.987078+00:00 · methodology

0 comments
read the original abstract

The search for neutrinoless double electron capture ($0\nu\mathrm{2EC}$) provides a sensitive probe of lepton-number violation and the Majorana nature of neutrinos. We investigate the $0\nu\mathrm{2EC}$ decay of $^{40}$Ca using cryogenic detectors equipped with metallic magnetic calorimeters in the AMoRE-I experiment. The analysis is based on a physics dataset corresponding to a total exposure of 7.32 kg$\cdot$yr from thirteen $^{40}$Ca$^{100}$MoO$_4$ crystals. No significant excess is observed, and a lower limit on the half-life is obtained as $T^{0\nu}_{1/2} > 1.7 \times 10^{22}$ yr at 90$\%$ confidence level. An improved sensitivity is expected for the upcoming AMoRE-II experiment. These results demonstrate the potential of CaMoO$_4$ detectors to explore rare decay processes beyond the primary $^{100}$Mo $0\nu\beta\beta$ search program.

discussion (0)

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