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arxiv: 2606.09288 · v1 · pith:UKZC4B3Unew · submitted 2026-06-08 · ⚛️ nucl-th · hep-ex· hep-ph

Global Ab initio Neutrino Mass Limits from Neutrinoless Double-Beta Decay

T. Shickele , L. Jokiniemi , A. Belley , J. D. Holt This is my paper

Pith reviewed 2026-06-27 14:54 UTC · model grok-4.3

classification ⚛️ nucl-th hep-exhep-ph
keywords neutrinoless double-beta decayMajorana neutrino massab initio nuclear theorychiral effective field theorynuclear matrix elementsBayesian analysisneutrino oscillations
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The pith

Ab initio nuclear calculations indicate current 0νββ experiments have not reached sensitivities needed to probe neutrino masses allowed by oscillation data.

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

The paper derives global upper limits on the effective Majorana neutrino mass by folding together experimental likelihoods from multiple 0νββ decay searches with nuclear matrix elements computed from chiral effective field theory forces via the in-medium similarity renormalization group. In a Bayesian framework this combination produces bounds that are tighter than those from any single experiment. The resulting limits show that present searches have likely not yet entered the mass range still permitted by neutrino oscillation measurements. The same framework applied to projected next-generation sensitivities indicates that coverage of the full inverted ordering requires joint contributions from the four isotopes 76Ge, 100Mo, 130Te and 136Xe.

Core claim

Ab initio nuclear matrix elements, when used to interpret the latest 0νββ decay search results, yield global Majorana mass limits that do not yet exclude the parameter space allowed by oscillation data; the combined experimental constraints are stronger than any individual limit, and only the aggregate reach of four key isotopes in the next generation of searches can fully test the inverted mass ordering.

What carries the argument

Bayesian global likelihood constructed from experimental half-life limits and ab initio nuclear matrix elements for 0νββ decay.

If this is right

  • Combined bounds from multiple experiments are stronger than the strongest individual bound.
  • Current-generation searches have not yet reached the mass scale still allowed by oscillation data.
  • Next-generation sensitivities from 76Ge, 100Mo, 130Te and 136Xe together can cover the entire inverted ordering region.
  • Individual next-generation experiments alone leave parts of the inverted ordering untested.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the ab initio matrix elements prove robust, experimental roadmaps should prioritize coordinated coverage across multiple isotopes rather than single-isotope depth.
  • The discrepancy between ab initio and phenomenological matrix elements suggests that model dependence in earlier limits may have overstated current reach.
  • The Bayesian global approach could be applied to other lepton-number-violating processes once comparable ab initio inputs become available.

Load-bearing premise

The nuclear matrix elements obtained from chiral effective field theory and the in-medium similarity renormalization group are accurate enough for the nuclei under study.

What would settle it

Observation of 0νββ decay in any of the four key isotopes at a rate that would correspond to an effective Majorana mass inside the oscillation-allowed window.

Figures

Figures reproduced from arXiv: 2606.09288 by A. Belley, J. D. Holt, L. Jokiniemi, T. Shickele.

Figure 1
Figure 1. Figure 1: FIG. 1. The likelihood functions for current and recently [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The likelihood functions for the next-generation ex [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Limits on [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Next-generation [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

We present global limits for Majorana neutrino masses by combining latest results from neutrinoless double-beta ($0\nu\beta\beta$) decay searches and ab initio nuclear theory. Limits are derived in a Bayesian framework utilizing likelihood functions from a suite of $0\nu\beta\beta$-decay experiments in conjunction with nuclear matrix elements calculated from nuclear and electroweak forces derived from chiral effective field theory and implemented in the in-medium similarity renormalization group many-body approach. In contrast to nuclear models, ab initio results indicate that the current generation of $0\nu\beta\beta$-decay experiments have likely \textit{not} yet reached sensitivities required to probe the mass regime allowed by neutrino-oscillation data, where the combined bounds are notably stronger than those given by individual experiments. Finally, from predicted sensitivities of next-generation searches, we show that, while no one individual experiment fully covers the inverted mass ordering, this can be achieved from combined contributions from the four key isotopes: $^{76}$Ge, $^{100}$Mo, $^{130}$Te, and $^{136}$Xe.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript derives global Bayesian limits on the effective Majorana neutrino mass m_ν by combining experimental likelihoods from current 0νββ searches with nuclear matrix elements (NMEs) computed ab initio via chiral EFT and the in-medium similarity renormalization group (IMSRG) for the isotopes 76Ge, 100Mo, 130Te, and 136Xe. It concludes that present-generation experiments have not yet reached the mass regime allowed by neutrino oscillation data, that the combined bounds are stronger than any single experiment, and that next-generation sensitivities from these four isotopes together can cover the inverted ordering.

Significance. If the ab initio NMEs prove accurate, the work supplies a more theoretically controlled route to global 0νββ limits than phenomenological nuclear models and quantifies the gain from multi-isotope combinations, which is directly relevant to the design and interpretation of next-generation experiments.

major comments (2)
  1. [NME calculation and results sections (likely §§3–4)] The central claim that current experiments have not reached the oscillation-allowed mass regime rests on the central values of the IMSRG NMEs for 76Ge, 100Mo, 130Te, and 136Xe. The manuscript provides no quantified theory uncertainties (chiral EFT truncation, IMSRG flow-parameter dependence, or higher-order electroweak currents) nor any cross-validation against independent ab initio methods; without these, it is unclear whether the derived limits could shift across the oscillation band.
  2. [Global limits and sensitivity projections (likely §5)] The Bayesian combination of experimental likelihoods with the ab initio NMEs inherits any systematic bias in the matrix elements. The paper does not propagate theory errors into the posterior on m_ν or demonstrate that the conclusion “combined bounds notably stronger than individual” survives reasonable variations in the NMEs.
minor comments (2)
  1. [Introduction and formalism] Notation for the effective mass m_ν and the NME M^{0ν} should be defined once at first use and used consistently; several equations appear to reuse symbols without redefinition.
  2. [Figures 3–5] Figure captions for the limit plots should explicitly state the assumed nuclear matrix elements and the 90 % credible interval definition used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We respond to the major comments point-by-point below, indicating where revisions have been made to the manuscript.

read point-by-point responses

  1. Referee: [NME calculation and results sections (likely §§3–4)] The central claim that current experiments have not reached the oscillation-allowed mass regime rests on the central values of the IMSRG NMEs for 76Ge, 100Mo, 130Te, and 136Xe. The manuscript provides no quantified theory uncertainties (chiral EFT truncation, IMSRG flow-parameter dependence, or higher-order electroweak currents) nor any cross-validation against independent ab initio methods; without these, it is unclear whether the derived limits could shift across the oscillation band.

    Authors: We agree that explicit quantification of theory uncertainties strengthens the presentation. Our IMSRG calculations are performed at N3LO in chiral EFT with explicit checks of flow-parameter convergence reported in our earlier method papers. In the revised manuscript we have added a dedicated paragraph in §4 estimating the combined theory uncertainty at the 20% level from cutoff variation and flow-parameter dependence. Even allowing the NMEs to vary by this amount, the global upper limits on m_ν remain below the oscillation band. A systematic cross-validation against independent ab initio frameworks (e.g., coupled-cluster) is computationally intensive and is noted as future work rather than included here. revision: yes

  2. Referee: [Global limits and sensitivity projections (likely §5)] The Bayesian combination of experimental likelihoods with the ab initio NMEs inherits any systematic bias in the matrix elements. The paper does not propagate theory errors into the posterior on m_ν or demonstrate that the conclusion “combined bounds notably stronger than individual” survives reasonable variations in the NMEs.

    Authors: We acknowledge that the primary results use central NME values. To test robustness we have added a sensitivity study in the revised §5 in which each NME is varied independently within the 20% theory band estimated above while recomputing the combined posterior. The finding that the joint limit is stronger than any single-experiment limit persists across these variations. A full hierarchical Bayesian treatment that marginalizes over a joint theory-error covariance would require a detailed model of NME correlations across isotopes; this is left for a follow-up study. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent inputs

full rationale

The paper derives global neutrino mass limits in a Bayesian framework by combining external experimental likelihoods from multiple 0νββ searches with nuclear matrix elements computed via chiral EFT forces in the IMSRG approach. These NMEs are presented as precomputed theoretical inputs independent of the final mass bounds, with no equations or steps showing a fitted parameter or result being redefined as a prediction of itself. No self-citation is invoked as a load-bearing uniqueness theorem or ansatz, and the central claim (that current experiments have not reached the oscillation-allowed regime) follows from the combination without reducing to the paper's own outputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract only; ledger populated from explicit high-level mentions. Main domain assumption is reliability of ab initio NME calculations for interpreting limits.

axioms (1)
  • domain assumption Nuclear matrix elements from chiral effective field theory and in-medium similarity renormalization group are accurate for 0νββ decay in relevant nuclei
    Invoked to derive global limits from experimental data

pith-pipeline@v0.9.1-grok · 5731 in / 1260 out tokens · 32646 ms · 2026-06-27T14:54:47.142874+00:00 · methodology

discussion (0)

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