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arxiv: 2606.26097 · v1 · pith:ZAGMUU4Anew · submitted 2026-06-24 · ✦ hep-ph · nucl-ex· nucl-th

Positron-Emitting and Electron-Capturing Double-Beta Processes in the Standard Model and Beyond

Luk\'a\v{s} Gr\'af , Jenni Kotila , Oliver Scholer This is my paper

Pith reviewed 2026-06-25 19:01 UTC · model grok-4.3

classification ✦ hep-ph nucl-exnucl-th
keywords double beta decayneutrinoless double beta decaySMEFT operatorslepton number violationpositron emissionelectron capturenuclear matrix elementsphase space factors
0
0 comments X

The pith

Positron-emitting double beta decays can reach lepton-number violation scales of 1-100 TeV and resolve operator degeneracies when observed in multiple isotopes.

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

The paper calculates nuclear matrix elements and phase-space factors for positron-emitting and electron-capturing double-beta decays in the isotopes krypton-78, cadmium-106 and xenon-124. It finds that the two-neutrino modes with electron capture are the most accessible while double positron emission is strongly suppressed by phase space. For the neutrinoless channels the authors translate a projected half-life sensitivity of 10^24 years into limits on dimension-seven SMEFT operators and show that data from several isotopes can lift degeneracies among those operators.

Core claim

The central claim is that neutrinoless positron-emitting and electron-capturing double-beta processes, interpreted through dimension-seven SMEFT operators, yield sensitivity to lepton-number violating scales of order 1-100 TeV at a half-life reach of 10^24 years, and that simultaneous measurements across multiple isotopes break degeneracies that single-isotope data cannot resolve.

What carries the argument

Dimension-seven SMEFT operators that mediate lepton-number violation, linked to experiment through computed nuclear matrix elements and phase-space factors for the candidate isotopes.

If this is right

  • The 2νβ+EC and 2νECEC channels are the most experimentally accessible Standard-Model modes.
  • The 2νβ+β+ channel remains strongly phase-space suppressed.
  • Neutrinoless modes reach new-physics scales between 1 and 100 TeV.
  • Measurements in several isotopes together resolve degeneracies among multiple dimension-seven operators.

Where Pith is reading between the lines

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

  • These channels may constrain SMEFT operators whose contributions are suppressed or absent in conventional neutrinoless double beta decay.
  • Cross-isotope comparisons could map the flavor structure of lepton-number violation beyond what a single isotope provides.
  • The approach supplies an independent experimental handle on the same underlying lepton-number violation physics.

Load-bearing premise

The conversion of a projected half-life sensitivity of 10^24 years into new-physics scales assumes that background-free experimental reach at that level will be achieved.

What would settle it

A measured half-life in one isotope that cannot be fit by the same set of operator coefficients that fit the other isotopes, or a limit that falls short of the assumed 10^24-year sensitivity while standard neutrinoless double beta decay yields a signal, would test the complementarity claim.

read the original abstract

We study positron-emitting and electron-capturing double-beta-decay modes as probes complementary to the usual double beta decay. Motivated by the proposed NuDoubt++ experiment, we analyze the candidate isotopes ${}^{78}$Kr, ${}^{106}$Cd, and ${}^{124}$Xe, providing nuclear matrix elements and phase-space factors for both neutrinoful and neutrinoless modes. For the Standard-Model channels, we find that $2\nu$ECEC and $2\nu\beta^+$EC are the most experimentally accessible, whereas $2\nu\beta^+\beta^+$ remains strongly phase-space suppressed. For the neutrinoless channel, we interpret a projected sensitivity of $T_{1/2}^{0\nu} = 10^{24}$ y in terms of dimension-seven SMEFT operators and find sensitivity to lepton-number-violating new-physics scales of order 1-100 TeV. We further show that measurements in multiple isotopes can help to resolve degeneracies in multi-operator scenarios, making positron-emitting double-beta searches a useful complement to conventional neutrinoless double beta decay experiments.

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

1 major / 0 minor

Summary. The manuscript studies positron-emitting (β⁺β⁺) and electron-capturing (β⁺EC, ECEC) double-beta decays in the isotopes ⁷⁸Kr, ¹⁰⁶Cd, and ¹²⁴Xe as potential complements to conventional 0νββ searches. Motivated by the proposed NuDoubt++ experiment, it supplies nuclear matrix elements and phase-space factors for both 2ν and 0ν modes, identifies the most accessible SM channels (2νECEC and 2νβ⁺EC), and interprets a projected half-life sensitivity of T_{1/2}^{0ν} = 10^{24} y in terms of dimension-seven SMEFT operators, claiming sensitivity to lepton-number-violating scales of 1–100 TeV and that multi-isotope measurements can resolve operator degeneracies.

Significance. If the computed NMEs and phase-space factors are robust and the experimental sensitivity projection holds, the work supplies concrete inputs for exploring a broader set of LNV operators than standard 0νββ and demonstrates a practical route to lifting degeneracies via isotope comparisons. The explicit provision of these matrix elements and factors for the positron-emitting channels is a tangible resource for the field.

major comments (1)
  1. [Abstract (final paragraph)] Abstract (final paragraph): The translation of the assumed T_{1/2}^{0ν} = 10^{24} y sensitivity into new-physics scales of 1–100 TeV for dimension-seven SMEFT operators (and the associated claim of degeneracy resolution across isotopes) rests on an external projection for NuDoubt++ that is neither derived nor referenced within the manuscript. This assumption is load-bearing for the quantitative complementarity statements.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback. We address the single major comment below and will revise the manuscript to strengthen the presentation.

read point-by-point responses

  1. Referee: The translation of the assumed T_{1/2}^{0ν} = 10^{24} y sensitivity into new-physics scales of 1–100 TeV for dimension-seven SMEFT operators (and the associated claim of degeneracy resolution across isotopes) rests on an external projection for NuDoubt++ that is neither derived nor referenced within the manuscript. This assumption is load-bearing for the quantitative complementarity statements.

    Authors: We agree that the NuDoubt++ sensitivity projection must be explicitly referenced to support the quantitative statements in the abstract. The value T_{1/2}^{0ν} = 10^{24} y is taken from the NuDoubt++ proposal (which is already cited in the introduction of the manuscript). We will add the appropriate citation directly to the final paragraph of the abstract and ensure the reference is visible in all sections discussing the 1–100 TeV scales and multi-isotope degeneracy resolution. This revision will make the complementarity claims fully traceable without altering the underlying physics results. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation uses external sensitivity assumption and computed NMEs without self-referential reduction.

full rationale

The abstract presents T_{1/2}^{0 u} = 10^{24} y as a projected sensitivity input and interprets it via NMEs and phase-space factors for ^{78}Kr, ^{106}Cd, ^{124}Xe. No quoted equations or steps reduce any claimed prediction (e.g., 1-100 TeV scales or degeneracy resolution) to a fitted parameter or self-citation by construction. The multi-isotope complementarity argument is independent content based on the provided quantities, satisfying self-contained status against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the 10^24 y sensitivity figure is an external experimental projection rather than a fitted quantity derived inside the work.

pith-pipeline@v0.9.1-grok · 5747 in / 1185 out tokens · 23780 ms · 2026-06-25T19:01:56.437734+00:00 · methodology

discussion (0)

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Reference graph

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