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Pinpointing the Mechanism of Neutrinoless Weak Decays with Positrons

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The ratio of the 124Xe electron-capture half-life to the 136Xe double-beta half-life separates the five possible long-range currents, with a value near 10 singling out the right-handed current.

desk verdict Solid ratio-based mechanism diagnostic for future positron-mode experiments, but the headline VRR test is explicitly conditional on Nature not activating two of the (VLL, T, S) triplet. read the letter →

arxiv 2608.04187 v1 pith:K63KNH7R submitted 2026-08-04 hep-ph

Julia Harz , George A. Parker This is my paper · ORCID
classification hep-ph
keywords neutrinolessdoublebetadecaypositron-emittingmodeselectroncapturehalf-liferatiosright-handedcurrentsleptonnumberviolationeffectivefieldtheorynuclearmatrixelements
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

This paper argues that the positron-emitting modes of neutrinoless weak decay, long dismissed as too slow to measure, carry a diagnostic the electron mode cannot: half-life ratios across modes identify which lepton-number-violating current drives the decay. The central example is the ratio $R = T_{1/2}^{0\nu}({}^{124}\mathrm{Xe},\mathrm{EC}\beta^+)/T_{1/2}^{0\nu}({}^{136}\mathrm{Xe},\beta^-\beta^-)$, predicted to be about $10$ for a purely right-handed current, about $199$ for the light-neutrino mass mechanism, and $95$--$307$ for scalar, tensor, and left-right vector currents. Because a captured bound-state electron flips the sign of certain interference terms, the $0\nu\mathrm{EC}\beta^+$ mode is selectively sensitive to the right-handed current. A measured ratio below about $83$, even with several currents interfering, would establish a right-handed contribution unless the signal comes from two or more members of an exactly degenerate triplet. This matters because a positron-mode non-observation already constrains the composition of an observed electron-mode signal.

What carries the argument

The load-bearing object is the cross-mode half-life ratio $R_i = C_i^{\beta^-\beta^-}({}^{136}\mathrm{Xe})/C_i^{\mathrm{EC}\beta^+}({}^{124}\mathrm{Xe})$, where each rate coefficient $C_i$ multiplies $|c_i|^2$ when one effective current dominates. The second ingredient is the sign-flip rule for the positron-emitting electron-capture mode: relative to $0\nu\beta^-\beta^-$, the interference phase-space factors transform as $G_{03} \to -f_e G_{03}$, $G_{04} \to f_e G_{04}$, and $G_{06} \to -f_e G_{06}$, with $f_e$ the bound-state correction; this reweighting is what makes $V_{\mathrm{RR}}$ stand out. The third is the normalized interference coefficient $\rho_{ij} = C_{ij}/\sqrt{C_{ii}C_{jj}}$, which measures whether two currents can be resolved by a single half-life. It shows an exact degeneracy among $V_{\mathrm{LL}}$, $T$, and $S$ in every mode, a mode-dependent tilt for $V_{\mathrm{LR}}$ interferences, and a nearly vanishing interference involving $V_{\mathrm{RR}}$, which is why the right-handed current remains the cleanest target.

What would settle it

Compute the $^{124}\mathrm{Xe}$ $0\nu\mathrm{EC}\beta^+$ nuclear matrix elements directly in a many-body method instead of inferring them from the electron-mode formula, and check the sign of the $G_{03}$ and $G_{06}$ interference contributions; alternatively, if $0\nu\beta^-\beta^-$ is observed in $^{136}\mathrm{Xe}$, measure the $^{124}\mathrm{Xe}$ $\mathrm{EC}\beta^+$ half-life and see whether the ratio falls at the predicted $V_{\mathrm{RR}}$ value near 10, or below 83 in a multi-current fit, rather than near the mass-mechanism value around 199.

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Extended reading notes

Core claim

The paper's central claim is that the half-life ratio $R = T_{1/2}^{0\nu}({}^{124}\mathrm{Xe},\mathrm{EC}\beta^+)/T_{1/2}^{0\nu}({}^{136}\mathrm{Xe},\beta^-\beta^-)$ is a mechanism discriminator that isotope ratios within a single mode cannot match. With the modern nuclear inputs, the single-current predictions are $R_{\mathrm{VRR}} \simeq 10$, $R_S \simeq 95$, $R_{\mathrm{VLL}} \simeq 199$, $R_T \simeq 261$, and $R_{\mathrm{VLR}} \simeq 307$; the same qualitative ordering survives in the legacy inputs. The physical reason is that in $0\nu\mathrm{EC}\beta^+$ the captured bound-state electron reverses the sign of the $\gamma^0$-containing interference terms, reweighting the phase-space factors so that $V_{\mathrm{RR}}$ is enhanced and the mass mechanism suppressed. When all five currents are allowed together, the ratio test remains meaningful: the interval spanned by all admixtures without $V_{\mathrm{RR}}$ has lower edge about $83$, while any admixture containing $V_{\mathrm{RR}}$ can reach ratios near $9$, so $R \lesssim 83$ identifies the right-handed current, with the single exception of an admixture drawn from the exactly degenerate $(V_{\mathrm{LL}},T,S)$ triplet.

Load-bearing premise

The whole $V_{\mathrm{RR}}$ discrimination rests on the assumption that $0\nu\beta^+\beta^+$ and $0\nu\mathrm{EC}\beta^+$ share the same nuclear matrix elements as each other for a given isotope, and that replacing an outgoing electron by a captured bound-state electron only flips the signs of the $\gamma^0$-containing phase-space interference terms in the stated way; if either piece is wrong, the predicted ratios shift and the fingerprint becomes an artifact.

Editorial extensions

If this is right

  • If $0\nu\beta^-\beta^-$ is observed near the current best limit, the same coupling strength implies a $0\nu\mathrm{EC}\beta^+$ signal in $^{124}\mathrm{Xe}$ about a factor 10 above that limit for $V_{\mathrm{RR}}$, but one to three orders of magnitude higher for the other four currents.
  • A $0\nu\mathrm{EC}\beta^+$ observation at the predicted $V_{\mathrm{RR}}$ crossover half-life would be a distinct signature of a right-handed current, while a null result at that level would exclude $V_{\mathrm{RR}}$ dominance of the electron-mode signal.
  • Even without a positron-mode observation, the bound $f_{V_{\mathrm{RR}}} \le (1/r - 1/R_{V_{\mathrm{LR}}})/(1/R_{V_{\mathrm{RR}}} - 1/R_{V_{\mathrm{LR}}})$ constrains the right-handed share of an observed electron-mode signal, independent of how the remaining share is distributed among the other currents.
  • Within the $\beta^-\beta^-$ mode alone, isotope-ratio discrimination is weak, with predictions agreeing within factors of a few, so the complementary positron modes are needed to break the degeneracies.
  • The threshold $R \lesssim 83$ remains the $V_{\mathrm{RR}}$ signature when interferences are included, provided the signal is not an admixture of two or more members of the $(V_{\mathrm{LL}},T,S)$ triplet.

Reading between the lines

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

  • Extending the same ratio test to other isotope pairs would probably reproduce the hierarchy because the selective reweighting is a property of the electron-capture mode, not of $^{124}\mathrm{Xe}$; the paper's own tables show $V_{\mathrm{RR}}$ lowest for every EC$\beta^+$ isotope considered.
  • A direct many-body calculation of the $0\nu\mathrm{EC}\beta^+$ matrix elements, rather than the crossing-symmetry assumption, would test the sign-flip rule that creates the $V_{\mathrm{RR}}$ enhancement; if the sign of $G_{03}$ or $G_{06}$ were different, the ratio hierarchy would change.
  • Combining the cross-mode ratio with the previously proposed isotope-ratio test could break the exact $(V_{\mathrm{LL}},T,S)$ degeneracy, because the degeneracy is tied to the single sub-amplitude $A_\nu$ while different isotopes weight the pieces of $A_\nu$ differently.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper extends the chiral-EFT master formula for neutrinoless double beta decay to the positron-emitting modes 0νβ+β+ and 0νECβ+, using crossing symmetry and a bound-state electron correction. The authors compute single-current sensitivities, crossover half-lives for the proposed NuDoubt++ experiment, and half-life ratios R = T_1/2[124Xe,ECβ+]/T_1/2[136Xe,β−β−] for the five long-range currents {VLL, VLR, VRR, T, S}. They find that the right-handed current VRR gives a parametrically smaller ratio (R ≈ 10) than the other single currents (R ≈ 95–307), and they analyze how this discrimination survives when multiple currents interfere. A key result is that a measured ratio R ≲ 83 would indicate a VRR contribution, provided the signal is not dominated by two or more members of the exactly degenerate (VLL, T, S) triplet. The implementation is validated against legacy DKT inputs, and results are shown for two independent nuclear-input sets.

Significance. If the results hold, the paper provides a concrete and parameter-free diagnostic for distinguishing new-physics mechanisms in neutrinoless weak decays: the half-life ratios involve no fitted couplings, and the VRR fingerprint is an order of magnitude below the other single-current predictions. The paper's strengths include a clean derivation of the positron-mode extension from crossing symmetry, a double-precision validation against the legacy DKT formalism, use of two independent nuclear input sets, and a systematic treatment of interference and degeneracies. The proposed NuDoubt++ experiment is an appropriate and timely target, and the paper's quantitative benchmarks are useful for experimental planning. The main limitation is that the headline discrimination criterion is conditional on assumptions that are partly acknowledged in Section VI but not fully carried through the abstract and Section V.

major comments (3)
  1. [Section VI / Table II / Appendix A.5] The headline VRR-discrimination threshold R ≲ 83 is not robust to the nuclear-structure input. Appendix A.5 states that if the scalar NME sign from [23] were opposite, the 'V RR-free' threshold would become R ≃ 50 rather than R ≃ 83. Since the central claim is the separation between the VRR interval (R_min ≈ 9) and the non-VRR intervals (R_min ≈ 83–97), this sign dependence is quantitatively material and should be propagated into the main-text statement of the criterion rather than confined to the appendix.
  2. [Section V / Abstract] The claim that a ratio R ≲ 83 (or the Section V statement R < 95) 'establishes a contribution from VRR' is valid only under the condition, stated in Section VI, that the admixture contains at most one member of the degenerate (VLL, T, S) triplet. Because VLL is the default mass mechanism and T and S are generated by dimension-7 operators that commonly co-exist, this is a plausible scenario rather than a remote corner. The abstract and the Section V single-current discussion do not carry this condition, so the headline result as advertised is stronger than what the analysis proves.
  3. [Section II.III / Appendix A.3] The positron-mode extension assumes that 0νβ+β+ and 0νECβ+ share the same NMEs for a given isotope and that the ECβ+ interference signs flip as specified in Eqs. (7)–(9). The numerical validation in Appendix A.3 is performed against the legacy DKT formalism, which encodes the same crossing and NME conventions, so it does not independently test these assumptions. Given that all positron-mode predictions and the VRR-discrimination claim rest on this step, an independent cross-check (for example, a direct computation or a second nuclear model for one isotope) or a more explicit discussion of the assumption's limitations is needed.
minor comments (5)
  1. [Section V heading] The heading 'AS A DISCRMNATOR' contains a typo; it should read 'AS A DISCRIMINATOR'.
  2. [Footnote 5] Footnote 5 refers to 'Section 5', but the paper uses Roman numerals; this should be 'Section V'.
  3. [Eq. (12)] The coupling bounds in Eq. (12) should explicitly state that the couplings are dimensionless, as implied by ε in Eq. (1).
  4. [Appendix A.4] Table III is computed at g_T' = 1 while the main analysis sets g_T' = 0; the caption and surrounding text should restate that this is a bounding exercise rather than the adopted input.
  5. [Reference [19]] Reference [19] has a stray quotation mark in the arXiv number ('1806.02780”') that should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the half-life ratios are parameter-free combinations of externally tabulated nuclear inputs, and the VLL-T-S degeneracy is explicitly flagged as a conditional limitation rather than assumed away.

full rationale

The derivation chain is self-contained. The inverse half-life for 0νβ−β− is taken from the chiral-EFT master formula of Refs. [19,20] (Eq. (5)), and the positron-mode extension is obtained by the crossing replacements of Eqs. (7)–(9) with nuclear inputs taken from Refs. [11–15]. The single-current ratios R_i in Eqs. (13)–(15) are ratios of precomputed coefficients C_i, in which the unknown coupling cancels; no parameter is fitted to the quantities being predicted. The multi-current analysis uses the same C matrices and the generalized eigenvalue problem of Eq. (21), again with no fitted input. The paper explicitly states that the legacy DKT inputs are used only for validation ('These legacy inputs serve for validation only'), and it explicitly conditions its main VRR criterion on the absence of two or more members of the exactly degenerate (VLL,T,S) triplet ('provided the signal is not caused by two or more members of the (Aν) triplet'). That is an honest limitation or physical assumption, not a reduction of the output to the input. There is no self-citation chain: the papers providing the master formula, NMEs, and PSFs [11–15,19,20] are not by the present authors. Uncertainties such as the sign of M_PS (Appendix 5) and g_T'=0 affect the numerical thresholds but do not make any equation definitionally equal to a fitted target. The central VRR-discrimination claim is therefore independent of the inputs that produce it, and no circular step is exhibited.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The paper introduces no fitted parameters and no new physical entities. Its predictions rest on external nuclear matrix elements, phase-space factors, and the chiral EFT master formula. The most important assumptions are the completeness of the long-range operator basis and the validity of the crossing-symmetry extension to positron modes, especially the shared-NME ansatz and the ECβ+ sign flips.

free parameters (1)
  • g_T' (tensor nucleon coupling) = 0
    Set to zero following the conservative choice of [14]. The paper notes that the value is otherwise undetermined and changes the tensor amplitude by O(10%) (Sec. II.II).
assumptions (5)
  • domain assumption The effective Lagrangian of Eq. (1), restricted to long-range light-neutrino exchange contributions, is complete for the three neutrinoless modes studied.
    Taken from [6,16,17]; short-range contributions are neglected throughout, which is standard but still an assumption about the new physics.
  • domain assumption The master formula of Eq. (5) and the sub-amplitude decomposition of Eq. (6) from [19,20] correctly describe 0νβ−β− with all five currents VLL, VLR, VRR, S, T.
    The paper builds directly on the chiral EFT result of [19,20] and does not re-derive it.
  • ad hoc to paper Crossing symmetry relates the positron modes to the electron mode: 0νβ+β+ uses Eq. (5) with unchanged leptonic-bilinear signs, and 0νECβ+ uses the sign replacements of Eqs. (7)-(9).
    This is the key novel extension. It is physically motivated by standard QFT crossing, but it is not proved in detail in the paper; it is only numerically checked against the legacy DKT inputs.
  • domain assumption For a given isotope, 0νβ+β+ and 0νECβ+ share the same nuclear matrix elements.
    Stated in Sec. II.III following [11,13]. If this fails, the ratio predictions would change.
  • domain assumption The positron-mode NMEs and PSFs from the cited literature (IBM-2 [14,15] and pnQRPA [12]) are valid and representative of the true nuclear structure.
    The paper uses two independent sets to bound the systematic uncertainty, but both are nuclear model calculations and could share common errors.

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Cite this review

Pith. "Pith review of Pinpointing the Mechanism of Neutrinoless Weak Decays with Positrons." pith.science (2026). https://pith.science/paper/K63KNH7R

@misc{pith2026260804187,
  author       = {Pith},
  title        = {Pith review of: Pinpointing the Mechanism of Neutrinoless Weak Decays with Positrons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K63KNH7R}},
  note         = {Machine review of arXiv:2608.04187}
}
read the original abstract

Neutrinoless double beta decay is the flagship laboratory probe of a Majorana contribution to the neutrino mass. However, besides the standard mass mechanism other higher- dimensional lepton number-violating interactions can enter, or even dominate, this process. The corresponding positron-emitting neutrinoless modes, such as electron capture or double-positron emission, have long been considered out of reach experimentally, due to their naturally smaller rates. Recently, innovative detector technologies as used in the proposed NuDoubt++ experiment are changing the game. In this work, we explore how a positron- and electron-mode detector can be complementary in the search for new physics. Assuming an observation of neutrinoless double beta decay, we predict the expected discovery half-life for the positron-modes. Using half-life ratios, especially between the double beta and electron capture modes, we demonstrate how underlying long-range interactions can be distinguished, in particular to identify a purely right-handed leptonic current.

Figures

Figures reproduced from arXiv: 2608.04187 by the authors.

Figure 1
Figure 1. FIG. 1. Long-range contributions to the three neutri [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Single-current sensitivities at [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Half-life sensitivity required on [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: applies this approach to all sixteen possi￾ble combinations: the four electron-mode isotopes and the six positron-mode isotopes in both decay channels, each using both positron datasets. Each cell shows the single-current half-life ratio with 136Xe: Ri [X] = T mode X T…
Figure 5
Figure 5. Figure 5: FIG. 5. Matrix of pairwise interference. Each cell shows the normalized interference coefficient [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Joint constraints in the scalar ( [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

Discussion (0). Continue with ORCID to comment.

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