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Half-life of $^{136}$Xe for neutrinoless double-$\beta$ decay calculated with effective axial-vector current coupling unified for two-neurtino and neutrinoless double-$\beta$ decay modes

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper predicts that the neutrinoless double-beta decay half-life of 136Xe is (1.3–3.0)×10^31 years for a Majorana neutrino mass of 1 meV, about an order of magnitude longer than most earlier calculations.

desk verdict A new half-life prediction for 136Xe 0νββ that deserves a careful referee but rests on an unquantified first-order transfer of g_A between the two decay modes. read the letter →

arxiv 2506.23239 v2 pith:7NPASIZK submitted 2025-06-29 nucl-th nucl-ex

J. Terasaki , O. Civitarese This is my paper
classification nucl-thnucl-ex PACS 23.40.-s21.60.Jz14.60.Pq
keywords neutrinolessdouble-betadecaytwo-neutrinoeffectiveaxial-vectorcoupling136Xenuclearmatrixelementsquasiparticlerandom-phaseapproximationSkyrmeenergydensityfunctionalMajorananeutrinomass
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 aims to pin down the half-life of the neutrinoless double-$\beta$ decay ($0\nu\beta\beta$) of $^{136}$Xe, the decay whose observation would prove that the neutrino is its own antiparticle. Its strategy is to take the effective axial-vector coupling constant ($g_A^{\rm eff}$) that reproduces the measured two-neutrino double-$\beta$ half-life and transfer it to the neutrinoless mode, using the ratio of perturbed to leading-order matrix elements computed for each mode. The central claim is that $g_A^{\rm eff}$ is nearly the same for the two modes — about 1.14 for the SkM* interaction — because the neutrino potential enters both the numerator and the denominator of the ratio and approximately cancels. With this unified coupling the paper predicts $T_{1/2}^{0\nu} = (1.3{-}3.0)\times10^{31}$ y for an assumed Majorana mass of $\langle m_\nu\rangle = 1$ meV, about an order of magnitude longer than the older compilation range it is measured against. If the prediction is right, the half-life that experiments must reach is longer and the neutrino-mass bounds drawn from any given experimental limit are correspondingly weaker.

What carries the argument

The load-bearing object is the ratio $R = g_{A,0\nu}^{\rm eff}({\rm ld;pt})/g_{A,2\nu}^{\rm eff}({\rm ld;pt})$, built from the effective couplings that make each mode's leading-order matrix element reproduce its perturbed matrix element; the perturbed matrix elements include the leading Gamow-Teller and Fermi terms, vertex corrections, and the two-body current correction shown in Fig. 1. For the SkM* Skyrme interaction the ratio is 1.14, while the less realistic SGII interaction gives 0.54. The transfer equations (20) and (21) multiply the experimentally calibrated two-neutrino couplings $g_{A,2\nu}^{\rm eff}({\rm ld;exp})$ and $g_{A,2\nu}^{\rm eff}({\rm pt;exp})$ by $R$ to obtain the estimated neutrinoless-mode couplings, a non-perturbative step because the experimental half-life carries the higher-order physics that the one-step perturbed matrix elements miss.

What would settle it

A direct measurement or stronger experimental limit on the $0\nu\beta\beta$ half-life of $^{136}$Xe, combined with an independent determination of the neutrino mass scale, would settle the $(1.3{-}3.0)\times10^{31}$ y window, since a true half-life far outside it at $\langle m_\nu\rangle = 1$ meV would falsify the ratio transfer. Theoretically, recomputing the matrix elements with the perturbation summed beyond lowest order would test whether $R$ stays near 1.14; the SGII value 0.54 already shows the ratio is not interaction-independent, so an all-order SkM* calculation is a direct arbiter.

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Extended reading notes

Core claim

The central discovery is that the effective axial-vector couplings of the two double-$\beta$ decay modes nearly coincide: $g_{A,0\nu}^{\rm eff}({\rm ld;pt}) \simeq g_{A,2\nu}^{\rm eff}({\rm ld;pt})$ for the SkM* interaction. The authors compute the $0\nu\beta\beta$ and $2\nu\beta\beta$ matrix elements of $^{136}$Xe in the quasiparticle random-phase approximation, perturbing the decay operator once by the nucleon-nucleon potential through vertex corrections and a two-body current term. For each mode an effective coupling is defined as the value that makes the leading-order matrix element reproduce the perturbed one, and they find the two effective couplings are close even though the neutrinoless mode's virtual neutrino can carry arbitrarily high momentum. They trace this to an approximate cancellation: the neutrino potential sits in both the numerator and the denominator of the ratio, so it factorizes and drops out. That near-equality licenses the paper's main move — using the experimentally calibrated two-neutrino coupling, rescaled by the ratio 1.14, as the coupling for the neutrinoless mode. Five such estimation methods yield half-lives that cluster, and the paper concludes that the reliable $0\nu\beta\beta$ half-life of $^{136}$Xe is $(1.3{-}3.0)\times10^{31}$ y at $\langle m_\nu\rangle = 1$ meV.

Load-bearing premise

The load-bearing assumption is that one round of perturbation on the decay operator is a faithful guide to the full physics, so that the SkM* ratio 1.14 equals the ratio of the true non-perturbative effective couplings; the paper states that higher-order corrections are ignored, and the SGII result of 0.54 shows the ratio is sensitive to the interaction.

Editorial extensions

If this is right

  • The $0\nu\beta\beta$ half-life of $^{136}$Xe is $(1.3{-}3.0)\times10^{31}$ y at $\langle m_\nu\rangle = 1$ meV, an order of magnitude longer than the $(3{-}30)\times10^{29}$ y compilation of older calculations it is compared with.
  • The same effective axial-vector coupling, near $g_A^{\rm eff}\approx 1$, works for both decay modes, so the neutrinoless mode inherits the calibration of the measured two-neutrino mode instead of an ad hoc quenching.
  • The predicted half-life is stable across the five extraction methods (Comparisons 3–5 for SkM*), so the spread seen among earlier predictions is attributed to using the bare coupling with under-corrected matrix elements.
  • Because the predicted half-life is longer, any given experimental limit on $0\nu\beta\beta$ decay converts to a weaker upper bound on the Majorana neutrino mass.
  • The predicted range partially overlaps recent quenched shell-model and chiral effective-field-theory results at the $10^{31}$ y scale, so the lengthening is not isolated to this calculation.

Reading between the lines

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

  • The ratio-transference scheme is portable in principle to other double-beta emitters such as $^{76}$Ge or $^{130}$Te, but because the paper shows the ratio is interaction-dependent (1.14 for SkM* versus 0.54 for SGII), each nucleus and each energy functional would need its own validation before its half-life is trusted.
  • A sharp cross-framework test would be to compute the same ratio $R$ in shell-model or ab initio frameworks that include two-body currents; if $R\approx 1$ survives there, the universality of the effective axial-vector coupling is a genuine nuclear-physics fact rather than a feature of this QRPA-plus-Skyrme setup.
  • The calibration rides on the measured two-neutrino half-life, so more precise $2\nu\beta\beta$ measurements, including spectral shapes, would either tighten or destabilize the predicted $0\nu\beta\beta$ half-life.
  • An independent determination of the in-medium axial coupling, for instance from super-allowed Gamow-Teller decays, would arbitrate between the SkM* branch (which supports $g_A^{\rm eff}\approx 1$) and the SGII branch of the argument.
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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

4 major / 5 minor

Summary. The paper calculates the neutrinoless double-beta-decay (0νββ) half-life of 136Xe using effective axial-vector coupling constants obtained from the two-neutrino double-beta-decay (2νββ) mode. The NMEs include leading-order, vertex-correction, and two-body-current contributions computed in lowest-order perturbation theory with Skyrme interactions SkM* and SGII. The key observation is the near equality g_A,0ν^eff(ld;pt) ≃ g_A,2ν^eff(ld;pt) for SkM* (Eq. 15), which is used in Eqs. (20)–(21) to transfer the experimentally calibrated 2νββ effective coupling to the 0νββ mode. The authors predict T_{1/2}^{0ν} = (1.3–3.0)×10^31 y for ⟨mν⟩ = 1 meV, about an order of magnitude longer than the compilation of Ref. [27].

Significance. If the central premise is valid, the paper provides a falsifiable prediction for the 0νββ half-life of 136Xe and supports the idea of a common effective axial coupling for 2νββ and 0νββ modes, consistent with recent claims of g_A^eff ≈ 1. The inclusion of vertex corrections and two-body currents is a step beyond leading-order treatments, and the explicit use of the measured 2νββ half-life as a non-perturbative calibration is a useful idea. The predicted half-life range is directly testable by upcoming 136Xe experiments. However, the significance is conditional on the validity of the first-order perturbative transfer, which is not yet established.

major comments (4)
  1. [Eqs. (20)–(21), Table III] The load-bearing step of the paper is the transfer of the experimentally calibrated 2νββ effective coupling to the 0νββ mode. This transfer depends on the ratio R = g_A,0ν(ld;pt)/g_A,2ν(ld;pt), which is 1.14 for SkM* but 0.54 for SGII. The paper argues that SkM* is more reliable because of binding-energy systematics, but that argument concerns the overall interaction strength, not the convergence or universality of the ratio R. Since the closeness in Eq. (15) is not a robust property across the two interactions, the paper needs a second-order perturbative calculation or at least an explicit estimate of the neglected higher-order terms before the half-life band (1.3–3.0)×10^31 y can be considered reliable.
  2. [Table I and Eq. (16)] The claimed convergence of g_A,0ν/g_A,2ν toward unity is not demonstrated. Eq. (16) states that g_A,0ν(ld;ld) = g_A,2ν(ld;ld) = g_A^bare, which is true by definition of the leading-order calculation; it contains no dynamical information about convergence. The first-order values being close for SkM* is a single data point. Table I shows that the perturbative corrections are large: for SkM*, the two-body-current GT term for 0νββ is -2.731 compared with the leading term 3.095, and the 2νββ GT matrix element changes sign under perturbation (0.102 to -0.035). A perturbative series with corrections of this size cannot be assumed to have converged at first order.
  3. [Table IV and Fig. 2] The 'stability' of Comparisons 3–5 is presented as evidence of convergence, but the spread among these three SkM* half-lives is a factor of about 2.4 (127, 140, and 304 in units of 10^29 y), and the selection of these comparisons as most reliable is made after excluding Comparisons 1 and 2. The analogous SGII results do not cluster at all (337, 3990, and 4210 in units of 10^29 y). A quantitative convergence criterion is needed, and the paper should explain why the SGII failure does not also undermine the SkM* result beyond the binding-energy argument.
  4. [Eq. (20) and surrounding text] The final 0νββ half-life is, through Eq. (20), essentially proportional to the experimental 2νββ half-life, because g_A,2ν(ld;exp) is defined to reproduce that measured value. This is a legitimate calibration strategy, but it means the predictive content of the method rests entirely on the correction factor R and the NME ratios. The paper should state this dependence more explicitly and should propagate the uncertainty in R—including its strong interaction dependence—into an error estimate for the final half-life, rather than selecting one interaction and one cluster of comparisons.
minor comments (5)
  1. [Eq. (16) and following sentence] The phrase 'close to the convergence at the first-order perturbation' is unclear; the authors likely mean that the series appears to be converging, but the sentence should be rewritten to say what is actually being compared.
  2. [Table II caption] The caption contains the sentence 'these results were taken from Ref. [31]' with a lowercase initial letter; this should be 'These results were taken from Ref. [31].'
  3. [Table II] The notation 'ld' and 'pt' in g_A^eff is explained in the text, but a one-line definition in the table caption would improve readability for the reader who jumps directly to the table.
  4. [Fig. 2 caption] The figure would benefit from an explicit statement that the filled and open symbols correspond to SkM* and SGII, respectively, and that the y-axis is logarithmic.
  5. [after Eq. (17)] The sentence 'If ⟨mν⟩ = 10 meV, the half-lives are two orders of magnitude shorter' is correct because T_{1/2} ∝ 1/⟨mν⟩^2, but it could be clarified that this applies to all entries in Table IV.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 0νββ half-life is calibrated to the external 2νββ half-life and nontrivial NME ratios; Eq. (15) is a numerical finding, not a definition.

full rationale

The derivation chain is: compute leading and perturbed NMEs (Table I), define effective couplings by matching half-lives (Eqs. 11–14), observe the numerical closeness Eq. (15) for SkM*, then use the experimental 2νββ half-life as an external anchor to estimate g_A^eff,0ν via Eqs. (20)–(21) and compute T^{0ν}_{1/2}. Each step is an inference from a distinct observable or from NMEs; no step defines the predicted quantity in terms of itself. The experimental 2νββ half-life is an input, but it is a different decay mode, and the NME ratios and the correction factor R are not fitted to the 0ν decay half-life, which is never used in the fit. The trivial identity Eq. (16) is invoked in the convergence argument, but this is a weak warrant rather than a circular reduction: Eq. (15) is a nontrivial numerical result of Table II, and the SGII entry (R = 0.54) shows that the closeness is not forced by construction. The reliance on Ref. [31] for the analytical factorization of the neutrino potential is a self-citation, but the NME values are reproduced in the present paper and the interaction dependence of R is explicitly shown, so the cited result is testable and does not constitute a self-citation chain that merely restates the conclusion. The main weaknesses—first-order perturbation theory, possible higher-order corrections, and the interaction dependence of R—are concerns about accuracy and robustness, not about circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim inherits the entire QRPA-Skyrme framework (wave functions, pairing strengths, Skyrme functionals) from earlier literature, and additionally assumes that a lowest-order perturbative treatment of the transition operator is sufficient and that the first-order ratio of effective couplings survives to all orders. These are the load-bearing inputs the reader does not pay for in this letter.

free parameters (2)
  • like-particle pairing strengths (contact) = not quoted (from Ref. [17])
    The QRPA ground states use contact like-particle pairing; strengths are fixed to nuclear pairing properties in the EDF framework of Ref. [17]. The 0νββ NMEs inherit this choice, and the letter does not quantify the sensitivity.
  • proton-neutron pairing strength = not quoted (from Ref. [17])
    The proton-neutron particle-particle channel is known to control the 2νββ and 0νββ NMEs in QRPA; the strength comes from Ref. [17] and is not varied here, so the quoted half-life has no sensitivity estimate.
assumptions (5)
  • domain assumption QRPA provides an adequate description of the 0νββ and 2νββ nuclear wave functions of 136Xe.
    The entire NME calculation rests on the QRPA method of Ref. [34]; QRPA is a standard but uncontrolled approximation for double-beta decay.
  • ad hoc to paper Lowest-order perturbation theory (second-order Rayleigh-Schrödinger) for the transition operator, taking only diagrams (a), (b), (c) of Fig. 1, is sufficient; higher-order corrections are negligible.
    Stated in the text: 'We used a few approximations in our perturbed-NME calculations. Above all, the higher-order corrections are ignored.' The corrections are numerically large, so this is a substantial assumption.
  • ad hoc to paper The ratio g_A^eff,0ν(ld;pt)/g_A^eff,2ν(ld;pt) computed at first order equals the ratio of the full non-perturbative effective couplings.
    Equations (20)-(21) transfer the experimentally determined 2ν-mode g_A^eff to the 0ν mode using the first-order ratio; no proof is given that the ratio is unchanged by higher orders.
  • domain assumption The neutrino potential approximately factorizes and cancels in the ratio of perturbed to leading-order 0νββ NMEs, so the 0ν and 2ν couplings are close (from Ref. [31]).
    Invoked to justify Eq. (15); the analytical demonstration is only referenced to [31], not reproduced here.
  • ad hoc to paper The effective axial-vector coupling is the same for the 2ν and 0νββ modes, so the measured 2ν half-life can calibrate the 0νββ calculation without additional mode-specific quenching.
    This is the assumption underlying Eqs. (20)-(21); the paper's evidence for it is Eq. (15), which is a first-order numerical coincidence for one interaction, and no all-order proof is given.

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Pith. "Pith review of Half-life of $^{136}$Xe for neutrinoless double-$\beta$ decay calculated with effective axial-vector current coupling unified for two-neurtino and neutrinoless double-$\beta$ decay modes." pith.science (2026). https://pith.science/paper/7NPASIZK

@misc{pith2026250623239,
  author       = {Pith},
  title        = {Pith review of: Half-life of $^136$Xe for neutrinoless double-$\beta$ decay calculated with effective axial-vector current coupling unified for two-neurtino and neutrinoless double-$\beta$ decay modes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7NPASIZK}},
  note         = {Machine review of arXiv:2506.23239}
}
abstract

The upper limit on the mass of the Majorana neutrino, extracted from the limits on the nonobservation of the neutrinoless double-$\beta$ ($0\nu\beta\beta$) decay, is hampered by uncertainties in the matrix elements of the transition operators. Recently, we have shown that the values of the effective axial-vector current coupling constants ($g_A^\textrm{eff}$) for the $0\nu\beta\beta$ and the two-neutrino double-$\beta$ decays are close. This striking result was obtained for the first time by including vertex corrections and two-body currents in these matrix elements. In this letter, we calculate the half-life for the $0\nu\beta\beta$ decay ($T_{1/2}^{0\nu}$) of $^{136}$Xe using this closeness and show the convergence of the half-life with respect to the variation of the method to determine $g_A^\textrm{eff}$. The closeness of the $g_A^\textrm{eff}$ of the two decay modes plays a decisive role in predicting $T_{1/2}^{0\nu}$. The appropriate value of $g_A^\textrm{eff}$ depends on the assumptions made for the sectors of the nuclear structure and transition operators of the calculations within the perturbation scheme. The value $g_A^\textrm{eff}\approx 1$ is obtained when the SkM$^\ast$ is used to describe the nuclear structure component, while a smaller value of $g_A^\textrm{eff}$ is obtained by applying a less realistic interaction like the SGII one.

Figures

Figures reproduced from arXiv: 2506.23239 by the authors.

Figure 1
Figure 1. FIG. 1: Diagrams calculated for 0 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Illustration of calculated [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

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Reviewed August 6, 2026 · model on record in the stance chip above.