{"id":"eb5035ad-c737-4fff-b3ea-804a5479b758","arxiv_id":"2608.04187","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Half-life ratios between neutrinoless double beta decay and its positron-emitting electron-capture version can single out a purely right-handed current, predicting a 0νECβ+ half-life in 124Xe about 20 times shorter than for the mass mechanism.","lead":"This paper shows that if neutrinoless double beta decay is ever seen, a companion positron-emitting process could reveal whether the decay is driven by a right-handed weak interaction rather than by neutrino mass. The right-handed option would appear roughly twenty times earlier in a proposed detector, turning a hard-to-build experiment into a diagnostic tool.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The VLL–T–S exact degeneracy lets non-VRR admixtures mimic any ratio, including R≈10, so the R<83 test establishes VRR only under the paper's explicit at-most-one-Aν-current assumption.","rationale":"The reader's ACCEPT verdict is sound in its conditional form. I identify a different load-bearing point than the reader's sign/shared-NME worry: the exact VLL–T–S degeneracy. It is not a numerical or technical error but a structural limitation of the half-life-ratio observable. However, the paper explicitly flags this degeneracy and conditions its central conclusion on it, so the argument is internally consistent. The concrete test would confirm what the paper's own rank-one argument already implies: any non-VRR mixture of the Aν-triplet currents can produce the VRR-like ratio. This does not invalidate the paper, but it should be kept prominent in any presentation of the result; in particular, 'identify a purely right-handed current' should be read as 'identify VRR conditioned on at most one Aν-current being active.' Since that conditioning is present in the body and the reader's summary, I do not change the verdict.","tokens_in":20704,"tokens_out":17950,"duration_ms":178946,"concrete_test":"Reconstruct the 2×2 rate matrices C_{ββ} and C_{EC} for the (VLL,T) subspace from the NMEs of [20] (136Xe) and [14] (124Xe) using Eq. (5) and Eq. (6) with only VLL and T nonzero. Solve det(C_{ββ} − R C_{EC}) = 0; if the generalized spectrum is [0,∞], exhibit a normalized vector (VLL,T) giving R = 9.8, the VRR single-current value. If such a vector exists, the 'R<83 ⇒ VRR' criterion is demonstrably fakeable by a VLL+T admixture; if the interval does not include 9.8, the degeneracy concern is mitigated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section VI (family (a), Table II) shows that VLL, T, and S enter the rate only through the sub-amplitude Aν. For each mode, the rate matrix on this subspace is therefore rank one: in an ECβ+ measurement the rate is G01^{EC}|A^{EC}·c|^2 and in β−β− it is G01^{ββ}|A^{ββ}·c|^2, with the same two-current coefficient vector c. The half-life ratio R(c) is then the ratio of projections of c onto two different NME vectors A^{ββ} and A^{EC}; unless these vectors are parallel, R ranges over [0,∞] as the admixture of, say, VLL and T is varied. Consequently a VLL+T (or VLL+S or T+S) mixture can reproduce R≈10, the VRR fingerprint, with no right-handed current at all. The paper's headline criterion 'R≲83 establishes VRR' is therefore valid only under the additional assumption that at most one element of the (VLL,T,S) triplet is present. That assumption is not guaranteed: the mass mechanism VLL is a default expectation for Majorana neutrinos, and S/T are generated by common dimension-7 operators, so a multi-current admixture is a plausible scenario rather than an exotic corner. The paper states this caveat in Section VI and the conclusions, but it is the load-bearing condition of the central claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":21058,"tokens_out":5734,"duration_ms":53484,"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":[{"comment":"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.","section":"Section VI / Table II / Appendix A.5"},{"comment":"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.","section":"Section V / Abstract"},{"comment":"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.","section":"Section II.III / Appendix A.3"}],"minor_comments":[{"comment":"The heading 'AS A DISCRMNATOR' contains a typo; it should read 'AS A DISCRIMINATOR'.","section":"Section V heading"},{"comment":"Footnote 5 refers to 'Section 5', but the paper uses Roman numerals; this should be 'Section V'.","section":"Footnote 5"},{"comment":"The coupling bounds in Eq. (12) should explicitly state that the couplings are dimensionless, as implied by ε in Eq. (1).","section":"Eq. (12)"},{"comment":"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.","section":"Appendix A.4"},{"comment":"Reference [19] has a stray quotation mark in the arXiv number ('1806.02780”') that should be corrected.","section":"Reference [19]"}],"recommendation":"major_revision","confidential_remarks":"The paper is careful and the main caveat is acknowledged in Section VI, but the abstract and Section V oversell the unconditional identification of VRR. The appendix's R ≃ 50 alternative threshold is the strongest reason the main text needs revision: the central claim is defensible only if the criterion is presented with its nuclear-sign dependence and with the at-most-one-Aν-triplet condition prominently attached. If the authors reframe the claim accordingly and incorporate the nuclear-input range into the main text, I would be happy to support acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a solid, honest paper. The new piece is a concrete diagnostic: given a 0νββ discovery in 136Xe or 76Ge, the 124Xe ECβ+ half-life ratio separates the right-handed vector current VRR (R≈10) from the mass mechanism and scalar/tensor/left-right currents (R≈95–307). The crossover half-life benchmark (~4×10^27 yr for VRR) and the cross-mode ratio atlas are genuinely new, and the two independent nuclear input sets agree on the VRR hierarchy. The chiral-EFT extension to positron modes is transparent; the crossing-symmetry sign flips in Eqs. (7)-(9) are standard, and the appendix shows the implementation matches the legacy DKT formalism to double precision. No fitting is involved; the coupling cancels in the ratios.\n\nThe soft spot is the one the authors acknowledge but arguably underplay. VLL, T, and S enter the rate only through the single sub-amplitude Aν. On that subspace the rate matrix is rank one for any mode, so a VLL+T admixture can reproduce essentially any ratio, including R≈10, with no right-handed current at all. The paper's criterion 'R≲83 establishes VRR' is therefore true only if at most one of the Aν triplet is active. The paper states this caveat in Section VI and the conclusions, but it is load-bearing rather than a corner case: the light-neutrino mass mechanism is the default expectation, and S or T are natural dimension-seven SMEFT effects. If Nature activates two of them, the headline diagnostic fails. The authors should make this condition explicit in the abstract and should quantify how a third observable (another isotope pair, or angular correlations) can break the degeneracy.\n\nMinor concerns: the shared-NME assumption for β+β+ and ECβ+ is inherited from the legacy literature and not cross-checked by a dedicated positron-mode calculation, and g_T′=0 is a conservative choice that leaves an O(10%) uncertainty on the tensor bounds. Both are clearly stated. The citation pattern is fine; the comparison with the overlapping recent paper [14] is fair and reproducible.\n\nVerdict: the single-current and crossover results are solid and should be published; the multi-current discrimination is real but conditional. This deserves a serious referee, and I would cite it. My recommendation: send to peer review, with a request to foreground the triplet degeneracy and propose concrete ways to break it.","headline":"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.","tokens_in":21562,"tokens_out":4075,"would_cite":true,"duration_ms":38380,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["neutrinoless double beta decay","positron-emitting decay modes","electron capture","half-life ratios","right-handed currents","lepton number violation","effective field theory","nuclear matrix elements"],"falsifier":"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.","tokens_in":20500,"feed_emoji":"⚛️","tokens_out":9625,"duration_ms":74808,"temperature":0.7,"pith_summary":"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.","feed_headline":"A ratio near 10 exposes right-handed neutrinoless decay","feed_subtitle":"If double beta decay is seen, the xenon positron-capture mode separates five new-physics mechanisms.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the chiral effective field theory master formula and sub-amplitude decomposition that the paper extends to the positron-emitting modes.","marker":"[19, 20]"},{"why":"Supplies the original positron-mode nuclear matrix elements and rate formalism used for validation and as the legacy input.","marker":"[12]"},{"why":"Supplies the updated tabulated positron-mode nuclear matrix elements and phase-space factors used as the modern input, along with an overlapping independent analysis.","marker":"[14]"},{"why":"Supplies the phase-space factors for $\\beta^+\\beta^+$ and electron-capture modes in the modern input set.","marker":"[13]"},{"why":"Supplies the interacting-boson-model nuclear matrix elements with isospin restoration behind the modern positron-mode calculations.","marker":"[15]"},{"why":"Supplies the legacy phase-space factors and original positron-mode rate formulas used as the second input set.","marker":"[11]"},{"why":"Supplies the electron-mode nuclear matrix elements and phase-space factors for the four $\\beta^-\\beta^-$ isotopes.","marker":"[23]"},{"why":"Proposed half-life ratios of different isotopes as a mechanism discriminator; the paper compares this with cross-mode ratios and finds the latter much more powerful.","marker":"[8]"},{"why":"Provides the current best half-life limit used to set the crossover benchmarks and coupling bounds.","marker":"[2]"}],"fun_headline_variants":["Half-life ratio near 10 pinpoints right-handed neutrinoless decay","Positron-mode ratio distinguishes five new-physics mechanisms","Xenon ECβ+ ratio identifies right-handed leptonic current","Neutrinoless decay: positron mode ratio reveals mechanism","Electron-capture double-beta ratio exposes right-handed current"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Half-life ratio near 10 pinpoints right-handed neutrinoless decay","Positron-mode ratio distinguishes five new-physics mechanisms","Xenon ECβ+ ratio identifies right-handed leptonic current","Neutrinoless decay: positron mode ratio reveals mechanism","Electron-capture double-beta ratio exposes right-handed current"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000722,"raw_usage":{"total_tokens":3278,"prompt_tokens":1025,"completion_tokens":2253,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":641,"completion_tokens_details":{"reasoning_tokens":2164}},"tokens_in":641,"tokens_out":2253,"duration_ms":16054,"temperature":1.0,"reasoning_tokens":2164,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:41:43.240487+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Hirsch, K","cited_arxiv_id":null,"evidence_quote":"Supplies the original positron-mode nuclear matrix elements and rate formalism used for validation and as the legacy input."},{"cited_title":"Positron-Emitting and Electron-Capturing Double-Beta Processes in the Standard Model and Beyond","cited_arxiv_id":"2606.26097","evidence_quote":"Supplies the updated tabulated positron-mode nuclear matrix elements and phase-space factors used as the modern input, along with an overlapping independent analysis."},{"cited_title":"Doi and T","cited_arxiv_id":null,"evidence_quote":"Supplies the legacy phase-space factors and original positron-mode rate formulas used as the second input set."}],"review_version":1}