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REVIEW 3 major objections 5 minor 16 references

Multi-isotope 0νββ limits are most stable for light-Majorana exchange; short-range operators can swing by large factors across nuclei and nuclear methods.

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2026-07-11 11:16 UTC pith:5MW425KN

load-bearing objection Clean, reproducible diagnostic that ranks operator interpretability by multi-isotope/NME spread; hierarchy is real under the stated single-operator, fixed-LEC setup. the 3 major comments →

arxiv 2607.04932 v1 pith:5MW425KN submitted 2026-07-06 hep-ph

Beyond Half-Life Limits: Robust Operator-Level Interpretation of Multi-Isotope Neutrinoless Double-Beta Decay

K. Ishidoshiro This is my paper
classification hep-ph
keywords neutrinoless double-beta decaylepton-number violationlow-energy operatorsnuclear matrix elementsmulti-isotope programisotope half-life ratiosoperator interpretability
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Half-life limits alone do not tell you how reliably you can map a neutrinoless double-beta result onto a low-energy lepton-number-violating coefficient. This paper converts current and projected half-life sensitivities into coefficient limits for several isotopes and nuclear matrix-element methods, then measures how much those limits change when isotope and method are varied. For the operators studied, the standard light-Majorana exchange mechanism is the most stable; selected long-range dimension-six operators stay moderately stable; short-range dimension-nine examples can shift by much larger factors. The same ranking appears when one asks, after a hypothetical discovery in one isotope, how stably the same operator predicts half-lives in other isotopes. A multi-isotope program therefore does more than deepen the half-life reach: it tests whether the operator interpretation itself is trustworthy before one tries to connect it to ultraviolet models.

Core claim

Across the benchmark current and future multi-isotope sets, the light-Majorana mechanism yields the most stable coefficient limits and the most stable post-discovery isotope half-life ratios; selected dimension-six operators remain reasonably robust; short-range dimension-nine examples show stronger isotope- and nuclear-method dependence, so multi-isotope data test interpretive stability beyond raw half-life sensitivity.

What carries the argument

Benchmark-set spread of coefficient limits (worst-to-best ratio over isotope × nuclear-method combinations) and post-discovery ratio spread of isotope-to-isotope half-life ratios under single-operator dominance; both are worst-case stability diagnostics, not full statistical uncertainties.

Load-bearing premise

The post-discovery tests assume one operator dominates and fix the coefficient from a single reference isotope, while the nuclear and hadronic inputs used for the rate factors are held fixed rather than varied.

What would settle it

If, for the same future isotope set and operator classes, varying nuclear matrix-element methods and isotopes produced a reversed or erased stability hierarchy (e.g., light-Majorana no longer the smallest spread, or short-range dimension-nine no longer the largest), the claimed ranking of interpretive stability would fail.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper argues that multi-isotope 0νββ programs should be judged not only by half-life reach but by the stability of the inferred low-energy LNV coefficients under changes of isotope and NME method. Using νDoBe rate factors, it converts current and future half-life benchmarks for 136Xe, 76Ge, 130Te/100Mo into coefficient limits for a compact operator set (m_ββ, V_L^(6), T^(6), 3L^(9), 6^(9)), quantifies non-observation stability by the benchmark-set spread S_bench = |C|_worst_max / |C|_best_max, and quantifies post-discovery stability by the spread of isotope-to-isotope half-life ratios under single-operator dominance. For these examples the light-Majorana case is most stable (future S_bench ≈ 2.22), selected dim-6 operators are intermediate (≈ 3.1), and short-range dim-9 examples range from moderate (≈ 4.24) to large (≈ 29); the same hierarchy appears in ratio spreads (Table III). Appendices decompose the spread into NME-only and isotope-only pieces and check the compact set against a full operator survey.

Significance. If the reported hierarchy holds under the stated assumptions, the work supplies a practical, reproducible diagnostic for deciding which low-energy operator scenarios can support isotope-ratio tests after a discovery and which require more care before UV matching. Strengths include transparent use of the public νDoBe package, explicit best/worst limits and spreads (Table II, Fig. 1), NME-only and isotope-only decompositions (Appendix A), a full-operator survey (Appendix B), and an explicit interpretability plane (Fig. 2). The analysis is comparative rather than a full uncertainty budget, but it cleanly separates sensitivity reach from interpretive robustness—an issue of genuine interest for next-generation multi-isotope programs.

major comments (3)
  1. Sec. II B and Eqs. (8)–(9): all coefficient limits and spreads are obtained by switching on one operator at a time. Sec. V correctly notes that realistic UV footprints can generate several operators with model-dependent weights and interference. Because the central claim is a hierarchy of interpretive stability used to classify which operators are “suitable for isotope-ratio tests,” the manuscript should either (i) demonstrate that the hierarchy is stable under a few representative mixed-operator footprints, or (ii) state more sharply that the classification is a single-operator baseline only and that mixed-operator reordering remains untested. Without one of these, the practical recommendation in the abstract and conclusions over-reaches the calculation.
  2. Sec. V and Appendix A (esp. Table IV for 6^(9)): hadronic LECs are held fixed at the νDoBe defaults, yet short-range dim-9 operators are known to be most sensitive to poorly constrained LECs. The extreme S_bench ≈ 29 for 6^(9) is already driven by large NME variation in 136Xe; O(1) LEC shifts would act on the same short-range matrix elements and could reorder the dim-9 sector relative to dim-6. A minimal sensitivity check (e.g., rescaling the dominant short-range LECs by factors of a few for 3L^(9) and 6^(9)) is needed before the hierarchy is used to decide which operators require “more care before being connected to ultraviolet models.”
  3. Sec. II A and Table II: the future isotope set replaces 130Te by 100Mo and adopts specific design sensitivities (Xe 2e27 yr, Ge 1e28 yr, Mo 1.6e27 yr). The reduction of future spreads for m_ββ and dim-6 is attributed to a “more balanced” reach. Because S_bench mixes experimental sensitivity pattern with nuclear variation, the hierarchy could shift under a different but still plausible future set (e.g., retaining Te or different CUPID/LEGEND targets). A short robustness check with one alternate future triple would show whether the reported ordering is an artifact of the chosen benchmarks.
minor comments (5)
  1. Eq. (9) and surrounding text: clarify that |C|_max is the upper bound allowed by a given half-life, not a maximum over isotopes/methods; the wording is correct but easy to misread when “best/worst” appear later.
  2. Table I and Sec. II B: mass dimensions of the coefficients differ; a one-sentence reminder that numerical |C| values for different dimensions are not directly comparable would help non-EFT readers.
  3. Fig. 1 right panel and Fig. 4: the log-scale spread axis jumps from 4 to 10 to 30; a minor tick or annotation for the moderate dim-9 cluster would improve readability.
  4. Sec. IV A: the choice of 136Xe as the sole reference isotope for all ratio spreads is convenient but not motivated; a brief note that the hierarchy is stable under Ge or Mo as reference (or a short check) would strengthen the post-discovery section.
  5. Appendix B / Table VI: the grouping of dim-9 operators into “moderate / large / extreme” patterns is useful diagnostically; state explicitly that it is basis- and benchmark-dependent, as already hinted in the text.

Circularity Check

0 steps flagged

No significant circularity: coefficient limits and spreads are direct computational outputs from external half-life inputs and independent νDoBe rate factors, not tautological restatements or fitted predictions.

full rationale

The derivation chain is self-contained and non-circular. Half-life limits/sensitivities (Eqs. 1–6) are taken from published experimental sources; rate factors K_x are evaluated with the external public νDoBe package (Ref. [6]); coefficient limits follow by the elementary inversion |C|_max = 1/sqrt(K_x T_1/2) (Eq. 9); and the diagnostics S_bench, S_NME, S_iso and ratio spreads are simply max/min ratios of those computed numbers (Eqs. 11–13, 17). No parameter is fitted to a data subset and then re-presented as a prediction; no uniqueness theorem or ansatz is imported via self-citation; operator labels and normalizations are those of the published νDoBe basis. The single-operator and fixed-LEC assumptions are stated explicitly as limitations (Secs. II B, V), not hidden premises that force the hierarchy by construction. The reported stability ordering is therefore an empirical output of the chosen benchmark set, not a circular restatement of the inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 3 invented entities

The central hierarchy is a computational comparison inside a fixed low-energy EFT tool. Load-bearing inputs are published half-life benchmarks, the νDoBe rate-factor library (including its NME sets and fixed hadronic LECs), single-operator switching, and the authors’ choice of representative isotope and operator sets. No new particles or forces are postulated; the invented objects are diagnostic statistics.

free parameters (2)
  • Future half-life benchmark values (Xe 2e27 yr, Ge 1e28 yr, Mo 1.6e27 yr)
    Chosen as representative design/target sensitivities rather than measured data; they set the absolute scale of future |C|_max and which isotope wins the best limit, though uniform rescaling would leave spreads unchanged.
  • Compact operator subset {m_ββ, V_L^(6), T^(6), 3L^(9), 6^(9)}
    Hand-selected to sample stable / intermediate / large-spread patterns; the full survey (Appendix B) is used only as a check that the patterns are representative.
axioms (4)
  • domain assumption νDoBe rate factors K_x correctly encode phase space, NMEs, and hadronic matching for each isotope–operator–NME combination in a common convention.
    All coefficient limits and ratios are obtained from Eq. (8)–(9) and Eq. (16) using those factors (Sec. II B).
  • domain assumption Single-operator dominance: only one low-energy coefficient is switched on at a time; interference is neglected.
    Stated explicitly for both non-observation limits and post-discovery benchmarks (Sec. II B, Sec. IV).
  • domain assumption Hadronic low-energy constants in the chiral matching are held fixed at the νDoBe defaults.
    Discussion (Sec. V) notes they are not varied; spreads are therefore diagnostics at fixed LEC input.
  • ad hoc to paper The four NME methods (CDFT, IBM2, QRPA, SM) and the chosen current/future isotope triples adequately sample the relevant interpretive variation.
    Benchmark sets are representative choices, not a complete experimental or nuclear survey (Sec. II A).
invented entities (3)
  • Benchmark-set spread S_bench(O) = |C|_worst_max / |C|_best_max over isotope×NME combinations no independent evidence
    purpose: Worst-case diagnostic of interpretive stability for non-observation coefficient limits.
    Defined in Sec. II B; not a statistical uncertainty but a classifier used throughout the paper.
  • Post-discovery ratio spread (max/min of T_target/T_ref over NME methods) no independent evidence
    purpose: Quantify method dependence of predicted isotope half-life patterns under single-operator dominance.
    Defined in Sec. IV A; used to build the interpretability plane (Fig. 2).
  • Interpretability plane (S_bench vs ratio spread) no independent evidence
    purpose: Visual summary of which operator classes are stable enough for multi-isotope tests.
    Introduced in Sec. V / Fig. 2 as a combined diagnostic.

pith-pipeline@v1.1.0-grok45 · 17556 in / 3285 out tokens · 33022 ms · 2026-07-11T11:16:59.863150+00:00 · methodology

0 comments
read the original abstract

Current and future neutrinoless double-beta decay ($0\nu\beta\beta$) searches are usually characterized by half-life limits or projected sensitivities. For operator-level interpretation, however, the relevant question is not only the strength of the limit, but also the stability of the inferred constraints on low-energy lepton-number-violating (LNV) coefficients under changes of isotope and nuclear matrix-element (NME) method. Using $\nu$DoBe, we convert half-life limits or projected sensitivities into limits on low-energy LNV coefficients for several choices of isotope, operator class, and NME method. We then compare the resulting limits across isotopes and NME methods. We quantify the stability by the spread of coefficient limits in non-observation scenarios and, for single-operator post-discovery benchmarks, by the spread of isotope-to-isotope half-life ratios. For the operator examples considered in this paper, the light-Majorana exchange mechanism gives the most stable interpretation. The selected dimension-six operators remain reasonably robust, while the short-range dimension-nine examples show a stronger dependence on isotope and NME-method choices. The same hierarchy appears in post-discovery benchmarks based on isotope-to-isotope half-life ratios: the reliability of such tests depends on whether the predicted half-life pattern remains stable across NME methods. A multi-isotope $0\nu\beta\beta$ program therefore provides information beyond half-life reach by testing the stability of the operator interpretation. This spread-based analysis provides a practical way to identify which low-energy operator scenarios are suitable for isotope-ratio tests after a possible discovery, and which require more care before being connected to ultraviolet models of lepton-number violation.

Figures

Figures reproduced from arXiv: 2607.04932 by K. Ishidoshiro.

Figure 1
Figure 1. Figure 1: FIG. 1. Summary of the compact operator set. The left panel shows the best coefficient limits in the current and future sets. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Interpretability plane for the selected operator [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Full operator-by-operator counterpart of the left panel of Fig. 1. The figure shows the best coefficient limits for all [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Full operator-by-operator counterpart of the right panel of Fig. 1. The figure shows the spread of coefficient limits [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

discussion (0)

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Reference graph

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