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arxiv: 2606.26926 · v1 · pith:4CRJUJ43new · submitted 2026-06-25 · ⚛️ nucl-th

Challenging chiral EFT with tritium beta decay

D.F. Ramirez Jimenez , S. Heihoff , J. Golak , E. Epelbaum , H. Krebs , P. Reinert , R. Skibinski , K. Topolnicki
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H. Witala
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Pith reviewed 2026-06-26 02:05 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords chiral effective field theorytritium beta decayGamow-Teller matrix elementaxial current operatornucleon-deuteron scatteringlow-energy constantsN2LOtritium half-life
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The pith

Chiral effective field theory at N2LO overestimates the tritium Gamow-Teller reduced matrix element when the short-range axial current is fixed from nucleon-deuteron scattering.

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

The paper investigates tritium beta decay in chiral effective field theory up to N2LO with LENPIC interactions. Instead of fitting the low-energy constant D to the decay, the authors determine it from nucleon-deuteron scattering observables that govern short-range parts of the axial current and three-nucleon forces. The resulting predictions for the Gamow-Teller reduced matrix element exceed the measured value, and this mismatch holds when the pion-nucleon couplings or regularization scheme are varied within reasonable ranges. The work identifies fine-tuning between long-range and short-range pieces that makes the observable sensitive to higher-order terms. A reader would care because tritium beta decay provides a clean test of how well chiral EFT describes weak transitions in light nuclei without extra tuning.

Core claim

Using nucleon-deuteron scattering observables to fix the low-energy constant D that controls short-range two-body axial currents, chiral EFT at N2LO produces parameter-free predictions for the tritium Gamow-Teller reduced matrix element that considerably overestimate the empirical value, a result robust to reasonable changes in pion-nucleon couplings and regularization.

What carries the argument

The low-energy constant D in the short-range part of the exchange axial current operator, fixed from nucleon-deuteron scattering observables.

If this is right

  • The Gamow-Teller matrix element in tritium exhibits fine-tuned cancellations between long-range and short-range contributions at N2LO.
  • There is considerable N2LO truncation uncertainty for tritium beta decay.
  • Large higher-order two-body corrections to the axial current are expected.
  • More definite conclusions require a full fourth-order analysis of both nucleon-deuteron scattering and the tritium half-life.

Where Pith is reading between the lines

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

  • If the discrepancy survives at N3LO, the method of fixing short-range currents from scattering data may need to be revisited for consistency across few-body systems.
  • Similar overestimations could appear in other weak processes in light nuclei that rely on the same axial current operators.
  • The observed fine-tuning implies that tritium beta decay may be unusually sensitive to the balance of contributions that are treated perturbatively in chiral EFT.

Load-bearing premise

The low-energy constant D fixed from nucleon-deuteron scattering observables correctly captures the short-range contributions to the axial current operator inside the tritium nucleus.

What would settle it

A complete N3LO calculation of nucleon-deuteron scattering observables together with the tritium Gamow-Teller matrix element that brings the prediction into agreement with the empirical value.

Figures

Figures reproduced from arXiv: 2606.26926 by D.F. Ramirez Jimenez, E. Epelbaum, H. Krebs, H. Witala, J. Golak, K. Topolnicki, P. Reinert, R. Skibinski, S. Heihoff.

Figure 1
Figure 1. Figure 1: FIG. 1: (Color online). Constraints on the values of [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
read the original abstract

We present a detailed investigation of tritium beta decay up to third order (N2LO) in chiral effective field theory (EFT) using the LENPIC interactions. Unlike existing studies, we use nucleon-deuteron scattering observables to fix the low-energy constant D that governs the strength of the short-range contributions to the exchange axial current operator and three-nucleon forces. Surprisingly, the resulting parameter-free predictions for the tritium Gamow-Teller reduced matrix element are found to considerably overestimate its empirical value. This result remains robust against reasonable variations of the pion-nucleon coupling constants and regularization scheme. A closer look at the size of the parameter-free long-range two-body contributions to the Gamow-Teller matrix element reveals the fine-tuned nature this observable in chiral EFT, which may partially explain the observed deviation. Our results indicate a considerable N2LO truncation uncertainty for tritium beta decay and point towards large higher-order two-body corrections. More definite conclusions await a complete fourth-order analysis of nucleon-deuteron scattering observables and tritium half-life.

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

3 major / 2 minor

Summary. The manuscript calculates the tritium Gamow-Teller reduced matrix element in chiral EFT up to N2LO with LENPIC interactions. The LEC D governing short-range two-body axial currents and 3NF is fixed from nucleon-deuteron scattering observables, yielding parameter-free predictions that considerably overestimate the empirical value. The overestimation is reported as robust to variations in g_A and regularization scheme; the authors attribute part of the discrepancy to fine-tuning in the long-range two-body contributions and conclude that N2LO truncation uncertainty is large, calling for a full N3LO analysis.

Significance. If the central result holds, the work provides a concrete, parameter-free test of chiral EFT convergence for a weak observable in the A=3 system, highlighting both the fine-tuned cancellation between one- and two-body currents and the potential size of higher-order two-body corrections. The use of independent scattering data to determine D is a methodological strength that lowers circularity.

major comments (3)
  1. [axial current operator and Nd fit procedure] The central claim that the N2LO prediction is parameter-free and diagnostic of truncation error rests on the assumption that the single LEC D, determined from Nd scattering, correctly parametrizes the short-range axial current contribution in tritium beta decay. The manuscript does not demonstrate that the linear combination of short-range operators appearing in the tritium Gamow-Teller matrix element is the same combination constrained by the Nd observables used in the fit (see the section on the axial current operator and the Nd fit procedure).
  2. [robustness analysis] The robustness analysis varies g_A and the regularization scheme but does not test sensitivity to the precise set of Nd scattering observables or to possible additional short-range axial LECs that might enter at this order in the A=3 system. This directly affects whether the observed overestimation can be attributed to missing long-range higher-order terms.
  3. [discussion of long-range two-body contributions] The discussion of fine-tuning in the long-range two-body contributions is presented as partial explanation for the deviation, yet no quantitative decomposition (e.g., separate one-body, long-range two-body, and short-range two-body contributions with uncertainties) is provided to show how large the cancellation must be to reach the empirical value.
minor comments (2)
  1. [Abstract] Notation for chiral orders should be stated explicitly once (LO, NLO, N2LO) to avoid any ambiguity with the phrase 'third order (N2LO)'.
  2. Figure captions and table headings should include the precise definition of the Gamow-Teller reduced matrix element used (including any normalization factors) for direct comparison with experimental extractions.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We respond to each major comment below.

read point-by-point responses

  1. Referee: [axial current operator and Nd fit procedure] The central claim that the N2LO prediction is parameter-free and diagnostic of truncation error rests on the assumption that the single LEC D, determined from Nd scattering, correctly parametrizes the short-range axial current contribution in tritium beta decay. The manuscript does not demonstrate that the linear combination of short-range operators appearing in the tritium Gamow-Teller matrix element is the same combination constrained by the Nd observables used in the fit (see the section on the axial current operator and the Nd fit procedure).

    Authors: In the standard formulation of chiral EFT at N2LO, the LEC D multiplies the single short-range two-body axial current operator that enters both Nd scattering and the tritium Gamow-Teller matrix element; the same linear combination therefore appears in both cases. We will add an explicit statement of this operator equivalence (with reference to the relevant chiral Lagrangian terms) to the revised manuscript to make the connection unambiguous. revision: yes

  2. Referee: [robustness analysis] The robustness analysis varies g_A and the regularization scheme but does not test sensitivity to the precise set of Nd scattering observables or to possible additional short-range axial LECs that might enter at this order in the A=3 system. This directly affects whether the observed overestimation can be attributed to missing long-range higher-order terms.

    Authors: At N2LO only a single short-range axial LEC (D) appears, so no additional LECs enter the A=3 system at this order. We agree, however, that the dependence on the precise choice of Nd observables used to determine D should be quantified. We will add a sensitivity study that refits D to different subsets of the Nd data and reports the resulting variation in the tritium matrix element. revision: yes

  3. Referee: [discussion of long-range two-body contributions] The discussion of fine-tuning in the long-range two-body contributions is presented as partial explanation for the deviation, yet no quantitative decomposition (e.g., separate one-body, long-range two-body, and short-range two-body contributions with uncertainties) is provided to show how large the cancellation must be to reach the empirical value.

    Authors: We agree that an explicit numerical decomposition would strengthen the argument. The present manuscript only quotes the magnitude of the long-range two-body piece; we will add a table (or figure) that separates the one-body, long-range two-body, and short-range two-body contributions together with chiral-EFT truncation uncertainties for each term. revision: yes

Circularity Check

0 steps flagged

No significant circularity: LEC fixed from independent Nd scattering, tritium GT is genuine prediction

full rationale

The derivation fixes LEC D from nucleon-deuteron scattering observables (independent data) and then computes the tritium Gamow-Teller matrix element without further adjustment, yielding a parameter-free prediction. No step reduces by construction to the target observable, no self-definitional loops, and no load-bearing self-citation chains are evident. The result is an honest out-of-sample test whose discrepancy is interpreted as truncation uncertainty, consistent with the paper's own framing.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the chiral EFT framework at N2LO, the LENPIC interactions, and the value of D determined from scattering data. The overestimation conclusion depends on these inputs being appropriate.

free parameters (1)
  • D
    Low-energy constant governing short-range contributions to the exchange axial current operator, fixed from nucleon-deuteron scattering observables
axioms (2)
  • domain assumption Chiral EFT expansion up to N2LO is applicable to tritium beta decay
    The calculation is performed at N2LO using LENPIC interactions
  • domain assumption The Gamow-Teller reduced matrix element is computed from the axial current operator within this EFT
    Core assumption for the beta decay observable

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discussion (0)

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Reference graph

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