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arxiv: 2508.01900 · v2 · submitted 2025-08-03 · ✦ hep-lat · hep-ph· nucl-th

Lattice Calculation of Short-Range Contributions to Neutrinoless Double-Beta Decay π^-toπ^+ ee at Physical Pion Mass

Peter Boyle , Felix Erben , Xu Feng , Jonathan M. Flynn , Nicolas Garron , Taku Izubuchi , Luchang Jin , Rajnandini Mukherjee
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J. Tobias Tsang Xin-Yu Tuo
This is my paper

Pith reviewed 2026-05-19 01:25 UTC · model grok-4.3

classification ✦ hep-lat hep-phnucl-th
keywords lattice QCDneutrinoless double-beta decayshort-range matrix elementspion exchangearound-the-world effectsnonperturbative renormalizationphysical pion mass
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The pith

Lattice QCD calculation at physical pion mass reduces uncertainties in short-range matrix elements for neutrinoless double-beta decay.

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

The paper computes the short-range matrix elements for the pion process that contributes at leading order to neutrinoless double-beta decay via pion exchange between nucleons. The calculation uses domain wall fermions at the physical pion mass and introduces a new technique to reconstruct and subtract around-the-world effects straight from the lattice data. Nonperturbative renormalization is applied in the RI/SMOM scheme. This produces smaller uncertainties than earlier work while supplying an independent cross-check that helps align previous lattice results. A reader would care because these matrix elements enter predictions for nuclear decay rates that test whether neutrinos are Majorana particles.

Core claim

We report a lattice QCD calculation of the π⁻ → π⁺ ee matrix elements at the physical pion mass. By reconstructing and subtracting around-the-world effects directly from the data and performing nonperturbative renormalization, we obtain results with reduced uncertainties that provide an independent cross-check on prior calculations and help reconcile their discrepancies.

What carries the argument

The new method to reconstruct and subtract around-the-world effects directly from lattice data, which removes contamination from the correlation functions used to extract the matrix elements.

If this is right

  • The matrix elements for the short-range contributions to nn → ppee carry smaller uncertainties than in previous lattice studies.
  • The results supply an independent cross-check that helps reconcile discrepancies among earlier lattice calculations.
  • These values furnish more precise inputs for nuclear many-body calculations of neutrinoless double-beta decay rates.

Where Pith is reading between the lines

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

  • The subtraction technique could be adapted to other lattice processes that suffer from similar around-the-world contamination in multi-hadron correlators.
  • Feeding the matrix elements into chiral effective field theory would allow more accurate nuclear matrix element estimates for heavier nuclei.
  • Repeating the computation at a second lattice spacing would test whether the uncertainty reduction holds under controlled continuum extrapolation.

Load-bearing premise

The new method to reconstruct and subtract around-the-world effects directly from lattice data removes contamination without introducing additional systematic bias or distorting the extracted matrix elements.

What would settle it

Recomputing the matrix elements with and without the new subtraction method and finding statistically significant differences, or obtaining final values that remain in clear disagreement with other lattice results beyond the quoted errors, would show the subtraction step fails to deliver unbiased results.

Figures

Figures reproduced from arXiv: 2508.01900 by Felix Erben, Jonathan M. Flynn, J. Tobias Tsang, Luchang Jin, Nicolas Garron, Peter Boyle, Rajnandini Mukherjee, Taku Izubuchi, Xin-Yu Tuo, Xu Feng.

Figure 1
Figure 1. Figure 1: Illustration of around-the-world effects. Dashed lines indicate the periodic temporal [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Extraction of the contribution from diagram B under the time setup ( [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between the effective bare matrix elements before subtraction of around [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Effective bare matrix elements in the 24IH1 and 24IH2 ensembles. The blue data points [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Same as Fig. 4, but with 32IH1 and 32IH2 ensembles. [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Same as Fig. 4, but with 48I and 64I ensembles. [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Renormalized matrix elements ⟨Oi⟩(µ = 3 GeV) [GeV4 ] computed using both the (γµ, γµ) and (/q, /q) schemes for the 48I and 64I ensembles, together with the corresponding continuum￾extrapolated results. The difference between results in (γµ, γµ) and (/q, /q) schemes can be viewed as an estimate of perturbative truncation errors. final results for the renormalized matrix elements ⟨Oi⟩ MS and the bag paramete… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison between the effective bare matrix elements before subtraction of around [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
read the original abstract

Neutrinoless double-beta ($0\nu\beta\beta$) decays provide an excellent probe for determining whether neutrinos are Dirac or Majorana fermions. The short-range matrix elements associated with the $\pi^- \to \pi^+ ee$ process contribute at leading order in the $0\nu\beta\beta$ decay channel $nn \to ppee$ through pion exchange between nucleons. However, current lattice calculations show notable discrepancies in predicting these short-range contributions. To address this issue, we perform a lattice QCD calculation of the $\pi^- \to \pi^+ ee$ matrix elements using domain wall fermion ensembles at the physical pion mass generated by the RBC and UKQCD Collaborations. To mitigate contamination from around-the-world effects, we develop a new method to reconstruct and subtract them directly from lattice data. We then perform a nonperturbative renormalization using the RI/SMOM scheme. Compared with previous studies, this work reduces the uncertainties in the matrix elements and provides an independent cross-check that helps to reconcile the discrepancies among previous lattice calculations.

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

1 major / 2 minor

Summary. The manuscript presents a lattice QCD calculation of the short-range matrix elements for the process π⁻ → π⁺ ee at the physical pion mass using RBC/UKQCD domain-wall fermion ensembles. It introduces a new method to reconstruct and subtract around-the-world effects directly from the lattice correlators, performs non-perturbative renormalization in the RI/SMOM scheme, and reports results with reduced uncertainties that help reconcile discrepancies among previous lattice calculations.

Significance. If the new subtraction procedure is free from residual bias, the work would supply a valuable independent determination at physical quark masses with smaller errors, strengthening the lattice input to 0νββ phenomenology and providing a useful cross-check on earlier results.

major comments (1)
  1. [§4] §4 (Around-the-world subtraction): The central claim of reduced uncertainties and reconciliation of prior discrepancies rests on the new data-driven reconstruction and subtraction of wrapping contributions. The manuscript provides insufficient validation that this procedure isolates the finite-T effects without shifting the physical matrix elements or altering the error budget; explicit tests on synthetic data, comparison with known analytic forms, or cross-checks against alternative subtraction methods are needed to establish that no additional systematic bias is introduced.
minor comments (2)
  1. [§5] The notation for the RI/SMOM renormalization constants and the matching to the continuum scheme could be made more explicit in the text and tables to aid reproducibility.
  2. [Figure 3] Figure 3: The caption should specify the fit ranges and the precise definition of the effective mass used for the ground-state extraction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive feedback. We address the major comment below and will revise the paper to incorporate additional validation as requested.

read point-by-point responses

  1. Referee: [§4] §4 (Around-the-world subtraction): The central claim of reduced uncertainties and reconciliation of prior discrepancies rests on the new data-driven reconstruction and subtraction of wrapping contributions. The manuscript provides insufficient validation that this procedure isolates the finite-T effects without shifting the physical matrix elements or altering the error budget; explicit tests on synthetic data, comparison with known analytic forms, or cross-checks against alternative subtraction methods are needed to establish that no additional systematic bias is introduced.

    Authors: We thank the referee for this important observation. Our subtraction reconstructs the around-the-world contributions directly from the large-time behavior of the lattice correlators, exploiting the known exponential decay set by the pion mass. In the revised manuscript we will add explicit validation tests on synthetic data generated with controlled input matrix elements and wrapping amplitudes; these tests will demonstrate recovery of the physical values to within statistical precision without bias. We will also include a direct comparison of our results with those obtained from an alternative global fit to the full correlator that incorporates the wrapping term analytically. These additions will confirm that the procedure does not shift the extracted matrix elements or inflate the error budget beyond the quoted uncertainties. revision: yes

Circularity Check

0 steps flagged

Direct lattice extraction with data-driven subtraction of around-the-world effects shows no circular reduction

full rationale

The paper computes the short-range matrix elements from three-point correlation functions on RBC/UKQCD domain-wall ensembles at physical pion mass, then applies a new reconstruction-and-subtraction procedure for around-the-world contamination that is performed directly on the same lattice data. No load-bearing equation or step reduces the final renormalized matrix elements (in RI/SMOM) to a quantity previously fitted to the identical data set or to a self-citation chain whose validity is presupposed by the present work. The comparison to earlier calculations is presented only as an independent cross-check, not as an input that forces the result. This keeps the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The calculation rests on pre-existing RBC/UKQCD domain-wall ensembles generated at the physical pion mass and on the assumption that the new subtraction procedure correctly isolates the desired matrix elements. No new particles or forces are postulated.

free parameters (1)
  • renormalization constants in RI/SMOM scheme
    Determined non-perturbatively from the lattice data; their precise values depend on the chosen momentum and fitting windows.
axioms (1)
  • domain assumption Domain wall fermions on the chosen ensembles reproduce QCD dynamics sufficiently accurately at the physical pion mass
    Standard assumption for lattice QCD calculations; invoked when the ensembles are selected and when results are interpreted as physical.

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Reference graph

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