Pith. sign in

REVIEW 1 major objections 2 minor 1 cited by

Lattice Calculation of Short-Range Contributions to Neutrinoless Double-Beta Decay $\pi^-\to\pi^+ ee$ at Physical Pion Mass

T0 review · 1 major / 2 minor · reviewed 2026-05-19 · grok-4.3

Challenge this review Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Lattice QCD calculation at physical pion mass reduces uncertainties in short-range matrix elements for neutrinoless double-beta decay.

desk verdict Physical-mass result with a new data-driven subtraction for around-the-world effects is the real advance, but the method needs explicit validation to support the reduced-uncertainty claim. read the letter →

arxiv 2508.01900 v2 submitted 2025-08-03 hep-lat hep-phnucl-th

Peter Boyle , Felix Erben , Xu Feng , Jonathan M. Flynn , Nicolas Garron , Taku Izubuchi , Luchang Jin , Rajnandini Mukherjee
show 2 more authors
J. Tobias Tsang Xin-Yu Tuo
This is my paper · ORCID
classification hep-lathep-phnucl-th
keywords latticeQCDneutrinolessdouble-betadecayshort-rangematrixelementspionexchangearound-the-worldeffectsnonperturbativerenormalizationphysicalmass
checked against Foundation.AbsoluteFloorClosurealexander_duality_circle_linking
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

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.

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.

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.

Watch

Extended reading notes

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.

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.

Editorial extensions

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.

Reading between the lines

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.
Share X Bluesky LinkedIn Reddit HN

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

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 · score 2.0 of 10

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.

Assumptions & free parameters 1 free parameters · 1 assumptions · 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.
assumptions (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.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Lattice Calculation of Short-Range Contributions to Neutrinoless Double-Beta Decay $\pi^-\to\pi^+ ee$ at Physical Pion Mass." pith.science (2026). https://pith.science/paper/2508.01900

@misc{pith2026250801900,
  author       = {Pith},
  title        = {Pith review of: Lattice Calculation of Short-Range Contributions to Neutrinoless Double-Beta Decay $\pi^-\to\pi^+ ee$ at Physical Pion Mass},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2508.01900}},
  note         = {Machine review of arXiv:2508.01900}
}
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.

Figures

Figures reproduced from arXiv: 2508.01900 by the authors.

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. 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. Comparison between the effective bare matrix elements before subtraction of around [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (5 more)
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]
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]
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]
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…
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]

Discussion (0). Continue with ORCID to comment.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Deformations of asymptotically cylindrical associative submanifolds

    math.DG 2025-08 unverdicted novelty 6.0 of 10

    The paper computes the virtual dimensions of moduli spaces of asymptotically cylindrical associative submanifolds and proves a Lagrangian embedding into the moduli space of holomorphic curves in the limiting Calabi-Ya...

Reference graph

Works this paper leans on

41 extracted references · 41 canonical work pages · cited by 1 Pith paper

  1. [1]

    moves these effects directly from the lattice data, thereby achieving stable plateaus in the ratio of three-point to two-point correlation functions

    and ( O2, O′ 2). moves these effects directly from the lattice data, thereby achieving stable plateaus in the ratio of three-point to two-point correlation functions. Next, we perform a nonperturba- tive renormalization of the four-quark operators using the RI/SMOM method in ( γµ, γµ) and ( /q, /q) schemes. We estimate the systematic error from perturbati...

    work page

  2. [2]

    Evidence for oscillation of atmospheric neutrinos

    Y. Fukuda et al. (Super-Kamiokande), Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81, 1562 (1998), arXiv:hep-ex/9807003

    work page Pith review arXiv 1998

  3. [3]

    Q. R. Ahmad et al. (SNO), Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory, Phys. Rev. Lett.89, 011301 (2002), arXiv:nucl-ex/0204008

    work page Pith review arXiv 2002

  4. [4]

    First Results from KamLAND: Evidence for Reactor Anti-Neutrino Disappearance

    K. Eguchi et al. (KamLAND), First results from KamLAND: Evidence for reactor anti- neutrino disappearance, Phys. Rev. Lett. 90, 021802 (2003), arXiv:hep-ex/0212021

    work page Pith review arXiv 2003

  5. [5]

    Strumia and F

    A. Strumia and F. Vissani, Neutrino masses and mixings and..., (2006), arXiv:hep- ph/0606054

    work page arXiv 2006

  6. [6]

    M. C. Gonzalez-Garcia and Y. Nir, Neutrino masses and mixing: evidence and implications, Rev. Mod. Phys. 75, 345 (2003)

    work page 2003

  7. [7]

    Majorana, Teoria simmetrica dell¡ ¯elettrone e del positrone, Nuovo Cim

    E. Majorana, Teoria simmetrica dell¡ ¯elettrone e del positrone, Nuovo Cim. 14, 171 (1937)

    work page 1937

  8. [8]

    Agostiniet al.(GERDA), Phys

    M. Agostini et al. (GERDA), Final Results of GERDA on the Search for Neutrinoless Double-β Decay, Phys. Rev. Lett. 125, 252502 (2020), arXiv:2009.06079 [nucl-ex]

    work page arXiv 2020

Show all 41 references
  1. [9]

    I. J. Arnquist et al. (Majorana), Final Result of the Majorana Demonstrator’s Search for Neutrinoless Double-β Decay in Ge76, Phys. Rev. Lett. 130, 062501 (2023), arXiv:2207.07638 [nucl-ex]

    2023

  2. [10]

    Abgrall et al

    N. Abgrall et al. (LEGEND), The Large Enriched Germanium Experiment for Neutrinolessββ Decay: LEGEND-1000 Preconceptual Design Report, (2021), arXiv:2107.11462 [physics.ins- det]

    2021

  3. [11]

    Abe et al

    S. Abe et al. (KamLAND-Zen), First Search for the Majorana Nature of Neutrinos in the Inverted Mass Ordering Region with KamLAND-Zen, (2022), arXiv:2203.02139 [hep-ex]

    2022

  4. [12]

    D. Q. Adams et al. (CUORE), Search for Majorana neutrinos exploiting millikelvin cryogenics with CUORE, Nature 604, 53 (2022), arXiv:2104.06906 [nucl-ex]

    2022

  5. [13]

    Azzolini et al

    O. Azzolini et al. (CUPID-0), Search for Majoron-like particles with CUPID-0, Phys. Rev. D 107, 032006 (2023), arXiv:2209.09490 [hep-ex]

    2023

  6. [14]

    Armengaud et al

    E. Armengaud et al. (CUPID), New Limit for Neutrinoless Double-Beta Decay of 100Mo from the CUPID-Mo Experiment, Phys. Rev. Lett. 126, 181802 (2021), arXiv:2011.13243 [nucl-ex]. 24

    2021

  7. [15]

    Anton et al

    G. Anton et al. (EXO-200), Search for Neutrinoless Double-β Decay with the Complete EXO- 200 Dataset, Phys. Rev. Lett. 123, 161802 (2019), arXiv:1906.02723 [hep-ex]

    2019

  8. [16]

    M. A. Luty, Baryogenesis via leptogenesis, Phys. Rev. D 45, 455 (1992)

    1992

  9. [17]

    Davidson, E

    S. Davidson, E. Nardi, and Y. Nir, Leptogenesis, Phys. Rept. 466, 105 (2008), arXiv:0802.2962 [hep-ph]

    2008 arXiv

  10. [18]

    Weinberg, Baryon and Lepton Nonconserving Processes, Phys

    S. Weinberg, Baryon and Lepton Nonconserving Processes, Phys. Rev. Lett. 43, 1566 (1979)

    1979

  11. [19]

    K. S. Babu and C. N. Leung, Classification of effective neutrino mass operators, Nucl. Phys. B 619, 667 (2001), arXiv:hep-ph/0106054

    2001 arXiv

  12. [20]

    Prezeau, M

    G. Prezeau, M. Ramsey-Musolf, and P. Vogel, Neutrinoless double beta decay and effective field theory, Phys. Rev. D 68, 034016 (2003), arXiv:hep-ph/0303205

    2003 arXiv

  13. [21]

    de Gouvea and J

    A. de Gouvea and J. Jenkins, A Survey of Lepton Number Violation Via Effective Operators, Phys. Rev. D 77, 013008 (2008), arXiv:0708.1344 [hep-ph]

    2008 arXiv

  14. [22]

    Lehman, Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators, Phys

    L. Lehman, Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators, Phys. Rev. D 90, 125023 (2014), arXiv:1410.4193 [hep-ph]

    2014 arXiv

  15. [23]

    M. L. Graesser, An electroweak basis for neutrinoless double β decay, JHEP 08, 099, arXiv:1606.04549 [hep-ph]

    arXiv

  16. [24]

    Cirigliano, W

    V. Cirigliano, W. Dekens, J. de Vries, M. L. Graesser, and E. Mereghetti, A neutrinoless double beta decay master formula from effective field theory, JHEP 12, 097, arXiv:1806.02780 [hep-ph]

    arXiv

  17. [25]

    Schechter and J

    J. Schechter and J. Valle, Neutrinoless Double beta Decay in SU(2) x U(1) Theories, Phys. Rev. D 25, 2951 (1982)

    1982

  18. [26]

    Cirigliano, W

    V. Cirigliano, W. Dekens, E. Mereghetti, and A. Walker-Loud, Neutrinoless double- β decay in effective field theory: The light-Majorana neutrino-exchange mechanism, Phys. Rev. C 97, 065501 (2018), [Erratum: Phys.Rev.C 100, 019903 (2019)], arXiv:1710.01729 [hep-ph]

    2018 arXiv

  19. [27]

    Cirigliano, W

    V. Cirigliano, W. Dekens, J. De Vries, M. L. Graesser, E. Mereghetti, S. Pastore, and U. Van Kolck, New Leading Contribution to Neutrinoless Double- β Decay, Phys. Rev. Lett. 120, 202001 (2018), arXiv:1802.10097 [hep-ph]

    2018 arXiv

  20. [28]

    Detmold and D

    W. Detmold and D. J. Murphy (NPLQCD), Neutrinoless Double Beta Decay from Lattice QCD: The Long-Distance π− → π+e−e− Amplitude, (2020), arXiv:2004.07404 [hep-lat]

    2020

  21. [29]

    Feng, L.-C

    X. Feng, L.-C. Jin, X.-Y. Tuo, and S.-C. Xia, Light-Neutrino Exchange and Long-Distance Contributions to 0 ν2β Decays: An Exploratory Study on ππ → ee, Phys. Rev. Lett. 122, 25 022001 (2019), arXiv:1809.10511 [hep-lat]

    2019 arXiv

  22. [30]

    X.-Y. Tuo, X. Feng, and L.-C. Jin, Long-distance contributions to neutrinoless double beta decay π− → π+ee, Phys. Rev. D 100, 094511 (2019), arXiv:1909.13525 [hep-lat]

    2019

  23. [31]

    Nicholson et al., Heavy physics contributions to neutrinoless double beta decay from QCD, Phys

    A. Nicholson et al., Heavy physics contributions to neutrinoless double beta decay from QCD, Phys. Rev. Lett. 121, 172501 (2018), arXiv:1805.02634 [nucl-th]

    2018 arXiv

  24. [32]

    Detmold, W

    W. Detmold, W. I. Jay, D. J. Murphy, P. R. Oare, and P. E. Shanahan, Neutrinoless double beta decay from lattice QCD: The short-distance π-→π+e-e- amplitude, Phys. Rev. D 107, 094501 (2023), arXiv:2208.05322 [hep-lat]

    2023

  25. [33]

    Navas et al

    S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024)

    2024

  26. [34]

    Sturm, Y

    C. Sturm, Y. Aoki, N. H. Christ, T. Izubuchi, C. T. C. Sachrajda, and A. Soni, Renormal- ization of quark bilinear operators in a momentum-subtraction scheme with a nonexceptional subtraction point, Phys. Rev. D 80, 014501 (2009), arXiv:0901.2599 [hep-ph]

    2009 arXiv

  27. [35]

    P. A. Boyle, F. Erben, J. M. Flynn, N. Garron, J. Kettle, R. Mukherjee, and J. T. Tsang (RBC, UKQCD), Kaon mixing beyond the standard model with physical masses, Phys. Rev. D 110, 034501 (2024), arXiv:2404.02297 [hep-lat]

    2024

  28. [36]

    P. A. Boyle, N. Garron, R. J. Hudspith, C. Lehner, and A. T. Lytle (RBC, UKQCD), Neutral kaon mixing beyond the Standard Model with nf = 2 + 1 chiral fermions. Part 2: non pertur- bative renormalisation of the ∆ F = 2 four-quark operators, JHEP 10, 054, arXiv:1708.03552 [hep-lat]

    arXiv

  29. [37]

    Aoki et al

    Y. Aoki et al. (RBC, UKQCD), Continuum Limit Physics from 2+1 Flavor Domain Wall QCD, Phys. Rev. D 83, 074508 (2011), arXiv:1011.0892 [hep-lat]

    2011 arXiv

  30. [38]

    Blum et al

    T. Blum et al. (RBC, UKQCD), Domain wall QCD with physical quark masses, Phys. Rev. D 93, 074505 (2016), arXiv:1411.7017 [hep-lat]

    2016 arXiv

  31. [39]

    Aoki et al

    Y. Aoki et al. , Continuum Limit of BK from 2+1 Flavor Domain Wall QCD, Phys. Rev. D 84, 014503 (2011), arXiv:1012.4178 [hep-lat]

    2011 arXiv

  32. [40]

    Aoki et al

    Y. Aoki et al. (Flavour Lattice Averaging Group (FLAG)), FLAG Review 2024, (2024), arXiv:2411.04268 [hep-lat]

    2024 arXiv

  33. [41]

    Gorbahn, S

    M. Gorbahn, S. J¨ ager, and S. Kvedaraite, RI-(S)MOM to MS conversion for BK at two-loop order, (2024), arXiv:2411.19861 [hep-ph]. 26

    2024

Pith tools

Reviewed May 19, 2026 · model on record in the stance chip above.