arxiv: 2605.14006 · v1 · submitted 2026-05-13 · ⚛️ nucl-th

Recognition: 2 theorem links

· Lean Theorem

Quantum Monte Carlo calculation of δ_C in the superallowed beta decay of ¹⁰C

Maria Piarulli , R. B. Wiringa , Alessandro Lovato , Garrett B. King , Saori Pastore

Authors on Pith no claims yet

Pith reviewed 2026-05-15 02:35 UTC · model grok-4.3

classification ⚛️ nucl-th

keywords quantum Monte Carlosuperallowed beta decayisospin symmetry breaking10CFermi matrix elementV_ud

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The pith

Ab initio quantum Monte Carlo calculations determine the isospin-symmetry-breaking correction δ_C for the superallowed beta decay of 10C to be 0.15-0.25%.

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

The paper performs quantum Monte Carlo calculations to find the isospin-symmetry-breaking correction δ_C in the superallowed beta decay of 10C. It uses both phenomenological and chiral nuclear interactions to compute the Fermi matrix element and measure its deviation from the canonical value of sqrt(2). The resulting δ_C lies between approximately 0.15 and 0.25 percent. These values remain consistent across the different Hamiltonians within their sizable uncertainties, showing no statistically significant dependence on the nuclear interaction. The extracted V_ud values are compatible with current determinations.

Core claim

Using quantum Monte Carlo methods with phenomenological and chiral nuclear interactions, the Fermi matrix element for the superallowed beta decay of 10C is evaluated, showing a deviation from sqrt(2) that corresponds to δ_C values in the range of 0.15 to 0.25%. The results are consistent within uncertainties of 34% to 65% across Hamiltonians, indicating no significant dependence on the choice of interaction, and the derived V_ud values match existing measurements.

What carries the argument

The Fermi matrix element in the 10C to 10B transition, computed ab initio via quantum Monte Carlo, whose deviation from sqrt(2) defines the correction δ_C.

If this is right

δ_C values are consistent across different nuclear interactions.
Extracted V_ud is compatible with current values.
No statistically significant Hamiltonian dependence is found.

Where Pith is reading between the lines

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

This method could be applied to other light nuclei to improve precision in CKM unitarity tests.
Uncertainties could be reduced with larger model spaces or improved interactions.
The consistency supports the reliability of current nuclear force models for isospin breaking.

Load-bearing premise

The quantum Monte Carlo sampling with the chosen phenomenological and chiral Hamiltonians fully captures isospin-symmetry-breaking effects without sizable systematic bias from finite model-space truncations or from the treatment of electromagnetic and charge-dependent forces.

What would settle it

A precise experimental measurement of the Fermi matrix element for the 10C beta decay that falls significantly outside the calculated 0.15-0.25% range for δ_C would challenge the results.

Figures

Figures reproduced from arXiv: 2605.14006 by Alessandro Lovato, Garrett B. King, Maria Piarulli, R. B. Wiringa, Saori Pastore.

**Figure 2.** Figure 2: FIG. 2: GFMC propagation of the [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: GFMC propagation of the Fermi matrix element as a function of the imaginary time [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗

read the original abstract

We perform an ab initio quantum Monte Carlo calculation of the isospin-symmetry-breaking correction $\delta_C$ to the superallowed $\beta$ decay of $^{10}{\rm C}$. Using both phenomenological and chiral nuclear interactions, we evaluate the Fermi matrix element and quantify its deviation from the canonical $\sqrt{2}$ value. The resulting $\delta_C$ values lie in the range $\approx 0.15$--$0.25\%$ and are consistent, within sizable uncertainties (approximately $34\%$--$65\%$ relative), across Hamiltonians, indicating no statistically significant dependence on the choice of nuclear interaction. The extracted values of $V_{ud}$ are also found to be compatible with current determinations within these uncertainties.

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.

Desk Editor's Note private letter to a colleague

New QMC numbers for δ_C in 10C sit at 0.15-0.25% with 30-60% errors and show no clear Hamiltonian dependence.

read the letter

The paper reports fresh quantum Monte Carlo results for the isospin-symmetry-breaking correction δ_C in the superallowed decay of 10C. Using both phenomenological and chiral interactions they find values in the 0.15-0.25% range that agree within the quoted uncertainties and produce V_ud values compatible with existing determinations. That is the concrete new output: specific numbers for this lightest superallowed case that were not in the literature they cite. The calculation itself is straightforward ab initio work on a ten-body system, which is a reasonable regime for QMC, and they do check consistency across two classes of Hamiltonians. That check is useful even if the errors are large. The main limitation is exactly those uncertainties, running 34-65% relative. For a correction this small the statistical errors dominate and leave the result too loose to shift current V_ud averages in any meaningful way. The stress-test point about possible common bias from model-space truncation or the long-range Coulomb treatment is worth watching; if the paper does not show explicit extrapolations or alternative regularizations, the quoted errors remain statistical only and a coherent shift could still be hidden. No obvious circularity or invented parameters appear in the approach. This work is mainly for groups doing precision beta-decay analyses or ab initio calculations of light nuclei. A reader who needs an independent anchor for δ_C in 10C will find the numbers worth noting, but the size of the errors means it functions more as a benchmark than a high-precision input. I would send it to peer review. The method is established, the system is tractable, and referees can usefully check the error budget and any missing systematics.

Referee Report

2 major / 2 minor

Summary. The paper performs an ab initio quantum Monte Carlo calculation of the isospin-symmetry-breaking correction δ_C in the superallowed beta decay of ¹⁰C. Using phenomenological and chiral nuclear interactions, it evaluates the Fermi matrix element and finds δ_C values approximately in the range 0.15--0.25%, consistent within large relative uncertainties of 34--65% across the different Hamiltonians. This suggests no statistically significant dependence on the nuclear interaction, and the extracted V_ud values are compatible with current determinations.

Significance. This work offers an important ab initio perspective on δ_C for light nuclei using the QMC method with multiple interactions. The consistency across Hamiltonians is a strength if the uncertainties are well-controlled. It contributes to the effort to reduce theoretical uncertainties in V_ud extractions from superallowed decays, which is relevant for CKM matrix unitarity tests. The large uncertainties, however, mean the result serves more as a benchmark than a precision determination.

major comments (2)

[Results] The claim of consistency across Hamiltonians with no statistically significant dependence is based on values within 34-65% relative uncertainties; however, without explicit model-space extrapolation or alternative treatments of the Coulomb force, common systematic errors could affect all calculations similarly, potentially undermining the robustness of the central claim.
[Error Analysis] The uncertainties appear to be statistical only; a detailed error budget separating statistical and systematic contributions (e.g., from finite model space or electromagnetic forces) is needed to support the conclusion that the results are not biased beyond the reported errors.

minor comments (2)

The abstract could benefit from specifying the exact δ_C and uncertainty for each Hamiltonian rather than a range.
Ensure that all figures and tables are clearly labeled and that the QMC methodology is described with sufficient detail for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work and for the constructive comments on the robustness of our conclusions. We address each major point below and have revised the manuscript to strengthen the discussion of systematics and error analysis.

read point-by-point responses

Referee: [Results] The claim of consistency across Hamiltonians with no statistically significant dependence is based on values within 34-65% relative uncertainties; however, without explicit model-space extrapolation or alternative treatments of the Coulomb force, common systematic errors could affect all calculations similarly, potentially undermining the robustness of the central claim.

Authors: We appreciate this observation. Our calculations were performed in model spaces large enough that the Fermi matrix element exhibits stability upon increasing the basis size, with this variation already folded into the reported uncertainties. While a formal extrapolation to infinite model space was not performed, the use of both phenomenological and chiral interactions—which differ substantially in their short-range structure—provides a cross-check against common systematics. We will add a dedicated paragraph in the revised manuscript discussing model-space convergence tests and the standard Coulomb treatment, explaining why these choices support the robustness of the observed consistency within the quoted uncertainties. revision: partial
Referee: [Error Analysis] The uncertainties appear to be statistical only; a detailed error budget separating statistical and systematic contributions (e.g., from finite model space or electromagnetic forces) is needed to support the conclusion that the results are not biased beyond the reported errors.

Authors: We agree that an explicit error budget would improve clarity. The dominant contribution to the quoted uncertainties is statistical from the Monte Carlo sampling, but we have performed auxiliary calculations to estimate systematic effects from model-space truncation and electromagnetic interactions. In the revised manuscript we will include a new section that tabulates the statistical and systematic components separately, with quantitative estimates drawn from our convergence studies. revision: yes

Circularity Check

0 steps flagged

No significant circularity; ab initio QMC derivation of δ_C is self-contained from independent Hamiltonians

full rationale

The paper computes δ_C directly from the Fermi matrix element via quantum Monte Carlo sampling on multiple phenomenological and chiral Hamiltonians taken from prior independent literature. No equation defines δ_C in terms of itself, fits a parameter to the same observable, or reduces the central result to a self-citation chain. The reported consistency across interactions and compatibility of V_ud values rest on explicit numerical evaluation rather than renaming or ansatz smuggling. This is the expected outcome for a first-principles calculation whose inputs (Hamiltonians, operators) are external to the target δ_C.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of quantum Monte Carlo for light nuclei and on the accuracy of the chosen nuclear Hamiltonians, both taken from prior literature rather than derived inside the paper.

axioms (2)

domain assumption Quantum Monte Carlo provides accurate solutions to the nuclear many-body problem for A=10 systems when standard phenomenological or chiral Hamiltonians are used.
This is the foundational assumption of the computational method invoked in the abstract.
domain assumption Isospin symmetry is broken at the percent level by electromagnetic and charge-dependent strong forces in light nuclei.
This defines the physical origin of the correction δ_C that the calculation aims to quantify.

pith-pipeline@v0.9.0 · 5442 in / 1517 out tokens · 51287 ms · 2026-05-15T02:35:24.266689+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We perform an ab initio quantum Monte Carlo calculation of the isospin-symmetry-breaking correction δ_C ... using both phenomenological and chiral nuclear interactions
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The GFMC framework introduces many-body correlations by removing excited state contamination ... in the charge basis

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.

Reference graph

Works this paper leans on

57 extracted references · 57 canonical work pages · 19 internal anchors

[1]

J. C. Hardy and I. S. Towner, Phys. Rev. C91, 025501 (2015), 1411.5987

work page arXiv 2015
[2]

J. C. Hardy and I. S. Towner, Phys. Rev. C102, 045501 (2020)

work page 2020
[3]

Cabibbo, Phys

N. Cabibbo, Phys. Rev. Lett.10, 531 (1963)

work page 1963
[4]

Kobayashi and T

M. Kobayashi and T. Maskawa, Prog. Theor. Phys.49, 652 (1973)

work page 1973
[5]

I. S. Towner and J. C. Hardy, Phys. Rev. C77, 025501 (2008), 0710.3181. 22

work page internal anchor Pith review Pith/arXiv arXiv 2008
[6]

W. J. Marciano and A. Sirlin, Phys. Rev. Lett.96, 032002 (2006), hep-ph/0510099

work page internal anchor Pith review Pith/arXiv arXiv 2006
[7]

C.-Y. Seng, M. Gorchtein, H. H. Patel, and M. J. Ramsey-Musolf, Phys. Rev. Lett.121, 241804 (2018), 1807.10197

work page internal anchor Pith review Pith/arXiv arXiv 2018
[8]

C. Y. Seng, M. Gorchtein, and M. J. Ramsey-Musolf, Phys. Rev. D100, 013001 (2019), 1812.03352

work page internal anchor Pith review Pith/arXiv arXiv 2019
[9]

Plestid and M

R. Plestid and M. B. Wise (2025), 2508.05540

work page arXiv 2025
[10]

Cirigliano, W

V. Cirigliano, W. Dekens, J. de Vries, S. Gandolfi, M. Hoferichter, and E. Mereghetti, Phys. Rev. C110, 055502 (2024), 2405.18464

work page arXiv 2024
[11]

Cirigliano, W

V. Cirigliano, W. Dekens, J. de Vries, S. Gandolfi, M. Hoferichter, and E. Mereghetti, Phys. Rev. Lett.133, 211801 (2024), 2405.18469

work page arXiv 2024
[12]

Gennari, M

M. Gennari, M. Drissi, M. Gorchtein, P. Navratil, and C.-Y. Seng, Phys. Rev. Lett.134, 012501 (2025), 2405.19281

work page arXiv 2025
[13]

G. B. King, J. Carlson, A. R. Flores, S. Gandolfi, E. Mereghetti, S. Pastore, M. Piarulli, and R. B. Wiringa (2025), 2509.07310

work page arXiv 2025
[14]

G. H. Sargsyan, G. B. King, A. Glick-Magid, and C.-Y. Seng (2026), 2602.00341

work page arXiv 2026
[15]

Seng and M

C.-Y. Seng and M. Gorchtein, Phys. Lett. B838, 137654 (2023), 2208.03037

work page arXiv 2023
[16]

Seng and M

C.-Y. Seng and M. Gorchtein, Phys. Rev. C109, 044302 (2024), 2304.03800

work page arXiv 2024
[17]

Xayavong, N

L. Xayavong, N. A. Smirnova, and F. Nowacki, Phys. Rev. C112, 055503 (2025), 2508.18189

work page arXiv 2025
[18]

B. S. Pudliner, V. R. Pandharipande, J. Carlson, S. C. Pieper, and R. B. Wiringa, Phys. Rev. C56, 1720 (1997), nucl-th/9705009

work page internal anchor Pith review Pith/arXiv arXiv 1997
[19]

S. C. Pieper and R. B. Wiringa, Ann. Rev. Nucl. Part. Sci.51, 53 (2001), nucl-th/0103005

work page internal anchor Pith review Pith/arXiv arXiv 2001
[20]

R. B. Wiringa, S. Pastore, S. C. Pieper, and G. A. Miller, Phys. Rev. C88, 044333 (2013), 1308.5670

work page internal anchor Pith review Pith/arXiv arXiv 2013
[21]

Light-nuclei spectra from chiral dynamics

M. Piarulli et al., Phys. Rev. Lett.120, 052503 (2018), 1707.02883

work page internal anchor Pith review Pith/arXiv arXiv 2018
[22]

G. B. King, G. Chambers-Wall, A. Gnech, S. Pastore, M. Piarulli, and R. B. Wiringa (2025), 2504.04201

work page arXiv 2025
[23]

R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Phys. Rev.C51, 38 (1995), nucl-th/9408016

work page internal anchor Pith review Pith/arXiv arXiv 1995
[24]

R. B. Wiringa, R. Schiavilla, S. C. Pieper, and J. Carlson, Phys. Rev. C89, 024305 (2014), URLhttps://link.aps.org/doi/10.1103/PhysRevC.89.024305

work page doi:10.1103/physrevc.89.024305 2014
[25]

Quantum Monte Carlo methods for nuclear physics

J. Carlson, S. Gandolfi, F. Pederiva, S. C. Pieper, R. Schiavilla, K. E. Schmidt, and R. B. Wiringa, Rev. Mod. Phys.87, 1067 (2015), 1412.3081. 23

work page internal anchor Pith review Pith/arXiv arXiv 2015
[26]

Minimally non-local nucleon-nucleon potentials with chiral two-pion exchange including $\Delta$'s

M. Piarulli, L. Girlanda, R. Schiavilla, R. Navarro P´ erez, J. E. Amaro, and E. Ruiz Arriola, Phys. Rev.C91, 024003 (2015), 1412.6446

work page internal anchor Pith review Pith/arXiv arXiv 2015
[27]

Local chiral potentials and the structure of light nuclei

M. Piarulli, L. Girlanda, R. Schiavilla, A. Kievsky, A. Lovato, L. E. Marcucci, S. C. Pieper, M. Viviani, and R. B. Wiringa, Phys. Rev.C94, 054007 (2016), 1606.06335

work page internal anchor Pith review Pith/arXiv arXiv 2016
[28]

Local chiral interactions, the tritium Gamow-Teller matrix element, and the three-nucleon contact term

A. Baroni et al., Phys. Rev.C98, 044003 (2018), 1806.10245

work page internal anchor Pith review Pith/arXiv arXiv 2018
[29]

V. G. J. Stoks, R. A. M. Klomp, M. C. M. Rentmeester, and J. J. de Swart, Phys. Rev.C48, 792 (1993)

work page 1993
[30]

H. W. Hammer, S. K¨ onig, and U. van Kolck, Rev. Mod. Phys.92, 025004 (2020), 1906.12122

work page arXiv 2020
[31]

Weinberg, Nucl

S. Weinberg, Nucl. Phys. B363, 3 (1991)

work page 1991
[32]

van Kolck, Phys

U. van Kolck, Phys. Rev.C49, 2932 (1994)

work page 1994
[33]

Three-Nucleon Forces from Chiral Effective Field Theory

E. Epelbaum, A. Nogga, W. Gloeckle, H. Kamada, U. G. Meissner, and H. Witala, Phys. Rev. C66, 064001 (2002), nucl-th/0208023

work page internal anchor Pith review Pith/arXiv arXiv 2002
[34]

Fujita and H

J. Fujita and H. Miyazawa, Prog. Theor. Phys.17, 360 (1957)

work page 1957
[35]

Piarulli and I

M. Piarulli and I. Tews, Front. in Phys.7, 245 (2020), 2002.00032

work page arXiv 2020
[36]

Coarse grained Potential analysis of neutron-proton and proton-proton scattering below pion production threshold

R. Navarro P´ erez, J. E. Amaro, and E. Ruiz Arriola, Phys. Rev.C88, 064002 (2013), [Erratum: Phys. Rev.C91,no.2,029901(2015)], 1310.2536

work page internal anchor Pith review Pith/arXiv arXiv 2013
[37]

Coarse grained NN potential with Chiral Two Pion Exchange

R. Navarro P´ erez, J. E. Amaro, and E. Ruiz Arriola, Phys. Rev. C89, 024004 (2014), 1310.6972

work page internal anchor Pith review Pith/arXiv arXiv 2014
[38]

Statistical Error analysis of Nucleon-Nucleon phenomenological potentials

R. Navarro Perez, J. E. Amaro, and E. Ruiz Arriola, Phys. Rev. C89, 064006 (2014), 1404.0314

work page internal anchor Pith review Pith/arXiv arXiv 2014
[39]

J. M. Bub, M. Piarulli, R. J. Furnstahl, S. Pastore, and D. R. Phillips, Phys. Rev. C111, 034005 (2025), 2408.02480

work page arXiv 2025
[40]

Somasundaram, J

R. Somasundaram, J. E. Lynn, L. Huth, A. Schwenk, and I. Tews, Phys. Rev. C109, 034005 (2024), 2306.13579

work page arXiv 2024
[41]

O. Thim, E. May, A. Ekstr¨ om, and C. Forss´ en, Phys. Rev. C108, 054002 (2023), 2302.12624

work page arXiv 2023
[42]

Svensson, A

I. Svensson, A. Ekstr¨ om, and C. Forss´ en, Phys. Rev. C109, 064003 (2024), 2304.02004

work page arXiv 2024
[43]

K¨ onig, A

S. K¨ onig, A. Ekstr¨ om, K. Hebeler, D. Lee, and A. Schwenk, Phys. Lett. B810, 135814 (2020), 1909.08446

work page arXiv 2020
[44]

Wesolowski, I

S. Wesolowski, I. Svensson, A. Ekstr¨ om, C. Forss´ en, R. J. Furnstahl, J. A. Melendez, and D. R. Phillips, Phys. Rev. C104, 064001 (2021), 2104.04441

work page arXiv 2021
[45]

Odell, P

D. Odell, P. Giuliani, K. Beyer, M. Catacora-Rios, M. Y. H. Chan, E. Bonilla, R. J. Furnstahl, 24 K. Godbey, and F. M. Nunes, Phys. Rev. C109, 044612 (2024), 2312.12426

work page arXiv 2024
[46]

K. S. Becker, K. D. Launey, A. Ekstr¨ om, and T. Dytrych, Front. in Phys.11, 1064601 (2023), 2303.00667

work page arXiv 2023
[47]

Somasundaram, C

R. Somasundaram, C. L. Armstrong, P. Giuliani, K. Godbey, S. Gandolfi, and I. Tews, Phys. Lett. B866, 139558 (2025), 2404.11566

work page arXiv 2025
[48]

C. L. Armstrong, P. Giuliani, K. Godbey, R. Somasundaram, and I. Tews (2025), 2502.03680

work page arXiv 2025
[49]

Gandolfi, D

S. Gandolfi, D. Lonardoni, A. Lovato, and M. Piarulli, Front. in Phys.8, 117 (2020), 2001.01374

work page arXiv 2020
[50]

G. B. King and S. Pastore, Ann. Rev. Nucl. Part. Sci.74, 343 (2024), 2402.06602

work page arXiv 2024
[51]

R. B. Wiringa, Phys. Rev. C73, 034317 (2006), nucl-th/0601064

work page internal anchor Pith review Pith/arXiv arXiv 2006
[52]

Quantum Monte Carlo calculations of electroweak transition matrix elements in A = 6,7 nuclei

M. Pervin, S. C. Pieper, and R. B. Wiringa, Phys. Rev. C76, 064319 (2007), 0710.1265

work page internal anchor Pith review Pith/arXiv arXiv 2007
[53]

Ohayon, Atomic Data and Nuclear Data Tables165, 101732 (2025), ISSN 0092-640X, URL https://www.sciencedirect.com/science/article/pii/S0092640X25000257

B. Ohayon, Atomic Data and Nuclear Data Tables165, 101732 (2025), ISSN 0092-640X, URL https://www.sciencedirect.com/science/article/pii/S0092640X25000257

work page 2025
[54]

Curry, J

R. Curry, J. E. Lynn, K. E. Schmidt, and A. Gezerlis, Phys. Rev. Res.5, L042021 (2023), 2302.07285

work page arXiv 2023
[55]

Fretwell et al

S. Fretwell et al. (BeEST), Phys. Rev. Lett.125, 032701 (2020), 2003.04921

work page arXiv 2020
[56]

Friedrich et al., Phys

S. Friedrich et al., Phys. Rev. Lett.126, 021803 (2021), 2010.09603

work page arXiv 2021
[57]

M. R. Dunlop et al., Phys. Rev. Lett.116, 172501 (2016). 25

work page 2016