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2+1 flavor light hadron spectrum with PACS10 configurations

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K.-I. Ishikawa, N. Ishizuka, Y. Kuramashi, Y. Nakamura, Y. Namekawa, K. Satoh, E. Shintani, Y. Taniguchi
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N. Ukita, H. Watanabe, T. Yamazaki, T. Yoshié (PACS Collaboration)

High Energy Physics - Lattice · Submitted 2 Nov 2026 · 44 references

Pith's verdict: Solid, mostly confirmatory PACS continuum-limit paper in which the interesting physics is the convention A/B spread; worth refereeing, with a request to test the transferred tuning coefficients.

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arXiv ID2611.02426 (version 1)
Pith IDTFC6DCTR, Pith's permanent record of this paper and its review
CitationE. Shintani, H. Watanabe, K.-I. Ishikawa, K. Satoh, N. Ishizuka, N. Ukita, T. Yamazaki, T. Yoshi\'e (PACS collaboration), Y. Kuramashi, Y. Nakamura, Y. Namekawa, Y. Taniguchi. "2+1 flavor light hadron spectrum with PACS10 configurations." arXiv:2611.02426 (2026). https://pith.science/paper/TFC6DCTR
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The paper

The paper claims

2+1 flavor QCD, simulated directly at the physical point on volumes beyond (10 fm)^4 at three lattice spacings, reproduces the octet baryon masses in the continuum limit within roughly 2 sigma, and shows that the apparent deviation of…

The reading

The paper argues that 2+1 flavor QCD, computed at the physical point on volumes exceeding (10 fm)^4 at three lattice spacings, predicts the continuum-limit octet baryon spectrum at sub-percent precision: the nucleon, Lambda, and Sigma masses land within roughly two $\sigma$ of the corresponding pseudoexperimental values. It further argues that whether the pseudoscalar decay constants and the light-quark mass ratio agree with the FLAG world average depends on how one defines the isosymmetric pseudoexperimental point: the FLAG-style convention B is consistent with FLAG, while the historically used convention A sits about 1 percent below FLAG for f_pi and f_K and slightly above it for m_s/m_ud. The spread between the two conventions persists in the continuum limit and is the paper's estimate of the residual QED and isospin ambiguity, so the convention-A deviation is presented as a definitional effect rather than a failure of QCD. Finally, the coarse-lattice comparison shows that hadron masses are nearly finite-size free at the 5.4 fm box, while the decay constants carry a shift roughly three times the one-loop chiral perturbation theory prediction.

What carries the argument

The load-bearing object is the mass-reweighting Taylor expansion of Eq. (43): the linear coefficients of $m_pi^{2}$, $m_K^{2}$, m_Xi, of the pseudoscalar decay constants, and of the octet baryon masses in the AWI quark masses (m_ud, m_s), extracted on the (5.4 fm)^4 lattice at the coarsest spacing and then carried over, with only a lattice-spacing-ratio rescaling for the dimensionful terms, to tune the physical point at the two finer spacings and to shift observables to that point. Around it sit the two conventions (A, the historical PACS choice; B, the FLAG/Edinburgh-consensus isospin average) that supply the pseudoexperimental inputs, and the continuum extrapolation linear in $a^{2}$, justified by the nonperturbative c_SW and the observationally vanishing c_A. The finite-size comparison on the matching 5.4 fm box against the one-loop SU(3) ChPT formulas provides the volume control.

Extended reading notes

Core claim

On its own terms, the paper's central result is the continuum-limit comparison of 2+1 flavor QCD at the physical point against two conventions for the isosymmetric pseudoexperimental values. With convention A the octet baryon masses are m_N = 939.2(10.8) MeV, m_Lambda = 1110.5(3.7) MeV, m_Sigma = 1193.3(3.6) MeV, all consistent with experiment within 2 sigma, while f_pi = 128.41(72) MeV, f_K = 154.29(56) MeV, f_K/f_pi = 1.1997(36), and m_s/m_ud = 27.659(98) deviate slightly from the FLAG 2024 summary beyond the error bars. With convention B, which uses isospin-averaged kaon and Xi inputs, the corresponding values f_pi = 129.55(88) MeV, f_K = 155.12(59) MeV, f_K/f_pi = 1.1959(55), and m_s/m_ud = 27.323(143) become consistent with FLAG, and the octet masses again agree within 2 sigma. Because the difference between conventions is retained in the continuum limit, the paper reads the convention spread as the residual QED and isospin ambiguity of the isosymmetric comparison, making the convention-A tension a definitional artifact of choosing the neutral kaon and neutral Xi as inputs rather than a sign that QCD fails to describe the spectrum.

Load-bearing premise

The quark-mass slopes that tune the physical point are measured on a 5.4 fm box at the coarsest lattice spacing and then carried unchanged, apart from a lattice-spacing rescaling, to the two finer lattices, so if those slopes shift with box size or spacing the tuned pion, kaon, and Xi masses move by amounts the error budget does not include.

Editorial extensions

If this is right

  • If the claim is correct, 2+1 flavor QCD computed directly at the physical point predicts the octet baryon masses in the continuum limit at sub-percent precision, with the nucleon, Lambda, and Sigma all within roughly two sigma of experiment.
  • The agreement of the decay constants and m_s/m_ud with FLAG under convention B implies that the residual isospin/QED ambiguity, as measured by the convention-A versus convention-B spread, dominates the apparent FLAG tension; the lattice calculation itself is not the limiting uncertainty.
  • The finite-size analysis shows that decay constants genuinely need the larger-than-10 fm boxes, since a 5.4 fm box shifts f_pi by about -0.44% and f_K by about -0.24%, larger than the one-loop ChPT estimate.
  • The PACS10 ensembles, being generated only at the physical point, provide a platform for other physical-point observables such as hadron structure with fine momentum resolution, with controlled continuum and finite-volume systematics as demonstrated here.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the convention-B agreement is the physics, then the historical convention-A input choice — neutral kaon and neutral Xi — carries a built-in offset of roughly 1% in f_pi and f_K and about 1% in m_s/m_ud relative to the FLAG definitions; other analyses that inherit convention-A inputs should be re-examined under the isospin-averaged choice.
  • The Taylor coefficients of Table VI are measured at one lattice spacing and one box size, then reused at finer spacings without a direct check; a reweighting run on L160 or L256 would test whether the physical-point tuning is stable and would likely reduce the dominant systematic.
  • The decay-constant finite-size shift being roughly three times the one-loop SU(3) ChPT prediction suggests higher-order chiral corrections operate at the experimentally relevant 1% level; a second half-size box at a finer spacing would distinguish finite-volume effects from lattice artifacts.
Original abstract

We present the results for the hadron spectrum, the pseudoscalar meson decay constants, and the quark mass ratio in the continuum limit using the ``PACS10'' gauge configurations generated with the $O(a)$-improved Wilson quark action and the Iwasaki gauge action. Numerical simulations are carried out at three lattice spacings keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. We calculate physical quantities with two choices of conventions to define pseudoexperimental values expected in the isosymmetric QCD. In order to investigate the finite size effects on the physical quantities we have additionally generated the (5.4 fm$)^4$ lattice at the coarsest lattice spacing of $a=0.08487(14)$~fm, which is a hypercube with half the length in each direction compared to the PACS10 configurations. While the finite size effect is hardly observed in comparison of the hadron effective masses on the (10.9 fm$)^4$ and (5.4 fm$)^4$ lattices, the results for the pseudoscalar meson decay constants show discrepancies beyond the error bars. The (5.4 fm$)^4$ lattice also serves for determining the expansion parameters of the pseudoscalar meson masses and decay constants, and the octet baryon masses in terms of the quark masses around the physical point with the aid of the mass reweighting technique. The expansion parameters are used for the fine-tuning of the physical point employing the pseudoexperimental masses of the $\pi$ meson, $K$ meson, and the $\Xi$ baryon as physical inputs in each convention. We compare the results for the octet baryon masses and the pseudoscalar decay constants in the continuum limit with the corresponding pseudoexperimental values in both conventions. We also discuss the deviation between two results with different conventions. As for the quark mass ratio the result is compared with the recent FLAG summary.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-11-03: 1 request, 7,985 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.81 · human participants 0.01 · controlled comparison 0.23 · randomized assignment 0.01 · states quantitative result 0.35 · compares with prior results 0.94 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We present the results for the hadron spectrum, the pseudoscalar meson decay constants, and the quark mass ratio in the continuum limit using the ``PACS10'' gauge configurations generated with the $O(a)$-improved Wilson quark action and the Iwasaki gauge action. Numerical simulations are carried out at three lattice spacings keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. We calculate physical quantities with two choices of conventions to define pseudoexperimental values expected in the isosymmetric QCD. In order to investigate the finite size effects on the physical quantities we have additionally generated the (5.4 fm$)^4$ lattice at the coarsest lattice spacing of $a=0.08487(14)$~fm, which is a hypercube with half the length in each direction compared to the PACS10 configurations. While the finite size effect is hardly observed in comparison of the hadron effective masses on the (10.9 fm$)^4$ and (5.4 fm$)^4$ lattices, the results for the pseudoscalar meson decay constants show discrepancies beyond the error bars. The (5.4 fm$)^4$ lattice also serves for determining the expansion parameters of the pseudoscalar meson masses and decay constants, and the octet baryon masses in terms of the quark masses around the physical point with the aid of the mass reweighting technique. The expansion parameters are used for the fine-tuning of the physical point employing the pseudoexperimental masses of the $\pi$ meson, $K$ meson, and the $\Xi$ baryon as physical inputs in each convention. We compare the results for the octet baryon masses and the pseudoscalar decay constants in the continuum limit with the corresponding pseudoexperimental values in both conventions. We also discuss the deviation between two results with different conventions. As for the quark mass ratio the result is compared with the recent FLAG summary.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present the results for the hadron spectrum, the pseudoscalar meson decay constants, and the quark mass ratio in the continuum limit using the ``PACS10'' gauge configurations generated with the $O(a)$-improved Wilson quark action and the Iwasaki gauge action. contribution 0.96 0.95 0.31 asserted 1.00
s1 Numerical simulations are carried out at three lattice spacings keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. method 0.99 0.94 0.04 asserted 1.00
s2 We calculate physical quantities with two choices of conventions to define pseudoexperimental values expected in the isosymmetric QCD. method 0.82 0.93 0.04 asserted 0.99
s3 In order to investigate the finite size effects on the physical quantities we have additionally generated the (5.4 fm$)^4$ lattice at the coarsest lattice spacing of $a=0.08487(14)$~fm, which is a hypercube with half the length in each direction compared to the PACS10 configurations. method 0.92 0.96 0.03 asserted 0.97
s4 While the finite size effect is hardly observed in comparison of the hadron effective masses on the (10.9 fm$)^4$ and (5.4 fm$)^4$ lattices, the results for the pseudoscalar meson decay constants show discrepancies beyond the error bars. result 0.99 0.96 0.13 asserted 0.98
s5 The (5.4 fm$)^4$ lattice also serves for determining the expansion parameters of the pseudoscalar meson masses and decay constants, and the octet baryon masses in terms of the quark masses around the physical point with the aid of the mass reweighting technique. method 0.94 0.95 0.04 asserted 1.00
s6 The expansion parameters are used for the fine-tuning of the physical point employing the pseudoexperimental masses of the $\pi$ meson, $K$ meson, and the $\Xi$ baryon as physical inputs in each convention. method 0.98 0.91 0.04 asserted 1.00
s7 We compare the results for the octet baryon masses and the pseudoscalar decay constants in the continuum limit with the corresponding pseudoexperimental values in both conventions. contribution 0.63 0.94 0.12 asserted 0.91
s8 We also discuss the deviation between two results with different conventions. contribution 0.84 0.87 0.06 unclear 0.65
s9 As for the quark mass ratio the result is compared with the recent FLAG summary. result 0.86 0.69 0.07 asserted 0.94

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. FIG. 1. Comparison of the effective masses for
Figure 2. FIG. 2. Comparison of
Figure 4. FIG. 4. Comparison of effective masses for
Figure 6. FIG. 6. Comparison of effective masses for ∆, Σ
Figure 7. FIG. 7. AWI quark mass dependence of
Figure 8. FIG. 8. Simulation point, reweighted points, and physical
Figure 9. FIG. 9. Effective masses for
Figure 10. FIG. 10. Effective masses for
Figure 11. FIG. 11. Effective masses for
Figure 12. FIG. 12. Effective masses for ∆, Σ
Figure 13. FIG. 13. Same as Fig. 9 but on the L256 lattice at
Figure 14. FIG. 14. Same as Fig. 10 but on the L256 lattice at
Figure 15. FIG. 15. Same as Fig. 11 but on the L256 lattice at
Figure 16. FIG. 16. Same as Fig. 12 but on the L256 lattice at
Figure 17. FIG. 17. Monte Carlo history of topological charge on the
Figure 19. FIG. 19. Continuum extrapolation of
Figure 20. FIG. 20. Continuum extrapolation of

Showing 17 of the paper's 20 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2611.02426 by the authors.

References

Discussion

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