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REVIEW 3 major objections 5 minor 155 references

Investigating the axial structure of the nucleon based on large-volume lattice QCD at the physical point

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Lattice QCD at physical quark masses shows the pion-pole dominance model for nucleon axial form factors holds to ten percent.

desk verdict A careful large-volume lattice QCD study of nucleon axial form factors whose central verification claims rest on an unvalidated single-πN-state subtraction ansatz and partly circular use of the same PCAC relation. read the letter →

arxiv 2505.10998 v1 pith:J6ZB22DS submitted 2025-05-16 hep-lat

Ryutaro Tsuji , Yasumichi Aoki , Ken-Ichi Ishikawa , Yoshinobu Kuramashi , Shoichi Sasaki , Kohei Sato , Eigo Shintani , Hiromasa Watanabe
show 1 more author
Takeshi Yamazaki (for the PACS Collaboration)
This is my paper · ORCID
classification hep-lat
keywords nucleonaxialformfactorslatticeQCDphysicalpointpion-poledominancegeneralizedGoldberger-TreimanrelationPCACexcited-statecontaminationneutrinooscillationinputs
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 aims to establish that large-volume lattice QCD at physical quark masses can reliably determine the nucleon's axial form factors—the axial-vector, induced pseudoscalar, and pseudoscalar form factors—and that these form factors obey the continuum axial Ward-Takahashi relations. Its central claim is that after subtracting the leading pion-nucleon excited-state contamination, the generalized Goldberger-Treiman relation ($R_1+R_2=1$) and the pion-pole dominance form ($R_3=1$) hold to about five percent for $q^2\lesssim 0.1\ \mathrm{GeV}^2$, with the pion-pole dominance form for $F_P$ remaining valid to less than ten percent up to $q^2\sim 0.42\ \mathrm{GeV}^2$. This matters because neutrino oscillation experiments rely on the axial form factors as inputs, and a pion-pole dominance model that works at the physical point would give neutrino event generators a theoretically grounded approximation.

What carries the argument

The central object is the leading $\pi N$ subtraction ansatz: the residual time dependence of the correlator ratios is written as $\Delta_\pm(t,t_{\mathrm{sep}};q)=B(q)e^{-(E_\pi+M_N-E_N)t}\pm C(q)e^{-(E_\pi-M_N+E_N)(t_{\mathrm{sep}}-t)}$, with $t$-independent coefficients $B(q)$ and $C(q)$. The time-derivative property of these functions, together with the axial Ward-Takahashi identity, lets the $\pi N$ contamination be removed from the $F_P$ and $G_P$ extraction, which is the step that makes the low-energy relations testable.

What would settle it

Repeat the analysis with a variational basis that includes an explicit $\pi N$ operator or with a multi-state fit that adds a second excited state, and check whether $R_1+R_2$ and $R_3$ remain consistent with unity; a shift beyond the quoted few-percent level would show the single-$\pi N$ subtraction is incomplete.

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Extended reading notes

Core claim

The paper claims that the long-standing excited-state contamination that biased lattice determinations of the induced pseudoscalar form factor $F_P$ and the pseudoscalar form factor $G_P$ is dominated by a single $\pi N$ intermediate state, and that removing this state with the proposed subtraction yields $F_P$ and $G_P$ whose $q^2$ dependence matches the pion-pole dominance predictions and satisfies the generalized Goldberger-Treiman relation. On the paper's own terms, the lattice data at the physical point, analyzed with this subtraction, reproduce the low-energy relations derived from the axial Ward-Takahashi identity within the quoted statistical precision, and the pion-pole dominance model—strictly valid only in the chiral limit—continues to describe the induced pseudoscalar form factor at the physical point.

Load-bearing premise

The entire analysis rests on the assumption that the only excited-state contamination in the $F_P$ and $G_P$ ratios is a single $\pi N$ intermediate state described by the two constants $B(q)$ and $C(q)$; if other excited states contribute, the subtraction is incomplete, the extracted form factors are biased, and the agreement with the Goldberger-Treiman and pion-pole relations becomes an artifact.

Editorial extensions

If this is right

  • If the central claim is correct, lattice QCD at the physical point can provide first-principles input for the axial form factors used in neutrino oscillation analyses, bypassing model assumptions for $F_A$ and $F_P$.
  • The pion-pole dominance form for $F_P$, previously justified only in the chiral limit, would be a quantitatively reliable approximation for $q^2\lesssim 0.42\ \mathrm{GeV}^2$ at the physical point.
  • The generalized Goldberger-Treiman relation, which appears violated in the traditional plateau analysis, would be restored once the leading $\pi N$ contamination is removed, confirming that the violation is an excited-state artifact rather than new physics.
  • The agreement between the two PCAC quark masses—one from pion two-point functions and one from nucleon three-point functions—would indicate that the lattice data inherit the continuum axial Ward-Takahashi physics within the quoted precision.
  • The comparison of coarse and fine lattice results would justify continuing toward a continuum limit with a third, finer lattice spacing, with the expectation that the low-energy relations remain satisfied.

Reading between the lines

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

  • If the single-$\pi N$ subtraction survives independent checks, the same technique could be applied to other nucleon matrix elements where pion-nucleon excited states contaminate the signal, extending the reach of plateau methods.
  • The paper leaves implicit that the success of the PPD model at the physical point does not automatically constrain the model's use at larger $q^2$ or at off-physical pion masses; those regimes still require separate lattice checks.
  • A testable extension would be to compare the subtracted form factors with results from a variational analysis using an explicit $\pi N$ operator; agreement would confirm that the omitted higher excited states are genuinely negligible.
  • The approximate ten percent discretization uncertainty seen in the axial radius suggests that a precise continuum limit, not just the low-energy relations, is the next bottleneck for neutrino-flux predictions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This manuscript reanalyzes PACS Collaboration lattice data for the isovector nucleon axial form factors FA, FP, and GP at physical quark masses on (10 fm)^3 volumes with lattice spacings a≈0.09 and 0.06 fm, together with a smaller-volume ensemble. The central methodological claim is that a leading πN excited-state subtraction, Eqs. (40)-(46), removes the dominant contamination in FP and GP, yielding couplings gA, gP*, and gπNN consistent with experiment. The paper then uses the extracted form factors to test the PCAC/GGT/PPD relations through R1+R2=1, R3=1, and R4=1 (Eq. 65), and maps their q² validity, claiming roughly 5% agreement for q²≲0.1 GeV² and validity of the PPD form for FP to within less than 10% up to q²≈0.42 GeV². It also introduces a nucleon-based PCAC mass mnucl_PCAC (Eq. 53) and reports agreement with the pion-based mπ_PCAC in the low-q² region.

Significance. If the central claims hold, this is a valuable contribution: physical-point, large-volume lattice data in the low-q² region directly relevant to neutrino-event generators, with a practical demonstration of how far the pion-pole-dominance model remains valid beyond the chiral limit. The paper has notable strengths: multiple tsep values, jackknife error estimation, volume checks, a clear traditional-versus-new analysis comparison, tabulated ratio data in Appendix A, and an independent correlation-function-level PCAC check in Sec. 6. However, the validation of the GGT/PPD statements is weakened by two load-bearing issues: the single-πN-state ansatz in Eq. (43) is not independently tested, and the GP extraction in Eq. (46) shares the same PCAC/GMOR input that the R4 test is supposed to verify. These issues must be addressed before the 5% and 10% statements can be taken as established.

major comments (3)
  1. [Sec. 3.2, Eq. (43); Secs. 5.3 and 7.2] The new analysis assumes that the entire excited-state contamination in the FP and GP ratios is a single πN intermediate state with t-independent coefficients B(q) and C(q) in Eq. (43). No variational or multi-state analysis is performed to test this assumption; Refs. [148-150] are cited as examples of such methods but are not applied here. The extracted FP and GP, and therefore the claims R1+R2≈1 and R3≈1, are only as good as this ansatz. The assertion in Sec. 5.3 that 'we have succeeded in completely removing the leading πN contribution' is not supported by a check that other states, such as N(1440)π or ρN, are negligible at the simulated tsep≈1.0-1.2 fm. A multi-state or variational cross-check, or at least a comparison with an independent extraction for one ensemble, is needed before the 5% statements can be accepted.
  2. [Sec. 3.2, Eq. (46); Sec. 7.1, Eqs. (63)-(64)] The GP extraction in Eq. (46) subtracts a term proportional to Z_A B0 = Z_A Mπ²/(2m_PCAC), where B0 is the GMOR low-energy constant introduced in Eq. (21). The ratio R4 defined in Eq. (64) is exactly the same combination (up to renormalization factors), so reporting R4≈1 is partly circular: the PCAC/GMOR relation used in the subtraction is being presented as a verified consequence. The R2 component of the GGT test also inherits this input through GP. The independent mnucl_PCAC comparison in Sec. 6 is a genuine, non-circular check and supports the low-q² region, but it does not by itself justify the form-factor-level subtraction. To make the test informative, the authors should either extract B0 from the data without imposing Eq. (21), or compare the extracted GP with an independent determination that does not use Z_A B0.
  3. [Sec. 8, Table 6 and Fig. 21] The high-q² extension to q²≈0.42 GeV² is based on a single coarse ensemble (PACS5/L64, a≈0.09 fm) without a continuum limit, and at the largest momentum Q8 the mnucl_PCAC comparison yields no signal, as Sec. 8 explicitly acknowledges. Nevertheless, the new analysis uses the PCAC relation mnucl_PCAC=mπ_PCAC in the entire range including Q8 as the input to Eq. (46). The subsequent claims that R1+R2 and R3 remain within 10% up to 0.42 GeV² therefore rest on an input that the paper itself cannot verify at that momentum. This limitation should be stated in the abstract and conclusions, and the 10% numbers should be labeled as upper bounds subject to uncontrolled discretization effects.
minor comments (5)
  1. [Sec. 1 and Sec. 4.3] There are several typos: 'performe' and 'reffered to' in Sec. 1, and 'spearing parameters' in Sec. 4.3.
  2. [Fig. 16 caption] The caption repeats 'Results for tsep/a={12,14,16} are plotted from top to bottom panels' after correctly listing {13,16,19} for PACS10/L160; the duplicate sentence should be removed.
  3. [Sec. 7.1 and figures] The notation mPCAC is used both for the bare quark mass and in figure labels such as '2mPCAC eGP'; define the symbol once in Sec. 7.1 and use it consistently in the figure axes and captions.
  4. [Sec. 3.2, Eq. (46)] Equation (46) is central to the paper, but its derivation is delegated to Ref. [60]. Since this manuscript applies the method to new physics tests, a short derivation or a clear restatement of the assumptions would improve standalone readability.
  5. [Abstract and Sec. 4.1] The abstract says calculations are carried out with 'two of three sets' of configurations; the status of the third ensemble and its planned role in the continuum extrapolation is only stated later in Sec. 5.4 and Sec. 9. Consider making this explicit near the ensemble description.

Circularity Check

2 steps flagged · score 6.0 of 10

GP is constructed using the same AWT/PCAC relation whose consequences the paper then claims to verify; the R4 test is invariant under the new analysis by construction.

  1. self definitional [Sec. 3.2 Eqs. (45)-(46); Sec. 7.1 Eq. (64); Sec. 7.2 R4 discussion]
    "eGP (q2) =KR5zP (t, q) iq3 + ZAB0K (∆EN)2− (Eπ)2 [∆EN ∂4R5zAi(t, q) qiq3 + ∂4R5zA4(t, q) iq3] ... The relation of R4 = 1 is interpreted as eGP(q2)/FP(q2) =B0 with the bare low-energy constant, B0 = M2π/(2mPCAC) ... the eFP and eGP form factors suffer from similar contaminations from the πN-state contribution, which are connected by the AWT identity."

    Let S be the derivative combination in Eq. (46). Using Eqs. (40)-(44), S is exactly the assumed πN contamination Δ+ that Eq. (45) removes from F_P. Hence F_P^new = F_P^trad + S and G_P^new = G_P^trad + Z_A B0 S, so G_P^new − Z_A B0 F_P^new = G_P^trad − Z_A B0 F_P^trad. The R4 test checks precisely G_P = Z_A B0 F_P (with B0 = Mπ^2/(2m_PCAC)), so R4 is unchanged by the new analysis; the paper itself states R4≈1 already in the traditional analysis because F_P and G_P receive the same AWT-connected πN contamination. Thus the R4=1 'verification' is not independent evidence for the ground-state GMOR/PPD relation; it restates the AWT relation used, via the self-cited Ref. [60], to model the contamination.

  2. other [Sec. 8, PACS5/L64 extension (Q8), before Fig. 23]
    "Although the PCAC relation of mnuclPCAC=mpionPCAC was not numerically confirmed at the highest q2∼0.42 [GeV2], we simply used the leading πN subtraction method, where this relation is used to determine the GP form factor, in the entire range of q2≲0.42 [GeV2]."

    At the highest momentum transfer the paper explicitly assumes the PCAC relation as an input for the GP extraction because m_nucl^PCAC has no valid signal. It then reports, in the same section, that the GGT relation and the PPD model for F_P(q2) hold up to q2∼0.42 GeV2. The GGT and R4 tests at Q8 use the GP constructed from that assumed relation, so the agreement at q2∼0.42 is conditional on the very relation the paper claims to verify. The R3 test for F_P alone is not affected by this input, which limits this circularity to the GP-dependent relations (R1+R2 and R4) at the upper end of the q2 range.

full rationale

The analysis is not fully circular: the R3 test for the PPD form of F_P uses Eq. (45), which contains no B0 and therefore provides independent evidence that F_P follows the pion-pole form; the Sec. 6 comparison of m_nucl^PCAC with m_pion^PCAC is an independent check; and g_A, g*_P, and gπNN are compared with experiment. However, the GP-dependent claims are partially circular. Eq. (46) constructs G_P by adding Z_A B0 times exactly the combination S that Eq. (45) removes from F_P. Consequently G_P − Z_A B0 F_P is invariant under the new analysis, so the R4=1 test that the paper interprets as eGP/FP = B0 cannot be changed by the subtraction; it already held in the traditional analysis because the assumed πN contamination in both channels is AWT-connected, as established in the same collaboration's Ref. [60]. At the upper end of the extended q2 range, the paper explicitly assumes the PCAC relation for the GP determination where m_nucl^PCAC has no signal, and then reports GGT/PPD validity up to q2∼0.42 GeV2. These steps make the GP-dependent low-energy relations at least partly self-referential. The single-πN ansatz of Eq. (43) is not validated by a variational or multi-state analysis, so if other excited states contribute, the observed R1+R2≈1 and R4≈1 would be artifacts of the subtraction rather than independent verifications. Because one of the three central tests (R4) is invariant by construction and the high-q2 GGT test uses the relation as input, the paper does not fully reduce by definition, but the circularity is substantial; score 6.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The claim relies on standard lattice QCD, the axial Ward-Takahashi identity, an ad hoc leading-πN ansatz, and z-expansion fits. No new particles or forces are introduced.

free parameters (3)
  • z-expansion coefficients c_k for FP(q^2)
    The q^2 dependence of (q^2+Mπ^2)FP(q^2) is fitted to a polynomial in z (Eq. 50) and used to evaluate g*_P and gπNN. The coefficients are determined by the lattice data, so they are fit parameters.
  • z-expansion coefficients c_k for FA(q^2)
    Used to extract the axial radius from the slope of FA at q^2=0; fitted to lattice data.
  • smearing parameters (A,B) = (1.2,0.16) coarse, (1.2,0.11) fine
    Hand-tuned to suppress excited states in the nucleon operator (Sec. 4.3); affects the plateau quality and thus the fitted form factors.
assumptions (5)
  • domain assumption The Euclidean lattice path integral with the PACS actions correctly represents continuum QCD in the measured region.
    The whole calculation assumes lattice QCD is the correct nonperturbative definition of QCD (Sec. 3.1).
  • domain assumption The axial Ward-Takahashi identity ∂αAα=2mP is used to relate the πN contamination in P to that in Aα in the new analysis.
    Used in Eq. (46) to construct the GP subtraction term and also as the basis for the GGT relation (Secs. 3.2, 3.4).
  • ad hoc to paper Excited-state contamination is dominated by a single πN intermediate state with coefficients B(q) and C(q) independent of t.
    Functional form in Eq. (43); no variational or multi-state check is provided in this paper.
  • domain assumption The O(a) improvement coefficient cA is negligible for the unimproved axial current in this calculation.
    The unimproved axial current is used; the paper concludes the correction is small because m_PCAC^nucl matches m_PCAC^pion (Secs. 6, Eqs. (58)-(59)).
  • domain assumption SU(2) isospin symmetry is exact in the 2+1 flavor ensembles, so disconnected diagrams cancel for isovector currents.
    Used to justify connected-only three-point functions for the isovector nucleon matrix elements (Sec. 3.2).

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Pith. "Pith review of Investigating the axial structure of the nucleon based on large-volume lattice QCD at the physical point." pith.science (2026). https://pith.science/paper/J6ZB22DS

@misc{pith2026250510998,
  author       = {Pith},
  title        = {Pith review of: Investigating the axial structure of the nucleon based on large-volume lattice QCD at the physical point},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J6ZB22DS}},
  note         = {Machine review of arXiv:2505.10998}
}
abstract

We present a short summary for the calculations of the nucleon $\textit{isovector}$ form factors, which are relevant to improving the accuracy of the current neutrino oscillation experiments. The calculations are carried out with two of three sets of the $2+1$ flavor lattice QCD configurations generated at the physical point in large spatial volumes by the PACS Collaboration. The two gauge configurations are generated with the six stout-smeared $O(a)$ improved Wilson quark action and Iwasaki gauge action at the lattice spacing of $0.09$ fm and $0.06$ fm. We summarize the results for three form factors as well as the nucleon axial-vector ($g_A$), induced pseudoscalar ($g_P^*$) and pion-nucleon ($g_{\pi NN}$) couplings. Although our couplings agree with the experimental data, a firm conclusion should be drawn only after a continuum limit extrapolation is taken. We investigate the partially conserved axial-vector current (PCAC) relation in the context of the nucleon correlation functions. The low-energy relations arising from the PCAC relation can be used to verify whether the lattice QCD data correctly reproduce the physics in the continuum within the statistical accuracy. It is demonstrated that our $\textit{new analysis}$ reduces the systematic uncertainty for the induced pseudoscalar and pseudoscalar form factors to a greater extent than the $\textit{traditional analysis}$, and the results offer a theoretical insight into the pion-pole dominance model. Finally, we examine the applicable $q^2$ region for the low-energy relations.

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Reference graph

Works this paper leans on

155 extracted references · 14 canonical work pages

  1. [1]

    Aoki et al

    Y. Aoki et al. (11 2024), arXiv:2411.04268, and relevant references therein

    arXiv 2024

  2. [2]

    Alessandro Barone, Shoji Hashimoto, Andreas J¨ uttner, Takashi Kaneko, and Ryan Kellermann, JHEP, 07, 145 (2023), arXiv:2305.14092

    arXiv 2023

  3. [3]

    Ryan Kellermann, Alessandro Barone, Ahmed Elgaziari, Shoji Hashimoto, Zhi Hu, Andreas J¨ uttner, and Takashi Kaneko (4 2025), arXiv:2504.03358

    arXiv 2025

  4. [4]

    (4 2025), arXiv:2504.06063

    Alessandro De Santis et al. (4 2025), arXiv:2504.06063

    arXiv 2025

  5. [5]

    (4 2025), arXiv:2504.06064

    Alessandro De Santis et al. (4 2025), arXiv:2504.06064

    arXiv 2025

  6. [6]

    Bauer et al., PRX Quantum, 4(2), 027001 (2023), arXiv:2204.03381, and relevant references therein

    Christian W. Bauer et al., PRX Quantum, 4(2), 027001 (2023), arXiv:2204.03381, and relevant references therein

    arXiv 2023

  7. [7]

    Choi, Hiroshi Ohno, Takayuki Sumimoto, and Akio Tomiya, PoS, LA TTICE2024, 033 (2024), arXiv:2411.18170

    Benjamin J. Choi, Hiroshi Ohno, Takayuki Sumimoto, and Akio Tomiya, PoS, LA TTICE2024, 033 (2024), arXiv:2411.18170

    arXiv 2024

  8. [8]

    Scott Lawrence, PoS, LA TTICE2024, 010 (2025), arXiv:2502.02670

    arXiv 2025

Show all 155 references
  1. [9]

    Akio Tomiya, J. Phys. Soc. Jap., 94(3), 031006 (2025)

    2025

  2. [10]

    M. J. Bangham L. Essen, R. W. Donaldson and E. G. Hope, Nature, 299, 110–111 (1971)

    1971

  3. [11]

    Eides, Howard Grotch, and Valery A

    Michael I. Eides, Howard Grotch, and Valery A. Shelyuto, Theory of Light Hydrogenic Bound States , volume 222, (Springer-Verlag, Berlin, 2007)

    2007

  4. [12]

    National Academies of Sciences, Engineering, and Medicine, An Assessment of U.S.-Based Electron-Ion Collider Science , (The National Academies Press, Washington, DC, 2018)

    2018

  5. [13]

    Abdul Khalek et al., Nucl

    R. Abdul Khalek et al., Nucl. Phys. A, 1026, 122447 (2022), arXiv:2103.05419

    2022 arXiv

  6. [14]

    V. W. Hughes and J. Kuti, Ann. Rev. Nucl. Part. Sci., 33, 611–644 (1983)

    1983

  7. [15]

    Ashman et al., Phys

    J. Ashman et al., Phys. Lett. B, 206, 364 (1988)

    1988

  8. [16]

    Ashman et al., Nucl

    J. Ashman et al., Nucl. Phys. B, 328, 1 (1989)

    1989

  9. [17]

    Daniel de Florian, Rodolfo Sassot, Marco Stratmann, and Werner Vogelsang, Phys. Rev. D, 80, 034030 (2009), arXiv:0904.3821

    2009 arXiv

  10. [18]

    Nocera, Richard D

    Emanuele R. Nocera, Richard D. Ball, Stefano Forte, Giovanni Ridolfi, and Juan Rojo, Nucl. Phys. B, 887, 276–308 (2014), arXiv:1406.5539

    2014 arXiv

  11. [19]

    J. J. Ethier, N. Sato, and W. Melnitchouk, Phys. Rev. Lett., 119(13), 132001 (2017), arXiv:1705.05889

    2017 arXiv

  12. [20]

    Xiangdong Ji, Front. Phys. (Beijing), 16(6), 64601 (2021), arXiv:2102.07830

    2021 arXiv

  13. [21]

    V. D. Burkert, L. Elouadrhiri, F. X. Girod, C. Lorc´ e, P. Schweitzer, and P. E. Shanahan, Rev. Mod. Phys., 95(4), 041002 (2023), arXiv:2303.08347

    2023 arXiv

  14. [22]

    Xiang-Dong Ji, Phys. Rev. Lett., 78, 610–613 (1997), hep-ph/9603249

    1997 arXiv

  15. [23]

    Yi-Bo Yang, Ying Chen, Terrence Draper, Ming Gong, Keh-Fei Liu, Zhaofeng Liu, and Jian-Ping Ma, Phys. Rev. D, 91(7), 074516 (2015), arXiv:1405.4440

    2015 arXiv

  16. [24]

    Yoshitaka Hatta, Abha Rajan, and Kazuhiro Tanaka, JHEP, 12, 008 (2018), arXiv:1810.05116

    2018 arXiv

  17. [25]

    Kazuhiro Tanaka, JHEP, 01, 120 (2019), arXiv:1811.07879

    2019 arXiv

  18. [26]

    Andreas Metz, Barbara Pasquini, and Simone Rodini, Phys. Rev. D, 102, 114042 (2020), arXiv:2006.11171

    2020 arXiv

  19. [27]

    Keh-Fei Liu, Phys. Rev. D, 104(7), 076010 (2021), arXiv:2103.15768

    2021 arXiv

  20. [28]

    Kazuhiro Tanaka, JHEP, 03, 013 (2023), arXiv:2212.09417

    2023 arXiv

  21. [29]

    C´ edric Lorc´ e, Luca Mantovani, and Barbara Pasquini, Phys. Lett. B,776, 38–47 (2018), arXiv:1704.08557

    2018 arXiv

  22. [30]

    Carlos Granados and Christian Weiss, Phys. Lett. B, 797, 134847 (2019), arXiv:1905.02742

    2019 arXiv

  23. [31]

    Peter Schweitzer and Kemal Tezgin, Phys. Lett. B, 796, 47–51 (2019), arXiv:1905.12336

    2019 arXiv

  24. [32]

    M. V. Polyakov and A. G. Shuvaev (7 2002), hep-ph/0207153

    2002 arXiv

  25. [33]

    M. V. Polyakov, Phys. Lett. B, 555, 57–62 (2003), hep-ph/0210165

    2003 arXiv

  26. [34]

    Pasquini, M

    B. Pasquini, M. V. Polyakov, and M. Vanderhaeghen, Phys. Lett. B, 739, 133–138 (2014), arXiv:1407.5960

    2014 arXiv

  27. [35]

    C´ edric Lorc´ e, JHEP,08, 045 (2015), arXiv:1502.06656

    2015 arXiv

  28. [36]

    Trawi´ nski, Eur

    C´ edric Lorc´ e, Herv´ e Moutarde, and Arkadiusz P. Trawi´ nski, Eur. Phys. J. C, 79(1), 89 (2019), arXiv:1810.09837

    2019 arXiv

  29. [37]

    Kumano, Qin-Tao Song, and O

    S. Kumano, Qin-Tao Song, and O. V. Teryaev, Phys. Rev. D, 97(1), 014020 (2018), arXiv:1711.08088

    2018 arXiv

  30. [38]

    V. D. Burkert, L. Elouadrhiri, and F. X. Girod, Nature, 557(7705), 396–399 (2018)

    2018

  31. [39]

    Polyakov and Peter Schweitzer, Int

    Maxim V. Polyakov and Peter Schweitzer, Int. J. Mod. Phys. A, 33(26), 1830025 (2018), arXiv:1805.06596

    2018 arXiv

  32. [40]

    R. L. Jaffe and Aneesh Manohar, Nucl. Phys. B, 337, 509–546 (1990)

    1990

  33. [41]

    Fukugita, Y

    M. Fukugita, Y. Kuramashi, M. Okawa, and A. Ukawa, Phys. Rev. Lett., 75, 2092–2095 (1995), hep- lat/9501010

    1995

  34. [42]

    S. J. Dong, J. F. Lagae, and K. F. Liu, Phys. Rev. Lett., 75, 2096–2099 (1995), hep-ph/9502334

    1995 arXiv

  35. [43]

    Alexandrou, M

    C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou, A. Vaquero Avil´ es-Casco, and C. Wiese, Phys. Rev. Lett.,119(14), 142002 (2017), arXiv:1706.02973. 60

    2017 arXiv

  36. [44]

    Jian Liang, Yi-Bo Yang, Terrence Draper, Ming Gong, and Keh-Fei Liu, Phys. Rev. D, 98(7), 074505 (2018), arXiv:1806.08366

    2018 arXiv

  37. [45]

    Huey-Wen Lin, Rajan Gupta, Boram Yoon, Yong-Chull Jang, and Tanmoy Bhattacharya, Phys. Rev. D, 98(9), 094512 (2018), arXiv:1806.10604

    2018 arXiv

  38. [46]

    Yi-Bo Yang, Jian Liang, Yu-Jiang Bi, Ying Chen, Terrence Draper, Keh-Fei Liu, and Zhaofeng Liu, Phys. Rev. Lett., 121(21), 212001 (2018), arXiv:1808.08677

    2018 arXiv

  39. [47]

    Keh-Fei Liu, AAPPS Bull., 32(1), 8 (2022), arXiv:2112.08416

    2022 arXiv

  40. [48]

    Hiroshi Suzuki, PTEP, 2013, 083B03, [Erratum: PTEP 2015, 079201 (2015)] (2013), arXiv:1304.0533

    2015 arXiv

  41. [49]

    Leonardo Giusti, Tim Harris, Alessandro Nada, and Stefan Schaefer, Eur. Phys. J. C, 79(7), 586 (2019), arXiv:1903.10447

    2019 arXiv

  42. [50]

    Antoine G´ erardin, Willem E. A. Verplanke, Gen Wang, Zoltan Fodor, Jana N. Guenther, Laurent Lellouch, Kalman K. Szabo, and Lukas Varnhorst, Phys. Rev. D, 111(5), 054511 (2025), arXiv:2305.04570

    2025 arXiv

  43. [51]

    K. I. Ishikawa, N. Ishizuka, Y. Kuramashi, Y. Nakamura, Y. Namekawa, Y. Taniguchi, N. Ukita, T. Yamazaki, and T. Yoshie, Phys. Rev. D, 99(1), 014504 (2019), arXiv:1807.06237

    2019 arXiv

  44. [52]

    Ken-Ichi Ishikawa, Yoshinobu Kuramashi, Shoichi Sasaki, Natsuki Tsukamoto, Akira Ukawa, and Takeshi Yamazaki, Phys. Rev. D, 98(7), 074510 (2018), arXiv:1807.03974

    2018 arXiv

  45. [53]

    Eigo Shintani, Ken-Ichi Ishikawa, Yoshinobu Kuramashi, Shoichi Sasaki, and Takeshi Yamazaki, Phys. Rev. D, 99(1), 014510, [Erratum: Phys. Rev. D 102, 019902 (2020)] (2019), arXiv:1811.07292

    2020 arXiv

  46. [54]

    Ken-Ichi Ishikawa, Yoshinobu Kuramashi, Shoichi Sasaki, Eigo Shintani, and Takeshi Yamazaki, Phys. Rev. D, 104(7), 074514 (2021), arXiv:2107.07085

    2021 arXiv

  47. [55]

    Ryutaro Tsuji, Natsuki Tsukamoto, Yasumichi Aoki, Ken-Ichi Ishikawa, Yoshinobu Kuramashi, Shoichi Sasaki, Eigo Shintani, and Takeshi Yamazaki, Phys. Rev. D, 106(9), 094505 (2022), arXiv:2207.11914

    2022 arXiv

  48. [56]

    Ryutaro Tsuji, Yasumichi Aoki, Ken-Ichi Ishikawa, Yoshinobu Kuramashi, Shoichi Sasaki, Kohei Sato, Eigo Shintani, Hiromasa Watanabe, and Takeshi Yamazaki, Phys. Rev. D,109(9), 094505 (2024), arXiv:2311.10345

    2024 arXiv

  49. [57]

    Ryutaro Tsuji, Yasumichi Aoki, Ken-Ichi Ishikawa, Yoshinobu Kuramashi, Shoichi Sasaki, Kohei Sato, Eigo Shintani, Hiromasa Watanabe, and Takeshi Yamazaki, PoS, LA TTICE2024, 318 (2025), arXiv:2411.16784

    2025 arXiv

  50. [58]

    Yasumichi Aoki, Ken-Ichi Ishikawa, Yoshinobu Kuramashi, Shoichi Sasaki, Kohei Sato, Eigo Shintani, Ryutaro Tsuji, Hiromasa Watanabe, and Takeshi Yamazaki (5 2025), arXiv:2505.06854

    2025

  51. [59]

    Ryutaro Tsuji, Yasumichi Aoki, Ken-Ichi Ishikawa, Yoshinobu Kuramashi, Shoichi Sasaki, Takeshi Yamazaki, and Eigo Shintani, PoS, LA TTICE2021, 504 (2022), arXiv:2112.15276

    2022 arXiv

  52. [60]

    Shoichi Sasaki, Yasumichi Aoki, Ken-Ichi Ishikawa, Yoshinobu Kuramashi, Kohei Sato, Eigo Shintani, Ryutaro Tsuji, Hiromasa Watanabe, and Takeshi Yamazaki, PoS, LA TTICE2024, 310 (2025), arXiv:2501.13490

    2025 arXiv

  53. [61]

    Kronfeld, David G

    Andreas S. Kronfeld, David G. Richards, William Detmold, Rajan Gupta, Huey-Wen Lin, Keh-Fei Liu, Aaron S. Meyer, Raza Sufian, and Sergey Syritsyn, Eur. Phys. J. A, 55(11), 196 (2019), arXiv:1904.09931

    2019 arXiv

  54. [62]

    Meyer, Andr´ e Walker-Loud, and Callum Wilkinson (1 2022), arXiv:2201.01839

    Aaron S. Meyer, Andr´ e Walker-Loud, and Callum Wilkinson (1 2022), arXiv:2201.01839

    2022 arXiv

  55. [63]

    Alvarez Ruso et al

    L. Alvarez Ruso et al. (3 2022), arXiv:2203.09030

    2022 arXiv

  56. [64]

    Ashkenazi, A

    A. Ashkenazi, A. Papadopoulou, N. Rocco, and J. E. Sobczyk (3 2025), arXiv:2503.23556, and relevant references therein

    2025 arXiv

  57. [65]

    Marciano, and Alberto Sirlin, Phys

    Andrzej Czarnecki, William J. Marciano, and Alberto Sirlin, Phys. Rev. Lett., 120(20), 202002 (2018), arXiv:1802.01804

    2018 arXiv

  58. [66]

    V. A. Andreev et al., Phys. Rev. C, 91(5), 055502 (2015), arXiv:1502.00913

    2015 arXiv

  59. [67]

    V. A. Babenko and N. M. Petrov (4 2016), arXiv:1604.02912

    2016 arXiv

  60. [68]

    Limkaisang, K

    V. Limkaisang, K. Harada, J. Nagata, H. Yoshino, Y. Yoshino, M. Shoji, and M. Matsuda, Prog. Theor. Phys., 105, 233–242 (2001)

    2001

  61. [69]

    Parke, and Jose W

    Hiroshi Nunokawa, Stephen J. Parke, and Jose W. F. Valle, Prog. Part. Nucl. Phys., 60, 338–402 (2008), arXiv:0710.0554

    2008 arXiv

  62. [70]

    Abe et al., Phys

    K. Abe et al., Phys. Rev. Lett., 107, 041801 (2011), arXiv:1106.2822

    2011 arXiv

  63. [71]

    Abe et al., Nucl

    K. Abe et al., Nucl. Instrum. Meth. A, 659, 106–135 (2011), arXiv:1106.1238

    2011

  64. [72]

    Abe et al., PTEP, 2015, 053C02 (2015), arXiv:1502.05199

    K. Abe et al., PTEP, 2015, 053C02 (2015), arXiv:1502.05199

    2015 arXiv

  65. [73]

    Acciarri et al

    R. Acciarri et al. (12 2015), arXiv:1512.06148

    2015

  66. [74]

    Abi et al., Eur

    B. Abi et al., Eur. Phys. J. C, 80(10), 978 (2020), arXiv:2006.16043

    2020

  67. [75]

    (2 2020), arXiv:2002.03005

    Babak Abi et al. (2 2020), arXiv:2002.03005

    2020

  68. [76]

    Meyer, PoS, LA TTICE2022, 240 (2023), arXiv:2301.04616

    Aaron S. Meyer, PoS, LA TTICE2022, 240 (2023), arXiv:2301.04616

    2023 arXiv

  69. [77]

    Abe et al., Phys

    K. Abe et al., Phys. Rev. Lett., 134(1), 011801 (2025), arXiv:2405.12488

    2025

  70. [78]

    Khachatryan et al., Nature, 599(7886), 565–570 (2021)

    M. Khachatryan et al., Nature, 599(7886), 565–570 (2021)

    2021

  71. [79]

    Abe et al., Eur

    K. Abe et al., Eur. Phys. J. C, 83(9), 782 (2023), arXiv:2303.03222

    2023

  72. [80]

    M. A. Acero et al., Phys. Rev. Lett., 123(15), 151803 (2019), arXiv:1906.04907

    2019 arXiv

  73. [81]

    Acciarri et al

    R. Acciarri et al. (3 2015), arXiv:1503.01520. 61

    2015

  74. [82]

    Abratenko et al., Phys

    P. Abratenko et al., Phys. Rev. Lett., 123(13), 131801 (2019), arXiv:1905.09694

    2019 arXiv

  75. [83]

    Abratenko et al., Phys

    P. Abratenko et al., Phys. Rev. Lett., 131(10), 101802 (2023), arXiv:2301.03706

    2023 arXiv

  76. [84]

    Nicola McConkey, J. Phys. Conf. Ser., 888(1), 012148 (2017)

    2017

  77. [85]

    Pedro AN Machado, Ornella Palamara, and David W Schmitz, Ann. Rev. Nucl. Part. Sci., 69, 363–387 (2019), arXiv:1903.04608

    2019 arXiv

  78. [86]

    Christian Farnese, Universe, 5(2), 49 (2019)

    2019

  79. [87]

    Brizzolari, JINST, 19(03), C03001 (2024)

    C. Brizzolari, JINST, 19(03), C03001 (2024)

    2024

  80. [88]

    Kyberd et al

    P. Kyberd et al. (6 2012), arXiv:1206.0294

    2012 arXiv

  81. [89]

    G. A. Fiorentini et al., Phys. Rev. Lett., 111, 022502 (2013), arXiv:1305.2243

    2013 arXiv

  82. [90]

    Cai et al., Nature, 614(7946), 48–53 (2023)

    T. Cai et al., Nature, 614(7946), 48–53 (2023)

    2023

  83. [91]

    M. G. Aartsen et al., Science, 342, 1242856 (2013), arXiv:1311.5238

    2013 arXiv

  84. [92]

    M. G. Aartsen et al., Phys. Rev. D, 99(3), 032007 (2019), arXiv:1901.05366

    2019 arXiv

  85. [93]

    Adrian-Martinez et al., J

    S. Adrian-Martinez et al., J. Phys. G, 43(8), 084001 (2016), arXiv:1601.07459

    2016 arXiv

  86. [94]

    Aiello et al., Astropart

    S. Aiello et al., Astropart. Phys., 111, 100–110 (2019), arXiv:1810.08499

    2019 arXiv

  87. [95]

    Aiello et al., Eur

    S. Aiello et al., Eur. Phys. J. C, 82(1), 26 (2022), arXiv:2103.09885

    2022 arXiv

  88. [96]

    Henso Abreu et al., Phys. Rev. Lett., 131(3), 031801 (2023), arXiv:2303.14185

    2023 arXiv

  89. [97]

    Roshan Mammen Abraham et al., Phys. Rev. Lett., 133(2), 021802 (2024), arXiv:2403.12520

    2024 arXiv

  90. [98]

    Baussan et al., Nucl

    E. Baussan et al., Nucl. Phys. B, 885, 127–149 (2014), arXiv:1309.7022

    2014 arXiv

  91. [99]

    Alekou et al., Eur

    A. Alekou et al., Eur. Phys. J. C, 81(12), 1130 (2021), arXiv:2107.07585

    2021 arXiv

  92. [100]

    C. H. Llewellyn Smith, Phys. Rept., 3, 261–379 (1972)

    1972

  93. [101]

    Oleksandr Tomalak, Rajan Gupta, and Tanmoy Bhattacharya, Phys. Rev. D, 108(7), 074514 (2023), arXiv:2307.14920

    2023 arXiv

  94. [102]

    Kuzmin, Vladimir V

    Konstantin S. Kuzmin, Vladimir V. Lyubushkin, and Vadim A. Naumov, Eur. Phys. J. C, 54, 517–538 (2008), arXiv:0712.4384

    2008 arXiv

  95. [103]

    Meyer, Minerba Betancourt, Richard Gran, and Richard J

    Aaron S. Meyer, Minerba Betancourt, Richard Gran, and Richard J. Hill, Phys. Rev. D, 93(11), 113015 (2016), arXiv:1603.03048

    2016 arXiv

  96. [104]

    N. J. Baker, A. M. Cnops, P. L. Connolly, S. A. Kahn, H. G. Kirk, M. J. Murtagh, R. B. Palmer, N. P. Samios, and M. Tanaka, Phys. Rev. D, 23, 2499–2505 (1981)

    1981

  97. [105]

    K. L. Miller et al., Phys. Rev. D, 26, 537–542 (1982)

    1982

  98. [106]

    Meissner, J

    Veronique Bernard, Latifa Elouadrhiri, and Ulf-G. Meissner, J. Phys. G, 28, R1–R35 (2002), hep-ph/0107088

    2002 arXiv

  99. [107]

    A. A. Aguilar-Arevalo et al., Phys. Rev. D, 81, 092005 (2010), arXiv:1002.2680

    2010 arXiv

  100. [108]

    Sobczyk, Phys

    Tomasz Golan, Cezary Juszczak, and Jan T. Sobczyk, Phys. Rev. C, 86, 015505 (2012), arXiv:1202.4197

    2012 arXiv

  101. [109]

    Kakorin, Konstantin S

    Igor D. Kakorin, Konstantin S. Kuzmin, and Vadim A. Naumov, Eur. Phys. J. C, 81(12), 1142 (2021), arXiv:2112.13745

    2021 arXiv

  102. [110]

    Yoichiro Nambu, Phys. Rev. Lett., 4, 380–382 (1960)

    1960

  103. [111]

    Murray Gell-Mann and M Levy, Nuovo Cim., 16, 705 (1960)

    1960

  104. [112]

    M. L. Goldberger and S. B. Treiman, Phys. Rev., 110, 1178–1184 (1958)

    1958

  105. [113]

    Gasser, M

    J. Gasser, M. E. Sainio, and A. Svarc, Nucl. Phys. B, 307, 779–853 (1988)

    1988

  106. [114]

    Weisberger, Phys

    William I. Weisberger, Phys. Rev., 143, 1302–1309 (1966)

    1966

  107. [115]

    Bernard, Norbert Kaiser, and Ulf G

    V. Bernard, Norbert Kaiser, and Ulf G. Meissner, Phys. Rev. D, 50, 6899–6901 (1994), hep-ph/9403351

    1994 arXiv

  108. [116]

    Shoichi Sasaki and Takeshi Yamazaki, Phys. Rev. D, 78, 014510 (2008), arXiv:0709.3150

    2008 arXiv

  109. [117]

    Gasser and H

    J. Gasser and H. Leutwyler, Annals Phys., 158, 142 (1984)

    1984

  110. [118]

    Murray Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev., 175, 2195–2199 (1968)

    1968

  111. [119]

    Jacob Finkenrath, Francesco Knechtli, and Bj¨ orn Leder, Nucl. Phys. B,877, 441–456, [Erratum: Nucl.Phys.B 880, 574–575 (2014)] (2013), arXiv:1306.3962

    2014 arXiv

  112. [120]

    Shoichi Sasaki, Tom Blum, and Shigemi Ohta, Phys. Rev. D, 65, 074503 (2002), hep-lat/0102010

    2002 arXiv

  113. [121]

    Kiyoshi Sasaki and Shoichi Sasaki, Phys. Rev. D, 72, 034502 (2005), hep-lat/0503026

    2005 arXiv

  114. [122]

    Gockeler, T

    M. Gockeler, T. R. Hemmert, R. Horsley, D. Pleiter, Paul E. L. Rakow, A. Schafer, and G. Schierholz, Phys. Rev. D, 71, 034508 (2005), hep-lat/0303019

    2005 arXiv

  115. [123]

    Negele, Dru Bryant Renner, W

    Philipp Hagler, John W. Negele, Dru Bryant Renner, W. Schroers, T. Lippert, and K. Schilling, Phys. Rev. D, 68, 034505 (2003), hep-lat/0304018

    2003 arXiv

  116. [124]

    Rajan Gupta, PoS, LA TTICE2023, 124 (2024)

    2024

  117. [125]

    Hill and Gil Paz, Phys

    Richard J. Hill and Gil Paz, Phys. Rev. D, 82, 113005 (2010), arXiv:1008.4619

    2010 arXiv

  118. [126]

    G. S. Bali, S. Collins, M. Gruber, A. Sch¨ afer, P. Wein, and T. Wurm, Phys. Lett. B, 789, 666–674 (2019), arXiv:1810.05569

    2019 arXiv

  119. [127]

    Iwasaki (12 1983), arXiv:1111.7054

    Y. Iwasaki (12 1983), arXiv:1111.7054

    1983 arXiv

  120. [128]

    Ken-ichi Ishikawa, Naruhito Ishizuka, Yoshinobu Kuramashi, Yusuke Namekawa, Yusuke Taniguchi, Naoya Ukita, Takeshi Yamazaki, and Tomoteru Yoshi´ e, Phys. Rev. D,106(9), 094501 (2022), arXiv:2206.08654. 62

    2022 arXiv

  121. [129]

    Peardon, Phys

    Colin Morningstar and Mike J. Peardon, Phys. Rev. D, 69, 054501 (2004), hep-lat/0311018

    2004 arXiv

  122. [130]

    Yusuke Taniguchi, PoS, LA TTICE2012, 236 (2012), arXiv:1303.0104

    2012 arXiv

  123. [131]

    Eigo Shintani and Yoshinobu Kuramashi, Phys. Rev. D, 100(3), 034517 (2019), arXiv:1902.00885

    2019 arXiv

  124. [132]

    K. I. Ishikawa, N. Ishizuka, Y. Kuramashi, Y. Nakamura, Y. Namekawa, E. Shintani, Y. Taniguchi, N. Ukita, T. Yamazaki, and T. Yoshi´ e, Phys. Rev. D,100(9), 094502 (2019), arXiv:1907.10846

    2019 arXiv

  125. [133]

    Parisi, Phys

    G. Parisi, Phys. Rept., 103, 203–211 (1984)

    1984

  126. [134]

    Peter Lepage, The Analysis of Algorithms for Lattice Field Theory, In Theoretical Advanced Study Institute in Elementary Particle Physics (6 1989)

    G. Peter Lepage, The Analysis of Algorithms for Lattice Field Theory, In Theoretical Advanced Study Institute in Elementary Particle Physics (6 1989)

    1989

  127. [135]

    Jacob Finkenrath, PoS, LA TTICE2022, 227 (2023), arXiv:2402.11704

    2023 arXiv

  128. [136]

    Thomas Blum, Taku Izubuchi, and Eigo Shintani, Phys. Rev. D, 88(9), 094503 (2013), arXiv:1208.4349

    2013 arXiv

  129. [137]

    Eigo Shintani, Rudy Arthur, Thomas Blum, Taku Izubuchi, Chulwoo Jung, and Christoph Lehner, Phys. Rev. D, 91(11), 114511 (2015), arXiv:1402.0244

    2015 arXiv

  130. [138]

    Rae, Eigo Shintani, and Hartmut Wittig, Nucl

    Georg von Hippel, Thomas D. Rae, Eigo Shintani, and Hartmut Wittig, Nucl. Phys. B, 914, 138–159 (2017), arXiv:1605.00564

    2017 arXiv

  131. [139]

    Bali, Sara Collins, and Andreas Schafer, Comput

    Gunnar S. Bali, Sara Collins, and Andreas Schafer, Comput. Phys. Commun., 181, 1570–1583 (2010), arXiv:0910.3970

    2010 arXiv

  132. [140]

    Junpei Kakazu, Ken-ichi Ishikawa, Naruhito Ishizuka, Yoshinobu Kuramashi, Yoshifumi Nakamura, Yusuke Namekawa, Yusuke Taniguchi, Naoya Ukita, Takeshi Yamazaki, and Tomoteru Yoshi´ e, Phys. Rev. D,101(9), 094504 (2020), arXiv:1912.13127

    2020 arXiv

  133. [141]

    Martin Luscher, Comput. Phys. Commun., 156, 209–220 (2004), hep-lat/0310048

    2004 arXiv

  134. [142]

    Martin Luscher, JHEP, 07, 081 (2007), arXiv:0706.2298

    2007 arXiv

  135. [143]

    Martinelli and Christopher T

    G. Martinelli and Christopher T. Sachrajda, Nucl. Phys. B, 316, 355–372 (1989)

    1989

  136. [144]

    Shoichi Sasaki, Kostas Orginos, Shigemi Ohta, and Tom Blum, Phys. Rev. D, 68, 054509 (2003), hep-lat/0306007

    2003 arXiv

  137. [145]

    R. L. Workman et al., PTEP, 2022, 083C01 (2022)

    2022

  138. [146]

    Fearing, Rev

    Tim Gorringe and Harold W. Fearing, Rev. Mod. Phys., 76, 31–91 (2004), nucl-th/0206039

    2004 arXiv

  139. [147]

    Seonho Choi et al., Phys. Rev. Lett., 71, 3927–3930 (1993)

    1993

  140. [148]

    Yong-Chull Jang, Rajan Gupta, Boram Yoon, and Tanmoy Bhattacharya, Phys. Rev. Lett., 124(7), 072002 (2020), arXiv:1905.06470

    2020 arXiv

  141. [149]

    Lorenzo Barca, Gunnar Bali, and Sara Collins, Phys. Rev. D, 107(5), L051505 (2023), arXiv:2211.12278

    2023 arXiv

  142. [150]

    Constantia Alexandrou, Giannis Koutsou, Yan Li, Marcus Petschlies, and Ferenc Pittler, Phys. Rev. D, 110(9), 094514 (2024), arXiv:2408.03893

    2024 arXiv

  143. [151]

    V. A. Andreev et al., Phys. Rev. Lett., 99, 032002 (2007), arXiv:0704.2072

    2007 arXiv

  144. [152]

    V. A. Andreev et al., Phys. Rev. Lett., 110(1), 012504 (2013), arXiv:1210.6545

    2013 arXiv

  145. [153]

    J. J. Kelly, Phys. Rev. C, 70, 068202 (2004)

    2004

  146. [154]

    Yong-Chull Jang, Rajan Gupta, Tanmoy Bhattacharya, Boram Yoon, and Huey-Wen Lin, Phys. Rev. D, 109(1), 014503 (2024), arXiv:2305.11330

    2024 arXiv

  147. [155]

    Takeshi Yamazaki, Yasumichi Aoki, Tom Blum, Huey-Wen Lin, Shigemi Ohta, Shoichi Sasaki, Robert Tweedie, and James Zanotti, Phys. Rev. D, 79, 114505 (2009), arXiv:0904.2039. 63

    2009 arXiv

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