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REVIEW 3 major objections 5 minor 78 references

This paper shows that a clover-on-HISQ mixed action yields light and strange quark masses, pion and kaon decay constants, and Omega baryon masses consistent with unitary 2+1 QCD after continuum extrapolation—and that the mixed action reduce

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2026-08-02 18:53 UTC pith:Y6I65VB4

load-bearing objection Clover-on-HISQ 2+1+1 and unitary clover 2+1 give consistent light-hadron results; the mixed-action 'better convergence' claim is plausible but needs an explicit a^4 stability check. the 3 major comments →

arxiv 2603.04230 v2 pith:Y6I65VB4 submitted 2026-03-04 hep-lat

Impact of Dynamical Charm Quark and Mixed Action Effect on Light Hadron Masses and Decay Constants

Tong-Wei Lin , Zun-Xian Zhang , Mengchu Cai , Hai-Yang Du , Bolun Hu , Xiangyu Jiang , Xiao-Lan Meng , Ji-Hao Wang
show 3 more authors
Peng Sun Yi-Bo Yang Dian-Jun Zhao
This is my paper
classification hep-lat PACS 11.15.Ha12.38.Gc
keywords lattice QCDmixed actionHISQclover fermioncontinuum extrapolationcharm quarklight hadron massesdecay constants
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that including a dynamical charm quark does not change low-energy hadron physics, and that a mixed action—clover valence fermions on HISQ sea ensembles—can actually reduce lattice discretization errors rather than add them. After continuum, chiral, and infinite-volume extrapolations, light and strange quark masses, pion and kaon decay constants, and Omega baryon masses agree between the 2+1+1 mixed-action setup and the unitary 2+1 clover setup. The smaller discretization errors in the mixed action are attributed to a cancellation between the valence action's own lattice artifacts and the additional mixed-action effects. A sympathetic reader would care because the finding suggests a cheaper route to precise continuum-limit results using staggered sea ensembles. The main caveat is that the conclusion depends on the assumed O(a^2) plus O(a alpha_s) scaling of discretization errors.

Core claim

The central discovery is that the clover-on-HISQ mixed action suppresses discretization errors for light hadron observables. When the same tadpole-improved clover valence action is placed on 2+1+1 HISQ ensembles at four lattice spacings, the resulting f_pi, f_K, m_l, m_s, and Omega masses extrapolate to values consistent with those from unitary 2+1 clover ensembles at six lattice spacings. The slopes in the lattice-spacing dependence are noticeably smaller for the mixed action, indicating that the extra discretization effects from the valence-sea mismatch cancel with the O(a^2) error of the valence action. The paper also finds that a dynamical charm quark has no significant effect on low-ene

What carries the argument

The central object is the mixed-action setup: a stout-smeared, tadpole-improved clover valence fermion action evaluated on gauge ensembles generated with HISQ sea fermions (2+1+1 flavors) and the same Symanzik gauge action. The continuum extrapolation is performed with partially quenched chiral perturbation theory plus empirical ansatze that include O(a^2) corrections and, for decay constants, an O(a alpha_s) term. The key mechanism is the cancellation between the valence action's discretization error and the mixed-action discretization effects, which the paper infers from the smaller lattice-spacing dependence of the CL@HI data.

Load-bearing premise

The results assume that discretization errors follow an O(a^2) form (with an extra O(a alpha_s) term for decay constants) and that O(a^4) contributions are negligible; if O(a^4) effects are significant at the coarsest lattice spacing, the apparent cancellation of errors in the mixed action would be an artifact of the fitting ansatz rather than a real improvement.

What would settle it

Compute f_pi or the Omega mass with the same clover-on-HISQ action at a lattice spacing finer than roughly 0.04 fm, where O(a^4) errors would be strongly suppressed, and check whether the extrapolated continuum value still agrees with the unitary 2+1 result and with the a^2-only fit. Alternatively, add an explicit a^4 term to the continuum extrapolation and see whether its coefficient is statistically different from zero; a nonzero coefficient at current lattice spacings would break the cancellation claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If correct, lattice collaborations can use staggered sea ensembles (cheaper to generate) with clover valence quarks and still obtain continuum-limit results competitive with unitary clover simulations.
  • The consistency between 2+1 and 2+1+1 results implies that charm-quark loop effects on light hadron masses and quark masses are within current statistical uncertainties.
  • The suppressed discretization errors in the mixed action could allow continuum extrapolations from fewer lattice spacings or with larger lattice spacings, reducing computational cost.
  • The same cancellation may apply to other observables, such as baryon masses and form factors, which would extend the utility of mixed-action setups.

Where Pith is reading between the lines

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

  • The cancellation could be specific to the combination of stout-smeared clover and HISQ; testing with other valence actions on HISQ seas would show whether the effect is generic.
  • A direct unitary 2+1+1 clover calculation (same clover action for sea and valence) would separate the effect of the charm quark from the mixed-action effect; the present comparisons are between different sea actions.
  • If O(a^4) terms are truly negligible, the continuum values from the mixed action should be independent of the renormalization scheme (MOM vs SMOM); the paper observes better scheme-consistency for the mixed action, but a dedicated analysis at the finest lattice spacing could sharpen this.

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

3 major / 5 minor

Summary. This paper compares light-hadron observables (m_l, m_s, f_π, f_K, m_φ, m_Ω, and some charmonium masses) computed with a stout-smeared, tadpole-improved clover valence action on two different sea sectors: unitary 2+1 clover ensembles at six lattice spacings and mixed-action 2+1+1 HISQ ensembles at four lattice spacings. The analysis uses PQχPT-based fit forms with O(a^2) and O(a α_s) discretization terms, infinite-volume exponential corrections, and quark-mass mistuning terms. The main claims are (i) the continuum, chiral, and infinite-volume extrapolated values are consistent between the two setups and with FLAG/PDG; (ii) the clover-on-HISQ mixed action shows smaller discretization errors than the unitary clover action, which the authors interpret as a cancellation between mixed-action and unitary discretization effects; and (iii) the dynamical charm sea has no visible effect on low-energy hadronic physics at the current precision. The paper also updates several low-energy constants from previous CLQCD work.

Significance. If the cancellation claim is correct, it is a practically useful result: it would mean that clover valence quarks on existing 2+1+1 HISQ ensembles can yield continuum extrapolations with smaller discretization errors than unitary clover ensembles, and it would support the decoupling of the dynamical charm quark in light-hadron physics. The paper is also valuable as a cross-check: it provides independent determinations of quark masses and decay constants consistent with FLAG, with two renormalization schemes and multiple gauge-action controls. The strengths are the breadth of ensembles, the use of three gauge actions to isolate action effects, the comparison with FLAG/PDG, and the explicit reporting of MOM/SMOM differences. The main weakness is that the cancellation claim rests on fitted O(a^2) coefficients in fits that omit the O(a^4) term, which is the leading mixed-action effect according to the paper's own cited literature.

major comments (3)
  1. [§III, Eqs. (6)–(12), Figs. 1 and 3] The central new claim — that the clover-on-HISQ mixed action exhibits 'better convergence' because mixed-action discretization effects cancel the unitary O(a^2) error — is inferred from fitted a^2 discretization coefficients. The fit ansatz contains no O(a^4) term. The Introduction itself states, citing Refs. [2,3], that the leading mixed-action effect scales as O(a^4). With only four HISQ spacings (coarsest a=0.108 fm, m_π≈310 MeV), an unmodeled a^4 term will be absorbed into the fitted a^2 coefficient, so a small fitted a^2 is not by itself evidence of cancellation. The abstract's statement that 'potential O(a^4) contributions remaining negligible within our statistical uncertainties' is an assertion: no a^4-inclusive fit or sensitivity test is reported for m_π, f_π, m_K, f_K, m_φ, or m_Ω. Please add such a test (for example, repeating the fits with a c a^4 term and checking the shifts
  2. [§II, Tables I–II; §IV] The conclusion that 'the inclusion of a dynamical charm quark sea does not alter low-energy hadronic physics' is based on the three 2+1 HISQ ensembles x24P31, y24P31, and z24P31, all at a≈0.11 fm and m_π≈310–320 MeV. Only y24P31 uses the same tadpole-improved Symanzik gauge action as the 2+1+1 main set; x24P31 and z24P31 intentionally vary the gauge action. Thus the comparison cannot separate a dynamical-charm effect from a gauge-action effect except at one lattice spacing and one pion mass. The body of the paper is appropriately cautious ('at a∼0.1 fm'), but the Summary states it as a general result. Please either restrict the conclusion to the tested parameter point or provide control data at finer spacings and lower m_π.
  3. [§III, Table IV] The consistency claim between CL@CL and CL@HI is made through Table IV, but for CL@CL the MOM and SMOM determinations differ by roughly 2σ for m_s (97.2(1.7) vs 92.7(1.0) MeV) and f_K (157.5(1.1) vs 155.1(1.1) MeV), and by similar amounts for m_l. Since the paper quotes these as separate results and does not state which scheme is used in the abstract's consistency statement, the reader cannot tell whether the agreement with CL@HI is scheme-dependent. Please state the scheme used for the headline comparison and fold the MOM–SMOM spread into the systematic uncertainty, or justify why it need not be included.
minor comments (5)
  1. [§IV] Typo: 'HSIQ' should be 'HISQ' in the opening sentence of the Summary.
  2. [Tables II and V] The column header 'mπ, ηs, ηc (In unit of MeV)' is inconsistent: m_ηc values are quoted in GeV (e.g., 2.973(12)). Please correct the units.
  3. [§II, Ref. [6]] The lattice spacings for the HISQ ensembles are taken from Ref. [6], which is unpublished ('in preparation'). This is a reproducibility concern; please provide the determination or cite a published source.
  4. [Fig. 3] The caption does not state which renormalization scheme is used for f_K (the text says RI/MOM). Add the scheme to the caption.
  5. [§III] The statistical error estimation on the 50-configuration HISQ ensembles is not described (binning, autocorrelation, jackknife details). Please state how the uncertainties were obtained and whether autocorrelations were accounted for.

Circularity Check

1 steps flagged

Partial ansatz-level circularity in the 'better convergence' claim: the continuum fits omit the O(a^4) term that the paper itself cites as the leading mixed-action effect, so the small fitted a^2 coefficient used as evidence is partly shaped by the ansatz; the continuum-limit values themselves are externally benchmarked against FLAG/PDG.

specific steps
  1. other [Abstract; Sec. I; Sec. II Eqs. (6),(7),(11),(12); Table IV]
    "Even though the mixed action setup can introduce additional discretization effects, our calculation shows evidences that those effects can cancel with the discretization error in the unitary setup, resulting in better convergence in the continuum extrapolation. ... we find that the discretization errors from this mixed-action setup are significantly reduced, with potential O(a^4) contributions remaining negligible within our statistical uncertainties."

    The evidence for 'cancellation / better convergence' is the smallness of the fitted a^2 coefficients for the CL@HI data (Table IV: d^pi_{a2}=0.63(69) vs -6.94(46) for CL@CL). But Eqs. (6),(7),(11),(12) parameterize discretization errors only by O(a^2) and O(a alpha_s) terms, while Sec. I itself states the leading mixed-action constant scales 'roughly O(a^4)' citing Refs. [2,3]. Any O(a^4) curvature in the four CL@HI lattice spacings is therefore absorbed into the fitted a^2 coefficient, so the small fitted a^2 - the basis of the 'better convergence' conclusion - is in part an artifact of the chosen ansatz rather than an independent measurement. The assertion that O(a^4) contributions are negligible is never tested by a fit containing an a^4 term. The raw CL@HI a-dependence (Figs. 1,3) and

full rationale

The paper's derivation chain is mostly self-contained: new correlation functions on two independent ensemble sets (2+1 clover and 2+1+1 HISQ seas) are fit with standard PQchiPT-plus-Symanzik ansatze (Eqs. (6)-(13); the PQchiPT form is externally grounded in Sharpe's partially quenched theory, Ref. [11], while the a^2/a-alpha_s treatment follows the collaboration's own Refs. [4,5]), and the resulting continuum-limit values are checked against FLAG/PDG and the earlier Ref. [4]. I found no by-construction identity between any prediction and an input: the quark masses, decay constants, and Omega masses are not defined in terms of the fitted coefficients, and the consistency between CL@CL and CL@HI continuvvum limits is a comparison of independent fits, not a forced result. The headline concern flagged as a step is an ansatz-level circularity at the interpretive level: the central new claim ('mixed-action effects cancel the unitary discretization error, giving better convergence') is read off fitted a^2 coefficients, yet the fit forms omit the O(a^4) term that the paper's own introduction (citing Refs. [2,3]) identifies as the leading mixed-action effect; hence the conclusion is partially shaped by the ansatz, and the abstract's 'O(a^4) contributions remaining negligible' is asserted rather than demonstrated by an a^4 refit. This is a model-robustness and correctness risk more than a strict logical reduction, so the score is moderate. The paper does carry a notable self-citation burden (unpublished 'Bottom physics, in preparation' [6] supplies all clover-ensemble lattice spacings; the HISQ ensembles and their parameters come from the companion preprint [3]); however, per the review rules these citations are externally falsifiable inputs rather than derived claims, so they support the score marginally without by themselves constituting circularity. The honest verdict is: no full circularity, but one partial, ansatz-dependent reading of the 'cancellation' claim that merits an explicit a^4-term stability test.

Axiom & Free-Parameter Ledger

18 free parameters · 6 axioms · 0 invented entities

The analysis introduces no new physical degrees of freedom. The free parameters are the standard fit parameters of lattice QCD chiral extrapolation and discretization-correction ansatze; they are numerous (~25) and are all fitted to the lattice correlation functions described in §II. The most load-bearing fitted coefficients are the O(a^2) discretization terms d^π_a2 and d^K_a2, which underpin the 'better convergence' claim. The axioms are the standard domain assumptions of lattice QCD at this precision; the least secure are the O(a^4) negligibility and the in-preparation self-cited lattice spacing.

free parameters (18)
  • Σ^{1/3} (chiral condensate in 2-flavor chiral limit) = 269.0(2.9) MeV (CL@CL MOM, this work); 275.5(4.4) MeV (CL@HI MOM)
    Fitted via the PQχPT ansatz (Eq. 6); defines the chiral expansion parameter y_v.
  • F (pion decay constant in chiral limit) = 85.8(0.9) MeV (CL@CL MOM); 88.1(2.2) MeV (CL@HI MOM)
    Fitted from Eq. (7); sets the χPT scale Λχ = 4πF.
  • ℓ3 = 2.57(35) (CL@CL MOM); 3.56(97) (CL@HI MOM)
    NLO low-energy constant combination from unitary pion fits (Eq. 8).
  • ℓ4 = 4.25(05) (CL@CL MOM); 4.02(13) (CL@HI MOM)
    NLO low-energy constant combination from unitary pion fits (Eq. 9).
  • c^π_s (strange mistuning coefficient for m_π^2) = 3.4(2.4)×10^-2 GeV^2 (CL@CL MOM, this work; see Table IV)
    Parameterizes m_η_s unphysical-strange-mass correction in Eq. (6).
  • d^π_s (strange mistuning coefficient for f_π) = 0.217(30) GeV^2 (CL@CL MOM, this work; see Table IV)
    Parameterizes m_η_s correction in Eq. (7).
  • b^v_s, b^s_s, b^v_l, b^s_l (m_K^2 quark-mass slope coefficients) = e.g., b^v_s = 2.505(35) GeV (CL@CL MOM; see Table IV)
    Linear coefficients for valence/sea strange/light mass dependence in Eq. (11).
  • d^fv_s, d^fs_s, d^fv_l, d^fs_l (f_K quark-mass slope coefficients) = e.g., d^fv_s = 0.1957(48) (CL@CL MOM; see Table IV)
    Linear coefficients for valence/sea mass dependence in Eq. (12).
  • c^K_l (Kaon light-mass curvature coefficient) = 1.1(0.5) GeV^-1 (CL@CL MOM; see Table IV)
    Captures higher-order light-quark mass dependence in Eq. (11).
  • c^π_a2 (discretization coefficient for m_π^2) = -1.4(0.7) fm^-2 (CL@CL MOM, this work); 0.03(1.04) fm^-2 (CL@HI MOM)
    O(a^2) term in Eq. (6); fitted to lattice data.
  • d^π_a2 (discretization coefficient for f_π) = -6.94(46) fm^-2 (CL@CL MOM, this work); value for CL@HI differs between schemes (Table IV, e.g., -2.24(60) or 0.63(69))
    O(a^2) term in Eq. (7); the 'better convergence' claim hinges on this coefficient being much smaller for CL@HI.
  • d^π_aαs (O(a α_s) coefficient for f_π) = 0.82(28) fm^-1 (CL@CL MOM); -0.130(93) fm^-1 (CL@HI MOM)
    Residual a α_s term in Eq. (7); added in this work to improve continuum extrapolation.
  • c^K_a2 (discretization coefficient for m_K^2) = -1.2(0.6) fm^-2 (CL@CL MOM); -0.4(0.9) fm^-2 (CL@HI MOM)
    O(a^2) term in Eq. (11).
  • d^K_a2 (discretization coefficient for f_K) = -7.6(0.9) fm^-2 (CL@CL MOM); ~ -3.14(52) fm^-2 (CL@HI, Table IV)
    O(a^2) term in Eq. (12); central to the f_K continuum comparison in Fig. 3.
  • d^K_aαs (O(a α_s) coefficient for f_K) = 0.99(78) fm^-1 (CL@CL MOM); -0.12(17) fm^-1 (CL@HI MOM)
    Residual a α_s term in Eq. (12).
  • c^π_L, d^π_L (finite-volume coefficients for m_π^2 and f_π) = c^π_L = 0.48(18), d^π_L = -0.60(12) (CL@CL MOM; see Table IV)
    Exponential finite-volume corrections in Eqs. (6)–(7).
  • c^K_L, d^K_L (finite-volume coefficients for m_K^2 and f_K) = c^K_L = 0.21(07), d^K_L = -0.301(50) (CL@CL MOM; see Table IV)
    Exponential finite-volume corrections in Eqs. (11)–(12).
  • c^H_i, c^H_a2, c^H_L (φ/Ω mass fit parameters) = Not listed explicitly in Table IV; fitted via Eq. (13)
    Empirical coefficients for strange-hadron masses as functions of sea/valence quark masses, a^2, and volume.
axioms (6)
  • domain assumption Partially quenched chiral perturbation theory at NLO (Eqs. 6–9) is valid for pion masses up to ~310 MeV and for the partial quenching used here.
    The fits assume the PQχPT logarithms and LEC expansions capture the quark-mass dependence over the simulated range; this is standard but an assumption, especially at the higher masses.
  • domain assumption Lattice discretization errors are dominated by O(a^2) (and O(a α_s) for f_π/f_K) over the range a ∈ [0.038, 0.112] fm, with O(a^4) effects negligible within the quoted statistical uncertainties.
    Explicit in the abstract and §III ('potential O(a^4) contributions remaining negligible'); the central 'better convergence' claim depends on this.
  • domain assumption The mixed-action low-energy constant from Refs. [2,3] scales as O(a^4) for the clover-on-HISQ action, so mixed-action discretization effects are no larger than O(a^4).
    The paper uses this as background to argue that mixed action effects are benign; the current data are not precise enough to test this independently at all spacings.
  • domain assumption The renormalization constants Z_A/Z_P, Z_A/Z_V from RI/MOM and SMOM, followed by perturbative matching to MS(2 GeV), are correct, with residual scheme dependence captured by the MOM vs SMOM difference.
    The paper reports ~2σ scheme differences for m_l and m_s, indicating this assumption is not fully satisfied; it is load-bearing for the absolute quark masses.
  • domain assumption The lattice spacing values from Ref. [6] (CLQCD, 'Bottom physics, in preparation') are correct.
    All continuum extrapolations rely on a; the reference is unpublished and self-cited, so this is an untestable input for an independent reader.
  • domain assumption The physical inputs m_ηs_phys = 689.89(49) MeV and QED-corrected m_Ds = 1966.7(1.5) MeV are correct and the valence strange/charm masses are tuned accordingly.
    Used to set the strange and charm valence quark masses; mistuning is only partially explored (ensemble c24P31s).

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read the original abstract

We investigate the impact of including a dynamical charm quark on the properties of light hadrons. Our study compares the calculations performed on 2+1+1 flavor (HISQ fermion) ensembles at four lattice spacings to those on 2+1 flavor (clover fermion) ensembles at six lattice spacings, with both sets of ensembles employing the identical Symanzik gauge action. For the light, strange and charm flavor observables, we employ the same tadpole-improved clover fermion action. From numerical results for light and strange quark masses, pion and kaon decay constants, and $\Omega$ and $\Omega_{ccc}$ baryon masses, we find that the values obtained after continuum, chiral, and infinite-volume extrapolations are consistent within uncertainties. Even though the mixed action setup can introduce additional discretization effects, our calculation shows evidences that those effects can cancel with the discretization error in the unitary setup, resulting in better convergence in the continuum extrapolation.

Figures

Figures reproduced from arXiv: 2603.04230 by Bolun Hu, Dian-Jun Zhao, Hai-Yang Du, Ji-Hao Wang, Mengchu Cai, Peng Sun, Tong-Wei Lin, Xiangyu Jiang, Xiao-Lan Meng, Yi-Bo Yang, Zun-Xian Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Lattice spacing dependence of the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Lattice spacing dependence of the charmonium [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Lattice spacing dependence of the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

78 extracted references · 73 linked inside Pith

  1. [1]

    Aokiet al.(Flavour Lattice Averaging Group (FLAG)), FLAG review 2024, Phys

    Y. Aokiet al.(Flavour Lattice Averaging Group (FLAG)), FLAG review 2024, Phys. Rev. D113, 014508 (2026), arXiv:2411.04268 [hep-lat]

    Pith/arXiv arXiv 2024

  2. [2]

    D.-J. Zhao, G. Wang, F. He, L. Jin, P. Sun, Y.-B. Yang, and K. Zhang (χQCD), Distance between various dis- cretized fermion actions, Phys. Rev. D107, L091501 (2023), arXiv:2207.14132 [hep-lat]

    Pith/arXiv arXiv 2023

  3. [3]

    Zhang, M

    Z.-X. Zhang, M. Cai, B. Hu, X. Jiang, Y.-B. Yang, and D.-J. Zhao, Comparison of the mixed-fermion-action Ef- fects using different fermion and gauge actions with 2+1 and 2+1+1 flavors, (2025), arXiv:2512.19265 [hep-lat]

    arXiv 2025

  4. [4]

    Huet al.(CLQCD), Quark masses and low-energy constants in the continuum from the tadpole-improved clover ensembles, Phys

    Z.-C. Huet al.(CLQCD), Quark masses and low-energy constants in the continuum from the tadpole-improved clover ensembles, Phys. Rev. D109, 054507 (2024), arXiv:2310.00814 [hep-lat]

    Pith/arXiv arXiv 2024

  5. [5]

    Duet al.(CLQCD), Charmed meson masses and decay constants in the continuum limit from the tadpole improved clover ensembles, Phys

    H.-Y. Duet al.(CLQCD), Charmed meson masses and decay constants in the continuum limit from the tadpole improved clover ensembles, Phys. Rev. D111, 054504 (2025), arXiv:2408.03548 [hep-lat]

    Pith/arXiv arXiv 2025

  6. [6]

    M. C. Caiet al.(CLQCD), Bottom physics, in prepara- tion

  7. [7]

    Ishikawaet al.(JLQCD), Light quark masses from un- quenched lattice QCD, Phys

    T. Ishikawaet al.(JLQCD), Light quark masses from un- quenched lattice QCD, Phys. Rev. D78, 011502 (2008), arXiv:0704.1937 [hep-lat]

    Pith/arXiv arXiv 2008

  8. [8]

    Martinelli, C

    G. Martinelli, C. Pittori, C. T. Sachrajda, M. Testa, and A. Vladikas, A general method for non-perturbative renormalization of lattice operators, Nucl. Phys. B445, 81 (1995), arXiv:hep-lat/9411010

    Pith/arXiv arXiv 1995

  9. [9]

    Z. Liu, Y. Chen, S.-J. Dong, M. Glatzmaier, M. Gong, A. Li, K.-F. Liu, Y.-B. Yang, and J.-B. Zhang (chiQCD), Nonperturbative renormalization of overlap quark bilin- ears on 2+1-flavor domain wall fermion configurations, Phys. Rev. D90, 034505 (2014), arXiv:1312.7628 [hep- lat]

    Pith/arXiv arXiv 2014

  10. [10]

    J. A. Gracey, Five loop anomalous dimension of non- singlet quark currents in the RI′ scheme, Eur. Phys. J. C 83, 181 (2023), arXiv:2210.12420 [hep-ph]

    Pith/arXiv arXiv 2023

  11. [11]

    S. R. Sharpe, Enhanced chiral logarithms in partially quenched QCD, Phys. Rev. D56, 7052 (1997), [Erratum: Phys.Rev.D 62, 099901 (2000)], arXiv:hep-lat/9707018

    Pith/arXiv arXiv 1997

  12. [12]

    M. G. Alford, W. Dimm, G. P. Lepage, G. Hockney, and P. B. Mackenzie, Lattice QCD on small computers, Phys. Lett. B361, 87 (1995), arXiv:hep-lat/9507010

    Pith/arXiv arXiv 1995

  13. [13]

    Alexandrouet al.(Extended Twisted Mass), Quark masses using twisted-mass fermion gauge ensembles, Phys

    C. Alexandrouet al.(Extended Twisted Mass), Quark masses using twisted-mass fermion gauge ensembles, Phys. Rev. D104, 074515 (2021), arXiv:2104.13408 [hep- lat]

    Pith/arXiv arXiv 2021

  14. [14]

    Borsanyiet al., Leading hadronic contribution to the muon magnetic moment from lattice QCD, Nature593, 51 (2021), arXiv:2002.12347 [hep-lat]

    S. Borsanyiet al., Leading hadronic contribution to the muon magnetic moment from lattice QCD, Nature593, 51 (2021), arXiv:2002.12347 [hep-lat]

    Pith/arXiv arXiv 2021

  15. [15]

    B. Hu, H. Du, X. Jiang, K.-F. Liu, P. Sun, and Y.-B. Yang, Unveiling the Strong Interaction origin of Baryon Masses with Lattice QCD, (2024), arXiv:2411.18402 [hep-lat]

    Pith/arXiv arXiv 2024

  16. [16]

    Aokiet al.(Flavour Lattice Averaging Group (FLAG)), FLAG Review 2021, Eur

    Y. Aokiet al.(Flavour Lattice Averaging Group (FLAG)), FLAG Review 2021, Eur. Phys. J. C82, 869 (2022), arXiv:2111.09849 [hep-lat]

    Pith/arXiv arXiv 2021

  17. [17]

    Arthuret al.(RBC, UKQCD), Domain Wall QCD with Near-Physical Pions, Phys

    R. Arthuret al.(RBC, UKQCD), Domain Wall QCD with Near-Physical Pions, Phys. Rev. D87, 094514 (2013), arXiv:1208.4412 [hep-lat]

    Pith/arXiv arXiv 2013

  18. [18]

    Bruno, I

    M. Bruno, I. Campos, P. Fritzsch, J. Koponen, C. Pena, D. Preti, A. Ramos, and A. Vladikas (ALPHA), Light quark masses inN f = 2 + 1 lattice QCD with Wilson fermions, Eur. Phys. J. C80, 169 (2020), arXiv:1911.08025 [hep-lat]

    Pith/arXiv arXiv 2020

  19. [19]

    Blumet al.(RBC, UKQCD), Domain wall QCD with physical quark masses, Phys

    T. Blumet al.(RBC, UKQCD), Domain wall QCD with physical quark masses, Phys. Rev. D93, 074505 (2016), arXiv:1411.7017 [hep-lat]

    Pith/arXiv arXiv 2016

  20. [20]

    Laiho and R

    J. Laiho and R. S. Van de Water, Pseudoscalar de- cay constants, light-quark masses, andB K from mixed- action lattice QCD, PoSLA TTICE2011, 293 (2011), arXiv:1112.4861 [hep-lat]. 8

    Pith/arXiv arXiv 2011

  21. [21]

    S. Durr, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K. K. Szabo, and G. Vulvert (BMW), Lattice QCD at the physical point: light quark masses, Phys. Lett. B701, 265 (2011), arXiv:1011.2403 [hep-lat]

    Pith/arXiv arXiv 2011

  22. [22]

    S. Durr, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K. K. Szabo, and G. Vulvert (BMW), Lattice QCD at the physical point: Simulation and analysis details, JHEP08, 148, arXiv:1011.2711 [hep-lat]

    Pith/arXiv arXiv

  23. [23]

    Bazavovet al., Staggered chiral perturbation theory in the two-flavor case and SU(2) analysis of the MILC data, PoSLA TTICE2010, 083 (2010), arXiv:1011.1792 [hep-lat]

    A. Bazavovet al., Staggered chiral perturbation theory in the two-flavor case and SU(2) analysis of the MILC data, PoSLA TTICE2010, 083 (2010), arXiv:1011.1792 [hep-lat]

    Pith/arXiv arXiv 2010

  24. [24]

    McNeile, C

    C. McNeile, C. T. H. Davies, E. Follana, K. Hornbostel, and G. P. Lepage, High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lat- tice and Continuum QCD, Phys. Rev. D82, 034512 (2010), arXiv:1004.4285 [hep-lat]

    Pith/arXiv arXiv 2010

  25. [25]

    Aokiet al.(RBC, UKQCD), Continuum Limit Physics from 2+1 Flavor Domain Wall QCD, Phys

    Y. Aokiet al.(RBC, UKQCD), Continuum Limit Physics from 2+1 Flavor Domain Wall QCD, Phys. Rev. D83, 074508 (2011), arXiv:1011.0892 [hep-lat]

    Pith/arXiv arXiv 2011

  26. [26]

    C. T. H. Davies, C. McNeile, K. Y. Wong, E. Follana, R. Horgan, K. Hornbostel, G. P. Lepage, J. Shigemitsu, and H. Trottier, Precise Charm to Strange Mass Ratio and Light Quark Masses from Full Lattice QCD, Phys. Rev. Lett.104, 132003 (2010), arXiv:0910.3102 [hep-ph]

    Pith/arXiv arXiv 2010

  27. [27]

    Bazavovet al.(MILC), MILC results for light pseu- doscalars, PoSCD09, 007 (2009), arXiv:0910.2966 [hep- ph]

    A. Bazavovet al.(MILC), MILC results for light pseu- doscalars, PoSCD09, 007 (2009), arXiv:0910.2966 [hep- ph]

    Pith/arXiv arXiv 2009

  28. [28]

    Bazavovet al.(MILC), Nonperturbative QCD Simu- lations with 2+1 Flavors of Improved Staggered Quarks, Rev

    A. Bazavovet al.(MILC), Nonperturbative QCD Simu- lations with 2+1 Flavors of Improved Staggered Quarks, Rev. Mod. Phys.82, 1349 (2010), arXiv:0903.3598 [hep- lat]

    Pith/arXiv arXiv 2010

  29. [29]

    Mason, H

    Q. Mason, H. D. Trottier, R. Horgan, C. T. H. Davies, and G. P. Lepage (HPQCD), High-precision determina- tion of the light-quark masses from realistic lattice QCD, Phys. Rev. D73, 114501 (2006), arXiv:hep-ph/0511160

    Pith/arXiv arXiv 2006

  30. [30]

    Aubin, C

    C. Aubin, C. Bernard, C. E. DeTar, J. Osborn, S. Got- tlieb, E. B. Gregory, D. Toussaint, U. M. Heller, J. E. Hetrick, and R. Sugar (MILC), Light pseudoscalar de- cay constants, quark masses, and low energy constants from three-flavor lattice QCD, Phys. Rev. D70, 114501 (2004), arXiv:hep-lat/0407028

    Pith/arXiv arXiv 2004

  31. [31]

    Aubinet al.(HPQCD, MILC, UKQCD), First deter- mination of the strange and light quark masses from full lattice QCD, Phys

    C. Aubinet al.(HPQCD, MILC, UKQCD), First deter- mination of the strange and light quark masses from full lattice QCD, Phys. Rev. D70, 031504 (2004), arXiv:hep- lat/0405022

    arXiv 2004

  32. [32]

    Bruno, I

    M. Bruno, I. Campos, J. Koponen, C. Pena, D. Preti, A. Ramos, and A. Vladikas (ALPHA), Light and strange quark masses fromN f = 2 + 1 simulations with Wilson fermions, PoSLA TTICE2018, 220 (2019), arXiv:1903.04094 [hep-lat]

    Pith/arXiv arXiv 2019

  33. [33]

    Carrascoet al.(European Twisted Mass), Up, down, strange and charm quark masses with N f = 2+1+1 twisted mass lattice QCD, Nucl

    N. Carrascoet al.(European Twisted Mass), Up, down, strange and charm quark masses with N f = 2+1+1 twisted mass lattice QCD, Nucl. Phys. B887, 19 (2014), arXiv:1403.4504 [hep-lat]

    Pith/arXiv arXiv 2014

  34. [34]

    Bazavovet al.(Fermilab Lattice, MILC, TUMQCD), Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD, Phys

    A. Bazavovet al.(Fermilab Lattice, MILC, TUMQCD), Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD, Phys. Rev. D98, 054517 (2018), arXiv:1802.04248 [hep-lat]

    Pith/arXiv arXiv 2018

  35. [35]

    A. T. Lytle, C. T. H. Davies, D. Hatton, G. P. Lep- age, and C. Sturm (HPQCD), Determination of quark masses fromn f =4lattice QCD and the RI-SMOM in- termediate scheme, Phys. Rev. D98, 014513 (2018), arXiv:1805.06225 [hep-lat]

    Pith/arXiv arXiv 2018

  36. [36]

    Chakraborty, C

    B. Chakraborty, C. T. H. Davies, B. Galloway, P. Knecht, J. Koponen, G. C. Donald, R. J. Dowdall, G. P. Lepage, and C. McNeile, High-precision quark masses and QCD coupling fromn f = 4 lattice QCD, Phys. Rev. D91, 054508 (2015), arXiv:1408.4169 [hep-lat]

    Pith/arXiv arXiv 2015

  37. [37]

    Bazavovet al.,B- andD-meson leptonic decay con- stants from four-flavor lattice QCD, Phys

    A. Bazavovet al.,B- andD-meson leptonic decay con- stants from four-flavor lattice QCD, Phys. Rev. D98, 074512 (2018), arXiv:1712.09262 [hep-lat]

    Pith/arXiv arXiv 2018

  38. [38]

    Bazavovet al.(Fermilab Lattice, MILC), Charmed and Light Pseudoscalar Meson Decay Constants from Four-Flavor Lattice QCD with Physical Light Quarks, Phys

    A. Bazavovet al.(Fermilab Lattice, MILC), Charmed and Light Pseudoscalar Meson Decay Constants from Four-Flavor Lattice QCD with Physical Light Quarks, Phys. Rev. D90, 074509 (2014), arXiv:1407.3772 [hep- lat]

    Pith/arXiv arXiv 2014

  39. [39]

    Alexandrouet al.(Extended Twisted Mass), Ratio of kaon and pion leptonic decay constants with Nf=2+1+1 Wilson-clover twisted-mass fermions, Phys

    C. Alexandrouet al.(Extended Twisted Mass), Ratio of kaon and pion leptonic decay constants with Nf=2+1+1 Wilson-clover twisted-mass fermions, Phys. Rev. D104, 074520 (2021), arXiv:2104.06747 [hep-lat]

    Pith/arXiv arXiv 2021

  40. [40]

    Milleret al.,F K /Fπ from M¨ obius Domain-Wall fermions solved on gradient-flowed HISQ ensembles, Phys

    N. Milleret al.,F K /Fπ from M¨ obius Domain-Wall fermions solved on gradient-flowed HISQ ensembles, Phys. Rev. D102, 034507 (2020), arXiv:2005.04795 [hep- lat]

    Pith/arXiv arXiv 2020

  41. [41]

    Carrascoet al., Leptonic decay constantsf K , fD,and fDs withN f = 2 + 1 + 1 twisted-mass lattice QCD, Phys

    N. Carrascoet al., Leptonic decay constantsf K , fD,and fDs withN f = 2 + 1 + 1 twisted-mass lattice QCD, Phys. Rev. D91, 054507 (2015), arXiv:1411.7908 [hep-lat]

    Pith/arXiv arXiv 2015

  42. [42]

    Dimopoulos, R

    P. Dimopoulos, R. Frezzotti, P. Lami, V. Lubicz, E. Picca, L. Riggio, G. C. Rossi, F. Sanfilippo, S. Simula, and C. Tarantino, Pseudoscalar decay constantsf K /fπ, fD andf Ds withN f = 2 + 1 + 1 ETMC configurations, PoSLA TTICE2013, 314 (2014), arXiv:1311.3080 [hep- lat]

    Pith/arXiv arXiv 2014

  43. [43]

    R. J. Dowdall, C. T. H. Davies, G. P. Lepage, and C. Mc- Neile, Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks, Phys. Rev. D 88, 074504 (2013), arXiv:1303.1670 [hep-lat]

    Pith/arXiv arXiv 2013

  44. [44]

    Bazavovet al.(MILC), Leptonic Decay-Constant Ratiof K+ /fπ+ from Lattice QCD with Physical Light Quarks, Phys

    A. Bazavovet al.(MILC), Leptonic Decay-Constant Ratiof K+ /fπ+ from Lattice QCD with Physical Light Quarks, Phys. Rev. Lett.110, 172003 (2013), arXiv:1301.5855 [hep-ph]

    Pith/arXiv arXiv 2013

  45. [45]

    Bazavovet al.(MILC), Properties of light pseu- doscalars from lattice QCD with HISQ ensembles, PoS LA TTICE2011, 107 (2011), arXiv:1111.4314 [hep-lat]

    A. Bazavovet al.(MILC), Properties of light pseu- doscalars from lattice QCD with HISQ ensembles, PoS LA TTICE2011, 107 (2011), arXiv:1111.4314 [hep-lat]

    Pith/arXiv arXiv 2011

  46. [46]

    Farchioni, G

    F. Farchioni, G. Herdoiza, K. Jansen, A. Nube, M. Petschlies, and C. Urbach, Pseudoscalar decay con- stants fromN f =2+1+1 twisted mass lattice QCD, PoS LA TTICE2010, 128 (2010), arXiv:1012.0200 [hep-lat]

    Pith/arXiv arXiv 2010

  47. [47]

    V. G. Bornyakov, R. Horsley, Y. Nakamura, H. Perlt, D. Pleiter, P. E. L. Rakow, G. Schierholz, A. Schiller, H. St¨ uben, and J. M. Zanotti (QCDSF–UKQCD), Flavour breaking effects in the pseudoscalar meson decay constants, Phys. Lett. B767, 366 (2017), arXiv:1612.04798 [hep-lat]

    Pith/arXiv arXiv 2017

  48. [48]

    D¨ urret al., Leptonic decay-constant ratiof K /fπ from lattice QCD using 2+1 clover-improved fermion flavors with 2-HEX smearing, Phys

    S. D¨ urret al., Leptonic decay-constant ratiof K /fπ from lattice QCD using 2+1 clover-improved fermion flavors with 2-HEX smearing, Phys. Rev. D95, 054513 (2017), arXiv:1601.05998 [hep-lat]

    Pith/arXiv arXiv 2017

  49. [49]

    E. E. Scholz and S. Durr, Leptonic decay-constant ra- tiof K /fπ from clover-improvedN f = 2 + 1 QCD, PoS LA TTICE2016, 283 (2016), arXiv:1610.00932 [hep-lat]

    Pith/arXiv arXiv 2016

  50. [50]

    Bazavovet al.(MILC), Results for light pseu- doscalar mesons, PoSLA TTICE2010, 074 (2010), arXiv:1012.0868 [hep-lat]

    A. Bazavovet al.(MILC), Results for light pseu- doscalar mesons, PoSLA TTICE2010, 074 (2010), arXiv:1012.0868 [hep-lat]. 9

    Pith/arXiv arXiv 2010

  51. [51]

    S. Durr, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, A. Ramos, and K. K. Szabo (BMW), The ratio FK/Fpi in QCD, Phys. Rev. D 81, 054507 (2010), arXiv:1001.4692 [hep-lat]

    Pith/arXiv arXiv 2010

  52. [52]

    Aubin, J

    C. Aubin, J. Laiho, and R. S. Van de Water, Light Pseu- doscalar Meson Masses and Decay Constants from Mixed Action Lattice QCD, PoSLA TTICE2008, 105 (2008), arXiv:0810.4328 [hep-lat]

    Pith/arXiv arXiv 2008

  53. [53]

    Follana, C

    E. Follana, C. T. H. Davies, G. P. Lepage, and J. Shigemitsu (HPQCD, UKQCD), High Precision de- termination of the pi, K, D and D(s) decay constants from lattice QCD, Phys. Rev. Lett.100, 062002 (2008), arXiv:0706.1726 [hep-lat]

    Pith/arXiv arXiv 2008

  54. [54]

    B. Fahy, G. Cossu, S. Hashimoto, T. Kaneko, J. Noaki, and M. Tomii (JLQCD), Decay constants and spectroscopy of mesons in lattice QCD using domain-wall fermions, PoSLA TTICE2015, 074 (2016), arXiv:1512.08599 [hep-lat]

    Pith/arXiv arXiv 2016

  55. [55]

    Liang, A

    J. Liang, A. Alexandru, Y.-J. Bi, T. Draper, K.-F. Liu, and Y.-B. Yang (χQCD), Detecting the flavor content of the vacuum using the Dirac operator spectrum, Phys. Rev. D110, 094513 (2024), arXiv:2102.05380 [hep-lat]

    Pith/arXiv arXiv 2024

  56. [56]

    Alexandrou, A

    C. Alexandrou, A. Athenodorou, K. Cichy, M. Constanti- nou, D. P. Horkel, K. Jansen, G. Koutsou, and C. Larkin, Topological susceptibility from twisted mass fermions us- ing spectral projectors and the gradient flow, Phys. Rev. D97, 074503 (2018), arXiv:1709.06596 [hep-lat]

    Pith/arXiv arXiv 2018

  57. [57]

    Cichy, E

    K. Cichy, E. Garcia-Ramos, and K. Jansen, Chiral con- densate from the twisted mass Dirac operator spectrum, JHEP10, 175, arXiv:1303.1954 [hep-lat]

    Pith/arXiv arXiv 1954

  58. [58]

    S. Aoki, G. Cossu, H. Fukaya, S. Hashimoto, and T. Kaneko (JLQCD), Topological susceptibility of QCD with dynamical M¨ obius domain-wall fermions, PTEP 2018, 043B07 (2018), arXiv:1705.10906 [hep-lat]

    Pith/arXiv arXiv 2018

  59. [59]

    P. A. Boyleet al., Low energy constants of SU(2) par- tially quenched chiral perturbation theory from Nf =2+1 domain wall QCD, Phys. Rev. D93, 054502 (2016), arXiv:1511.01950 [hep-lat]

    Pith/arXiv arXiv 2016

  60. [60]

    D¨ urret al.(BMW), Lattice QCD at the physical point meets SU(2) chiral perturbation theory, Phys

    S. D¨ urret al.(BMW), Lattice QCD at the physical point meets SU(2) chiral perturbation theory, Phys. Rev. D90, 114504 (2014), arXiv:1310.3626 [hep-lat]

    Pith/arXiv arXiv 2014

  61. [61]

    Borsanyi, S

    S. Borsanyi, S. Durr, Z. Fodor, S. Krieg, A. Schafer, E. E. Scholz, and K. K. Szabo, SU(2) chiral perturbation theory low-energy constants from 2+1 flavor staggered lattice simulations, Phys. Rev. D88, 014513 (2013), arXiv:1205.0788 [hep-lat]

    Pith/arXiv arXiv 2013

  62. [62]

    G. P. Engel, L. Giusti, S. Lottini, and R. Sommer, Spec- tral density of the Dirac operator in two-flavor QCD, Phys. Rev. D91, 054505 (2015), arXiv:1411.6386 [hep- lat]

    Pith/arXiv arXiv 2015

  63. [63]

    B. B. Brandt, A. J¨ uttner, and H. Wittig, The pion vector form factor from lattice QCD and NNLO chiral pertur- bation theory, JHEP11, 034, arXiv:1306.2916 [hep-lat]

    Pith/arXiv arXiv

  64. [64]

    Burger, V

    F. Burger, V. Lubicz, M. M¨ uller-Preussker, S. Simula, and C. Urbach, Quark mass and chiral condensate from the Wilson twisted mass lattice quark propagator, Phys. Rev. D87, 034514 (2013), arXiv:1210.0838 [hep-lat]

    Pith/arXiv arXiv 2013

  65. [65]

    Baronet al.(ETM), Light Meson Physics from Maximally Twisted Mass Lattice QCD, JHEP08, 097, arXiv:0911.5061 [hep-lat]

    R. Baronet al.(ETM), Light Meson Physics from Maximally Twisted Mass Lattice QCD, JHEP08, 097, arXiv:0911.5061 [hep-lat]

    Pith/arXiv arXiv

  66. [66]

    Frezzotti, V

    R. Frezzotti, V. Lubicz, and S. Simula (ETM), Electro- magnetic form factor of the pion from twisted-mass lat- tice QCD at N(f) = 2, Phys. Rev. D79, 074506 (2009), arXiv:0812.4042 [hep-lat]

    Pith/arXiv arXiv 2009

  67. [67]

    Baronet al.(ETM), Light hadrons from Nf=2+1+1 dynamical twisted mass fermions, PoSLA TTICE2010, 123 (2010), arXiv:1101.0518 [hep-lat]

    R. Baronet al.(ETM), Light hadrons from Nf=2+1+1 dynamical twisted mass fermions, PoSLA TTICE2010, 123 (2010), arXiv:1101.0518 [hep-lat]

    Pith/arXiv arXiv 2010

  68. [68]

    S. R. Beane, W. Detmold, P. M. Junnarkar, T. C. Luu, K. Orginos, A. Parreno, M. J. Savage, A. Torok, and A. Walker-Loud, SU(2) Low-Energy Constants from Mixed-Action Lattice QCD, Phys. Rev. D86, 094509 (2012), arXiv:1108.1380 [hep-lat]

    Pith/arXiv arXiv 2012

  69. [69]

    Horsley, Y

    R. Horsley, Y. Nakamura, A. Nobile, P. E. L. Rakow, G. Schierholz, and J. M. Zanotti, Nucleon axial charge and pion decay constant from two-flavor lattice QCD, Phys. Lett. B732, 41 (2014), arXiv:1302.2233 [hep-lat]

    Pith/arXiv arXiv 2014

  70. [70]

    Colangelo and S

    G. Colangelo and S. Durr, The Pion mass in finite volume, Eur. Phys. J. C33, 543 (2004), arXiv:hep- lat/0311023

    arXiv 2004

  71. [71]

    G¨ ulpers, G

    V. G¨ ulpers, G. von Hippel, and H. Wittig, The scalar radius of the pion from Lattice QCD in the continuum limit, Eur. Phys. J. A51, 158 (2015), arXiv:1507.01749 [hep-lat]

    Pith/arXiv arXiv 2015

  72. [72]

    Aokiet al.(JLQCD, TWQCD), Pion form factors from two-flavor lattice QCD with exact chiral symmetry, Phys

    S. Aokiet al.(JLQCD, TWQCD), Pion form factors from two-flavor lattice QCD with exact chiral symmetry, Phys. Rev. D80, 034508 (2009), arXiv:0905.2465 [hep-lat]

    Pith/arXiv arXiv 2009

  73. [73]

    Navaset al.(Particle Data Group), Review of particle physics, Phys

    S. Navaset al.(Particle Data Group), Review of particle physics, Phys. Rev. D110, 030001 (2024)

    2024

  74. [74]

    Jiang, C

    X. Jiang, C. Shi, Y. Chen, M. Gong, and Y.-B. Yang, Use QUDA for lattice QCD calculation with Python, (2024), arXiv:2411.08461 [hep-lat]

    Pith/arXiv arXiv 2024

  75. [75]

    M. A. Clark, R. Babich, K. Barros, R. C. Brower, and C. Rebbi (QUDA), Solving Lattice QCD systems of equa- tions using mixed precision solvers on GPUs, Comput. Phys. Commun.181, 1517 (2010), arXiv:0911.3191 [hep- lat]

    Pith/arXiv arXiv 2010

  76. [76]

    Babich, M

    R. Babich, M. A. Clark, B. Joo, G. Shi, R. C. Brower, and S. Gottlieb (QUDA), Scaling lattice QCD beyond 100 GPUs, inInternational Conference for High Per- formance Computing, Networking, Storage and Analysis (2011) arXiv:1109.2935 [hep-lat]

    Pith/arXiv arXiv 2011

  77. [77]

    M. A. Clark, B. Jo´ o, A. Strelchenko, M. Cheng, A. Gamb- hir, and R. C. Brower (QUDA), Accelerating lattice QCD multigrid on GPUs using fine-grained paralleliza- tion, inInternational Conference for High Performance Computing, Networking, Storage and Analysis(2016) arXiv:1612.07873 [hep-lat]

    Pith/arXiv arXiv 2016

  78. [78]

    Y.-J. Bi, Y. Xiao, W.-Y. Guo, M. Gong, P. Sun, S. Xu, and Y.-B. Yang, Lattice QCD package GWU-code and QUDA with HIP, PoSLA TTICE2019, 286 (2020), arXiv:2001.05706 [hep-lat]. 10 APPENDIX Table V lists the tadpole factorv 0 (derived from smeared links for the clover term) and the tuned dimensionless valence clover masses ˜mv l,s,c. These masses are tuned t...

    Pith/arXiv arXiv 2020