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REVIEW 3 major objections 6 minor 107 references

The determination of potential scales in 2+1 flavor QCD

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Lattice QCD determines the hadronic scales r0 and r1 from the static force at the physical point, with r0 = 0.4729(57)(48) fm, r1 = 0.3127(24)(32) fm, and r0/r1 = 1.532(12).

desk verdict New r0 and r1 values for CLS 2+1 QCD are trustworthy, but the abstract disagrees with the main text on r0 and the finest-spacing gap model needs explicit clarification. read the letter →

arxiv 2412.10215 v2 pith:KFRLLAX3 submitted 2024-12-13 hep-lat

Tom Matty Bo Asmussen , Roman Höllwieser , Francesco Knechtli , Tomasz Korzec This is my paper · ORCID
classification hep-lat
keywords latticeQCDstaticpotentialhadronicscaler0r1Wilsonloopsforcetree-levelimprovementcontinuumextrapolation
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 pin down the hadronic length scales r0 and r1, defined by the strength of the static quark-antiquark force at two reference distances, directly from lattice QCD with dynamical up, down, and strange quarks. These scales are widely used to convert lattice measurements into physical units, so precise values improve the comparability of many lattice results. The analysis extracts the static force from Wilson loops, uses a tree-level improved distance to suppress lattice artifacts, and extrapolates data at five lattice spacings and pion masses from 134 to 420 MeV to the continuum and physical mass limits. It reports r0 = 0.4729(57)(48) fm, r1 = 0.3127(24)(32) fm, and r0/r1 = 1.532(12), and as a byproduct converts the three-flavor QCD Lambda parameter to r0 units, obtaining r0 Lambda_MSbar^(3) = 0.820(28).

What carries the argument

The central object is the static quark-antiquark force F(r) = dV(r)/dr, computed from Wilson loops through a generalized eigenvalue problem, with lattice artifacts removed at tree level by replacing the separation r with an improved distance r_I chosen so that the tree-level continuum relation $r_I^{2}$ F_tree(r_I) = C_F $g0^{2}$/(4 pi) holds exactly. The scales r0 and r1 are defined through $r_i^{2}$ F(r_i) = c_i. The argument is carried by this improved force together with a two-step excited-state analysis: a global model for the energy gap $\Delta$ between the ground and first excited state is fitted on stable ensembles and then used to stabilize effective-mass fits on all ensembles, including the problematic near-physical-mass fine ensemble where the direct fit was unstable. Continuum and chiral limits are obtained by Akaike-weighted averages over four fit forms and several data cuts, with explicit checks of logarithmic scaling violations.

What would settle it

Repeat the analysis on the same ensembles with a purely data-driven determination of the first excited state, for example a full multi-exponential fit with a larger variational basis or a multilevel algorithm for dynamical fermions, and compare the resulting r1 at the physical point with 0.3127(24)(32) fm. A deviation larger than the combined error would show that the assumed gap model biases the ground-state potential.

Watch

Extended reading notes

Core claim

The central claim is that the hadronic scales r0 and r1 can be computed at the physical point of 2+1 flavor QCD with controlled statistical and systematic errors, using the tree-level improved static force F(r) extracted from Wilson loops. The scale r_i is defined by $r_i^{2}$ F(r_i) = c_i with c0 = 1.65 and c1 = 1, so these distances mark where the force takes a reference strength. Combining measurements on ensembles with five lattice spacings down to 0.039 fm and pion masses from 134 to 420 MeV, continuum and chiral extrapolations yield the values quoted above, with agreement across different fit ansatze and data cuts. The paper also shows that the shape parameter of the potential, c(r) = (1/2) $r^{3}$ V''(r), is distance-dependent in the probed range and follows a screened-logarithmic potential curve rather than the constant-shape model, indicating sensitivity to sea-quark effects.

Load-bearing premise

The analysis assumes that the energy gap between the ground state and first excited state of the Wilson-loop correlation functions follows a single four-parameter curve as the quark separation, pion mass, and lattice spacing vary; if that curve is wrong on the ensembles where the direct fit is unstable, the extracted potential, and therefore r0 and r1, would be biased.

Editorial extensions

If this is right

  • The reported r0 and r1 values give an absolute scale in fm for 2+1 flavor ensembles, so other lattice quantities measured on them can be converted from lattice units to physical units with these numbers.
  • Since r0/sqrt(t0) = 3.277(39) and r1/sqrt(t0) = 2.167(16), potential scales and gradient flow scales are now cross-calibrated, allowing direct comparison of scale-setting between the two conventions.
  • The value r0 Lambda_MSbar^(3) = 0.820(28) ties the nonperturbatively computed three-flavor Lambda parameter to a hadronic scale, offering a scale-setting-free comparison point for determinations of the strong coupling.
  • The ratio r0/r1 = 1.532(12) is a purely gluonic observable nearly independent of quark masses, so it can serve as a stringent test for other lattice actions and for effective field theory descriptions of the static potential.

Reading between the lines

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

  • If the quoted values hold, the r0/r1 ratio becomes a sharper cross-check of scale-setting than either scale alone, because the ratio is independent of the overall fm conversion and of sqrt(t0). A direct re-determination of r0/r1 on the same ensembles with a completely independent excited-state treatment would confirm whether the assumed gap model biases the force near r1.
  • The observation that the shape parameter c(r) is distance-dependent rather than constant suggests that phenomenological potential models used for heavy-quarkonium spectra may need a distance-dependent curvature term; this could be tested against charmonium spectra or against future 2+1+1 flavor determinations with a dynamical charm quark.
  • The E300-excluded analysis shifts r1 by about 0.002 fm, within the quoted error. A targeted reanalysis of that ensemble with larger statistics or multilevel algorithms for dynamical fermions would settle whether the outlier is a statistical fluctuation or a sign of a small systematic effect.
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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 / 6 minor

Summary. The paper determines the hadronic scales r0, r1 and their ratio in Nf=2+1 QCD from the static force measured with Wilson loops on 18 CLS ensembles covering five lattice spacings and pion masses from 134 to 420 MeV. The analysis uses a tree-level improved distance, a GEVP with HYP smearing, and a two-step procedure in which an empirical model for the excited-state gap (eq. 4.10) is fitted per lattice spacing and used to stabilize linear fits for problematic ensembles. The scales are extrapolated to the continuum and physical pion mass with four fit ansatze, several data cuts, logarithmic correction tests, and AIC averaging. The final results are r0=0.4729(57)(48) fm, r1=0.3127(24)(32) fm, r0/r1=1.532(12), plus a byproduct r0 Lambda_MSbar^(3)=0.820(28). The paper also studies the shape parameter c(r) and compares it to potential models.

Significance. If the identified gap-model issue for the finest lattice spacing is resolved, the paper provides a competitive, independent determination of r0 and r1 with a transparent error budget. Its strengths are the multiple cross-checks: three interpolation forms for the force, a pencil-of-functions analysis for the difficult E300 ensemble, four continuum/chiral fit ansatze, data cuts, logarithmic correction tests, and AIC weighting. The direct continuum extrapolation of r0/Lhad to obtain r0 Lambda is elegant and avoids a double continuum extrapolation. The results agree with the FLAG averages within errors, and the r0/r1 ratio is a valuable constraint for scale setting.

major comments (3)
  1. [4.3, Eq. (4.10)] The gap model in Eq. (4.10) contains two terms, -delta_hat0/(r sqrt(t0)) and -gamma_hat0 sqrt(t0)/r, which are linearly dependent for any single ensemble because sqrt(t0) is a fixed number in lattice units. With only one stable ensemble at beta=3.85 (J500), the parameters b_hat0, delta_hat0, and gamma_hat0 cannot be identified from the data. The manuscript does not state how Delta was assigned to J501, whose r1 plateau is described as problematic in Section 4.4, and no J501-excluded analysis is provided analogous to the E300 cut. If J501's r1/a in Table 5 was obtained with the constrained linear fit using Delta from this model, the finest-spacing continuum point inherits an unconstrained extrapolation in m_pi; please clarify the fitting procedure at beta=3.85 and add a J501-removed cross-check.
  2. [Abstract vs. Section 6.1] The abstract quotes r0 = 0.4757(64) fm, while Eq. (6.1) quotes r0 = 0.4729(57)(48) fm, and Table 6 indicates that the AIC average gives the latter value. These differ by about 0.003 fm, which is within the combined errors but is still an internal inconsistency in the primary result; the abstract should be updated to the final value or the discrepancy should be explained.
  3. [Table 6 and Section 5] For r1, all the global fits have chi^2/dof around 2.0 (e.g., Fit 1 with no cuts gives 30.4/15), which is poor for a fit with this number of degrees of freedom and indicates that the mass and lattice-spacing ansatz does not fully describe the r1 data. Since r1 is one of the two main results, the authors should either identify the source of the poor chi^2 and show that the fit is stable without the offending ensemble, or add a fit-systematic uncertainty that reflects the poor goodness of fit.
minor comments (6)
  1. [Figure 8 caption] The caption says 'On the left the values r0/sqrt(t0) and the right r0/sqrt(t0)' but the right panel appears to show r1/sqrt(t0); please correct the typo.
  2. [Section 4.4 title] The title 'Evalution of exceptionally problematic ensembles' contains a misspelling and should read 'Evaluation'.
  3. [Section 5, first paragraph] The phrase 'inter1 -extrapolation' appears to be a typo for 'inter-/extrapolation'.
  4. [Section 4.3] Please define the parameters delta_hat0, gamma_hat0, and b_hat0 in Eq. (4.10), and state the r-range used in the global fit, since the text notes that the first datapoints with large lattice artifacts were excluded from the fit.
  5. [Table 1] The entries for H102-1 and N300-1 do not list the hopping parameters (kappa_u,d, kappa_s) even though those values are needed to reproduce the ensembles; please add them or state that they are the same as the preceding row.
  6. [Introduction, references] The citation sequence in the introduction, '[18, 19, 19, 20] [21, 22]', contains a duplicated reference number and an unusual gap; please check the bibliography and correct the citation order.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the scales are derived directly from the static-force definition and external inputs are independent.

full rationale

The derivation is self-contained: r0/a and r1/a are extracted from the GEVP effective masses of Wilson loops and converted to physical values via the defining force condition r_i^2 F(r_i)=c_i (eq. 2.8) and the tree-level improved distance of section 4.2; the final physical-point values (eqs. 6.1-6.3) follow from continuum/chiral fits (section 5) whose parameters are fit to the measured lattice data, not to any previous r0/r1 determination. The only external inputs are sqrt(t0) in fm from the CLS scale-setting work [48] and the ALPHA Lhad*Lambda value [100]; both are independent, externally constrained quantities and are used only to convert the dimensionless ratios or to re-express the ALPHA result in r0 units (section 6.2), which the paper explicitly labels a byproduct. The excited-state gap model (eq. 4.10) is an intermediate fit used to stabilize plateau determination on difficult ensembles; it is calibrated on ensembles with stable fits, applied to E300 and J501, and its impact is probed by the E300-excluded analysis reported in section 6.1. No equation in the paper reduces an output to an input by construction, and no load-bearing argument depends on a self-citation chain.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the standard lattice QCD framework plus two fitted analysis layers: the global gap model (eq. 4.10) and the continuum/chiral extrapolation forms (eqs. 5.2-5.5). No new entities are introduced. The conversion to physical units uses √t0 from a prior CLS paper with overlapping authors, which is a mild self-citation but not a circular derivation.

free parameters (4)
  • Gap model parameters (Δhat_0, δhat_0, γhat_0, bhat_0) = fitted per lattice spacing, not tabulated in text
    Eq. (4.10); fitted to effective masses on ensembles where the direct three-parameter fit is stable, then used to fix the excited-state gap on all ensembles, including problematic ones like E300.
  • Force interpolation coefficients (fhat_0, fhat_1, fhat_2) = per ensemble and per scale
    Eqs. (4.11)-(4.12); local fits to F(r) r^2 used to locate r0 and r1.
  • Continuum/chiral fit coefficients c_i (Fits 1-4) = values in Table 6 (as r0, r1 results)
    Eqs. (5.2)-(5.5); fitted to extrapolate to the physical point and continuum limit.
  • AIC weights = derived from χ² per fit/cut
    Eq. (5.7); used to average fit results; final values exclude the coarsest lattice spacing.
assumptions (6)
  • domain assumption The static potential V(r) can be extracted from the GEVP of Wilson loop correlation functions with a spectral decomposition; the ground state dominates after the fitted exponentials are removed.
    Section 4.1-4.3, eq. (4.2).
  • domain assumption The tree-level improved distance r_I defined by eq. (4.5)-(4.6) removes the dominant lattice artifacts of the static force; residual artifacts are O(a²) with logarithmic corrections.
    Section 4.2, following [1,24].
  • domain assumption Continuum and chiral extrapolations assume lattice artifacts of the form (a/rsym)^2 (or with log terms) and quark mass dependence linear in (r0 mπ)^2 or φ2, with mistuning corrections linear in (1.098-φ4).
    Section 5, eqs. (5.2)-(5.5).
  • ad hoc to paper The global gap model eq. (4.10) (excited energy approximately constant in r, with 1/r and linear mπ² terms) describes the excited-state gap on all ensembles.
    Section 4.3; this is a fitted model introduced in this paper.
  • domain assumption The physical value of √t0 in fm from [48] and the ALPHA value Lhad Λ^(3) from [100] are correct inputs.
    Sections 5 and 6.2; these are external inputs from the cited literature.
  • domain assumption Ignoring quark-mass mistuning for gluonic observables is valid at the current precision.
    Section 3; justified by the D450 example (0.46 per mille shift).

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Pith. "Pith review of The determination of potential scales in 2+1 flavor QCD." pith.science (2026). https://pith.science/paper/KFRLLAX3

@misc{pith2026241210215,
  author       = {Pith},
  title        = {Pith review of: The determination of potential scales in 2+1 flavor QCD},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KFRLLAX3}},
  note         = {Machine review of arXiv:2412.10215}
}
abstract

We calculate the hadronic scales $r_0$, $r_1$ and their ratio $r_0/r_1$ on $N_{\rm f}=2+1$ flavor QCD ensembles generated by the CLS consortium. These scales are determined from a tree-level improved definition of the static force on the lattice, which we measure using Wilson loops. Our analysis involves various continuum and chiral extrapolations of data that cover pion masses between 134 MeV and 420 MeV and five lattice spacings down to 0.039 fm. We compare the potential scales to gradient flow scales by forming corresponding ratios. We find $r_0=0.4757(64)$ fm at the physical point. As a byproduct of our analysis we express the $N_{\rm f}=3$ QCD Lambda parameter determined by the ALPHA Collaboration in units of the scale $r_0$ and obtain $r_0 \Lambda^{(3)}_{\overline{\rm{MS}}} = 0.820(28)$. Furthermore we present results for the second derivative of the potential to study its shape and compare it to phenomenological potential models.

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Works this paper leans on

107 extracted references · 12 canonical work pages

  1. [1]

    A New way to set the energy scale in lattice gauge theories and its applications to the static force and alpha-s in SU(2) Yang-Mills theory,

    R. Sommer, “A New way to set the energy scale in lattice gauge theories and its applications to the static force and alpha-s in SU(2) Yang-Mills theory,”Nucl. Phys. B 411 (1994) 839–854, arXiv:hep-lat/9310022

    arXiv 1994

  2. [2]

    Confinement of Quarks,

    K. G. Wilson, “Confinement of Quarks,” Phys. Rev. D 10 (1974) 2445–2459

    1974

  3. [3]

    Evidence for Flux Tubes From Cooled QCD Configurations,

    A. Di Giacomo, M. Maggiore, and S. Olejnik, “Evidence for Flux Tubes From Cooled QCD Configurations,” Phys. Lett. B 236 (1990) 199–202

    1990

  4. [4]

    Confinement and Chromoelectric Flux Tubes in Lattice QCD,

    A. Di Giacomo, M. Maggiore, and S. Olejnik, “Confinement and Chromoelectric Flux Tubes in Lattice QCD,” Nucl. Phys. B 347 (1990) 441–460

    1990

  5. [5]

    Structure of Abrikosov vortices in SU(2) lattice gauge theory,

    V . Singh, D. A. Browne, and R. W. Haymaker, “Structure of Abrikosov vortices in SU(2) lattice gauge theory,” Phys. Lett. B 306 (1993) 115–119, arXiv:hep-lat/9301004

    arXiv 1993

  6. [6]

    Observing long color flux tubes in SU(2) lattice gauge theory,

    G. S. Bali, K. Schilling, and C. Schlichter, “Observing long color flux tubes in SU(2) lattice gauge theory,” Phys. Rev. D 51 (1995) 5165–5198, arXiv:hep-lat/9409005

    arXiv 1995

  7. [7]

    QCD forces and heavy quark bound states,

    G. S. Bali, “QCD forces and heavy quark bound states,” Phys. Rept. 343 (2001) 1–136, arXiv:hep-ph/0001312. 27

    arXiv 2001

  8. [8]

    Quark confinement and the bosonic string,

    M. Lüscher and P. Weisz, “Quark confinement and the bosonic string,” JHEP 07 (2002) 049, arXiv:hep-lat/0207003

    arXiv 2002

Show all 107 references
  1. [9]

    Localized eigenmodes of covariant Laplacians in the Yang-Mills vacuum,

    J. Greensite, S. Olejnik, M. Polikarpov, S. Syritsyn, and V . Zakharov, “Localized eigenmodes of covariant Laplacians in the Yang-Mills vacuum,”Phys. Rev. D 71 (2005) 114507, arXiv:hep-lat/0504008

    2005 arXiv

  2. [10]

    String Breaking, Baryons, Medium, and Gauge/String Duality,

    O. Andreev, “String Breaking, Baryons, Medium, and Gauge/String Duality,” Phys. Rev. D 101 no. 10, (2020) 106003, arXiv:2003.09880 [hep-ph]

    2020 arXiv

  3. [11]

    String breaking by light and strange quarks in QCD,

    J. Bulava, B. Hörz, F. Knechtli, V . Koch, G. Moir, C. Morningstar, and M. Peardon, “String breaking by light and strange quarks in QCD,” Phys. Lett. B 793 (2019) 493–498, arXiv:1902.04006 [hep-lat]

    2019 arXiv

  4. [12]

    The quark-mass dependence of the potential energy between static colour sources in the QCD vacuum with light and strange quarks,

    J. Bulava, F. Knechtli, V . Koch, C. Morningstar, and M. Peardon, “The quark-mass dependence of the potential energy between static colour sources in the QCD vacuum with light and strange quarks,” Phys. Lett. B 854 (2024) 138754, arXiv:2403.00754 [hep-lat]

    2024 arXiv

  5. [13]

    The Static quark potential in three flavor QCD,

    C. W. Bernard, T. Burch, K. Orginos, D. Toussaint, T. A. DeGrand, C. E. DeTar, S. A. Gottlieb, U. M. Heller, J. E. Hetrick, and B. Sugar, “The Static quark potential in three flavor QCD,” Phys. Rev. D 62 (2000) 034503, arXiv:hep-lat/0002028

    2000 arXiv

  6. [14]

    Equation of State in 2+1 Flavor QCD at High Temperatures,

    A. Bazavov, P. Petreczky, and J. H. Weber, “Equation of State in 2+1 Flavor QCD at High Temperatures,” Phys. Rev. D 97 no. 1, (2018) 014510, arXiv:1710.05024 [hep-lat]

    2018 arXiv

  7. [15]

    Simulation of QCD with Nf = 2 + 1 flavors of non-perturbatively improved Wilson fermions,

    M. Bruno et al., “Simulation of QCD with Nf = 2 + 1 flavors of non-perturbatively improved Wilson fermions,” JHEP 02 (2015) 043, arXiv:1411.3982 [hep-lat]

    2015 arXiv

  8. [16]

    CLS 2+1 flavor simulations at physical light- and strange-quark masses,

    D. Mohler, S. Schaefer, and J. Simeth, “CLS 2+1 flavor simulations at physical light- and strange-quark masses,” EPJ Web Conf. 175 (2018) 02010, arXiv:1712.04884 [hep-lat]

    2018 arXiv

  9. [17]

    Properties and uses of the Wilson flow in lattice QCD,

    M. Lüscher, “Properties and uses of the Wilson flow in lattice QCD,” JHEP 08 (2010) 071, arXiv:1006.4518 [hep-lat] . [Erratum: JHEP 03, 092 (2014)]

    2010 arXiv

  10. [18]

    The Static potential in QCD: A Full two loop calculation,

    M. Peter, “The Static potential in QCD: A Full two loop calculation,” Nucl. Phys. B 501 (1997) 471–494, arXiv:hep-ph/9702245

    1997 arXiv

  11. [19]

    The Static potential in QCD to two loops,

    Y . Schröder, “The Static potential in QCD to two loops,”Phys. Lett. B 447 (1999) 321–326, arXiv:hep-ph/9812205

    1999 arXiv

  12. [20]

    The Static QCD potential in coordinate space with quark masses through two loops,

    M. Melles, “The Static QCD potential in coordinate space with quark masses through two loops,” Phys. Rev. D 62 (2000) 074019, arXiv:hep-ph/0001295

    2000 arXiv

  13. [21]

    Static QCD potential at three-loop order,

    C. Anzai, Y . Kiyo, and Y . Sumino, “Static QCD potential at three-loop order,”Phys. Rev. Lett. 104 (2010) 112003, arXiv:0911.4335 [hep-ph]

    2010 arXiv

  14. [22]

    The QCD static energy at NNNLL,

    N. Brambilla, A. Vairo, X. Garcia i Tormo, and J. Soto, “The QCD static energy at NNNLL,” Phys. Rev. D 80 (2009) 034016, arXiv:0906.1390 [hep-ph] . 28

    2009 arXiv

  15. [23]

    The Two loop scale dependence of the static QCD potential including quark masses,

    S. J. Brodsky, M. Melles, and J. Rathsman, “The Two loop scale dependence of the static QCD potential including quark masses,” Phys. Rev. D 60 (1999) 096006, arXiv:hep-ph/9906324

    1999 arXiv

  16. [24]

    Determination of the Static Potential with Dynamical Fermions,

    M. Donnellan, F. Knechtli, B. Leder, and R. Sommer, “Determination of the Static Potential with Dynamical Fermions,” Nucl. Phys. B 849 (2011) 45–63, arXiv:1012.3037 [hep-lat]

    2011 arXiv

  17. [25]

    The Four loop beta function in quantum chromodynamics,

    T. van Ritbergen, J. A. M. Vermaseren, and S. A. Larin, “The Four loop beta function in quantum chromodynamics,” Phys. Lett. B 400 (1997) 379–384, arXiv:hep-ph/9701390

    1997 arXiv

  18. [26]

    The Four-loop QCD beta-function and anomalous dimensions,

    M. Czakon, “The Four-loop QCD beta-function and anomalous dimensions,” Nucl. Phys. B 710 (2005) 485–498, arXiv:hep-ph/0411261

    2005 arXiv

  19. [27]

    QCD and the String Model,

    Y . Nambu, “QCD and the String Model,”Phys. Lett. B 80 (1979) 372–376

    1979

  20. [28]

    Charmonium: The Model,

    E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T.-M. Yan, “Charmonium: The Model,” Phys. Rev. D 17 (1978) 3090. [Erratum: Phys.Rev.D 21, 313 (1980)]

    1978

  21. [29]

    Charmonium: Comparison with Experiment,

    E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T.-M. Yan, “Charmonium: Comparison with Experiment,” Phys. Rev. D 21 (1980) 203

    1980

  22. [30]

    The Heavy Quark Potential and the Upsilon, J/psi Systems,

    J. L. Richardson, “The Heavy Quark Potential and the Upsilon, J/psi Systems,” Phys. Lett. B 82 (1979) 272–274

    1979

  23. [31]

    Observation of string breaking in QCD,

    SESAM Collaboration, G. S. Bali, H. Neff, T. Duessel, T. Lippert, and K. Schilling, “Observation of string breaking in QCD,” Phys. Rev. D 71 (2005) 114513, arXiv:hep-lat/0505012

    2005 arXiv

  24. [32]

    On lattice actions for static quarks,

    M. Della Morte, A. Shindler, and R. Sommer, “On lattice actions for static quarks,” JHEP 08 (2005) 051, arXiv:hep-lat/0506008

    2005 arXiv

  25. [33]

    O(a) improvement of the HYP static axial and vector currents at one-loop order of perturbation theory,

    A. Grimbach, D. Guazzini, F. Knechtli, and F. Palombi, “O(a) improvement of the HYP static axial and vector currents at one-loop order of perturbation theory,” JHEP 03 (2008) 039, arXiv:0802.0862 [hep-lat]

    2008 arXiv

  26. [34]

    FLAG Review 2021,

    Flavour Lattice Averaging Group (FLAG)Collaboration, Y . Aokiet al., “FLAG Review 2021,” Eur . Phys. J. C82 no. 10, (2022) 869, arXiv:2111.09849 [hep-lat]

    2022 arXiv

  27. [35]

    High-precision scale setting in lattice QCD,

    BMW Collaboration, S. Borsányi, S. Dürr, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, and C. McNeile, “High-precision scale setting in lattice QCD,” JHEP 09 (2012) 010, arXiv:1203.4469 [hep-lat]

    2012 arXiv

  28. [36]

    On-shell improved lattice gauge theories,

    M. Lüscher and P. Weisz, “On-shell improved lattice gauge theories,” Commun. Math. Phys. 98 no. 3, (1985) 433. [Erratum: Commun.Math.Phys. 98, 433 (1985)]

    1985

  29. [37]

    Improved Continuum Limit Lattice Action for QCD with Wilson Fermions,

    B. Sheikholeslami and R. Wohlert, “Improved Continuum Limit Lattice Action for QCD with Wilson Fermions,” Nucl. Phys. B 259 (1985) 572. 29

    1985

  30. [38]

    Improvement of Nf = 3 lattice QCD with Wilson fermions and tree-level improved gauge action,

    J. Bulava and S. Schaefer, “Improvement of Nf = 3 lattice QCD with Wilson fermions and tree-level improved gauge action,” Nucl. Phys. B 874 (2013) 188–197, arXiv:1304.7093 [hep-lat]

    2013 arXiv

  31. [39]

    Lattice QCD without topology barriers,

    M. Lüscher and S. Schaefer, “Lattice QCD without topology barriers,” JHEP 07 (2011) 036, arXiv:1105.4749 [hep-lat]

    2011 arXiv

  32. [40]

    Hybrid Monte Carlo,

    S. Duane, A. D. Kennedy, B. J. Pendleton, and D. Roweth, “Hybrid Monte Carlo,” Phys. Lett. B 195 (1987) 216–222

    1987

  33. [41]

    Speeding up the hybrid Monte Carlo algorithm for dynamical fermions,

    M. Hasenbusch, “Speeding up the hybrid Monte Carlo algorithm for dynamical fermions,” Phys. Lett. B 519 (2001) 177–182, arXiv:hep-lat/0107019

    2001 arXiv

  34. [42]

    A New exact method for dynamical fermion computations with nonlocal actions,

    A. D. Kennedy, I. Horvath, and S. Sint, “A New exact method for dynamical fermion computations with nonlocal actions,” Nucl. Phys. B Proc. Suppl. 73 (1999) 834–836, arXiv:hep-lat/9809092

    1999 arXiv

  35. [43]

    Lattice QCD with open boundary conditions and twisted-mass reweighting,

    M. Lüscher and S. Schaefer, “Lattice QCD with open boundary conditions and twisted-mass reweighting,” Comput. Phys. Commun. 184 (2013) 519–528, arXiv:1206.2809 [hep-lat]

    2013 arXiv

  36. [44]

    https://luscher.web.cern.ch/luscher/openQCD/,

    M. Lüscher, “ https://luscher.web.cern.ch/luscher/openQCD/,”

  37. [45]

    Fluctuations and reweighting of the quark determinant on large lattices,

    M. Lüscher and F. Palombi, “Fluctuations and reweighting of the quark determinant on large lattices,” PoS LATTICE2008 (2008) 049, arXiv:0810.0946 [hep-lat]

    2008 arXiv

  38. [46]

    Low-mode deflation for twisted-mass and RHMC reweighting in lattice QCD,

    S. Kuberski, “Low-mode deflation for twisted-mass and RHMC reweighting in lattice QCD,” Comput. Phys. Commun. 300 (2024) 109173, arXiv:2306.02385 [hep-lat]

    2024 arXiv

  39. [47]

    Remarks on strange-quark simulations with Wilson fermions,

    D. Mohler and S. Schaefer, “Remarks on strange-quark simulations with Wilson fermions,” Phys. Rev. D 102 no. 7, (2020) 074506, arXiv:2003.13359 [hep-lat]

    2020 arXiv

  40. [48]

    Scale setting for CLS 2+1 simulations,

    B. Straßberger et al., “Scale setting for CLS 2+1 simulations,” PoS LATTICE2021 (2022) 135, arXiv:2112.06696 [hep-lat]

    2022 arXiv

  41. [49]

    Setting the scale for the CLS 2 + 1 flavor ensembles,

    M. Bruno, T. Korzec, and S. Schaefer, “Setting the scale for the CLS 2 + 1 flavor ensembles,” Phys. Rev. D 95 no. 7, (2017) 074504, arXiv:1608.08900 [hep-lat]

    2017 arXiv

  42. [50]

    Monte Carlo errors with less errors,

    ALPHA Collaboration, U. Wolff, “Monte Carlo errors with less errors,”Comput. Phys. Commun. 156 (2004) 143–153, arXiv:hep-lat/0306017. [Erratum: Comput.Phys.Commun. 176, 383 (2007)]

    2004 arXiv

  43. [51]

    Critical slowing down and error analysis in lattice QCD simulations,

    ALPHA Collaboration, S. Schaefer, R. Sommer, and F. Virotta, “Critical slowing down and error analysis in lattice QCD simulations,” Nucl. Phys. B 845 (2011) 93–119, arXiv:1009.5228 [hep-lat]

    2011 arXiv

  44. [52]

    General error computation in lattice gauge theory,

    H. Simma, R. Sommer, and F. Virotta, “General error computation in lattice gauge theory,” Internal notes of the ALPHA collaboration (2012-2014)

    2012

  45. [53]

    Automatic differentiation for error analysis of Monte Carlo data,

    A. Ramos, “Automatic differentiation for error analysis of Monte Carlo data,” Comput. Phys. Commun. 238 (2019) 19–35, arXiv:1809.01289 [hep-lat] . 30

    2019 arXiv

  46. [54]

    pyerrors: A python framework for error analysis of Monte Carlo data,

    F. Joswig, S. Kuberski, J. T. Kuhlmann, and J. Neuendorf, “pyerrors: A python framework for error analysis of Monte Carlo data,” Comput. Phys. Commun. 288 (2023) 108750, arXiv:2209.14371 [hep-lat]

    2023 arXiv

  47. [55]

    Wilson loop computation,

    B. Leder, “Wilson loop computation,” 2015. https://github.com/bjoern-leder/wloop

    2015

  48. [56]

    Flavor symmetry and the static potential with hypercubic blocking,

    A. Hasenfratz and F. Knechtli, “Flavor symmetry and the static potential with hypercubic blocking,” Phys. Rev. D 64 (2001) 034504, arXiv:hep-lat/0103029

    2001 arXiv

  49. [57]

    An Effective Field Theory for the Calculation of Matrix Elements Involving Heavy Quarks,

    E. Eichten and B. R. Hill, “An Effective Field Theory for the Calculation of Matrix Elements Involving Heavy Quarks,”Phys. Lett. B 234 (1990) 511–516

    1990

  50. [58]

    Heavy Quark Potentials and Hybrid Mesons From SU(3) Lattice Gauge Theory,

    N. A. Campbell, A. Huntley, and C. Michael, “Heavy Quark Potentials and Hybrid Mesons From SU(3) Lattice Gauge Theory,” Nucl. Phys. B 306 (1988) 51–62

    1988

  51. [59]

    Precision computation of a low-energy reference scale in quenched lattice QCD,

    ALPHA Collaboration, M. Guagnelli, R. Sommer, and H. Wittig, “Precision computation of a low-energy reference scale in quenched lattice QCD,” Nucl. Phys. B 535 (1998) 389–402, arXiv:hep-lat/9806005

    1998 arXiv

  52. [60]

    How to Calculate the Elastic Scattering Matrix in Two-dimensional Quantum Field Theories by Numerical Simulation,

    M. Lüscher and U. Wolff, “How to Calculate the Elastic Scattering Matrix in Two-dimensional Quantum Field Theories by Numerical Simulation,”Nucl. Phys. B 339 (1990) 222–252

    1990

  53. [61]

    On the generalized eigenvalue method for energies and matrix elements in lattice field theory,

    B. Blossier, M. Della Morte, G. von Hippel, T. Mendes, and R. Sommer, “On the generalized eigenvalue method for energies and matrix elements in lattice field theory,” JHEP 04 (2009) 094, arXiv:0902.1265 [hep-lat]

    2009 arXiv

  54. [62]

    On the generalised eigenvalue method and its relation to prony and generalised pencil of function methods,

    M. Fischer, B. Kostrzewa, J. Ostmeyer, K. Ottnad, M. Ueding, and C. Urbach, “On the generalised eigenvalue method and its relation to prony and generalised pencil of function methods,” The European Physical Journal A 56 no. 8, (Aug., 2020) . http://dx.doi.org/10.1140/epja/s100...

    2020 doi

  55. [63]

    A Measurement of the String Tension Near the Continuum Limit,

    G. Parisi, R. Petronzio, and F. Rapuano, “A Measurement of the String Tension Near the Continuum Limit,” Phys. Lett. B 128 (1983) 418–420

    1983

  56. [64]

    Locality and exponential error reduction in numerical lattice gauge theory,

    M. Lüscher and P. Weisz, “Locality and exponential error reduction in numerical lattice gauge theory,” JHEP 09 (2001) 010, arXiv:hep-lat/0108014

    2001 arXiv

  57. [65]

    The Static three quark SU(3) and four quark SU(4) potentials,

    C. Alexandrou, P. De Forcrand, and A. Tsapalis, “The Static three quark SU(3) and four quark SU(4) potentials,” Phys. Rev. D 65 (2002) 054503, arXiv:hep-lat/0107006

    2002 arXiv

  58. [66]

    The Static potential with hypercubic blocking,

    A. Hasenfratz, R. Hoffmann, and F. Knechtli, “The Static potential with hypercubic blocking,” Nucl. Phys. B Proc. Suppl. 106 (2002) 418–420, arXiv:hep-lat/0110168

    2002 arXiv

  59. [67]

    The Static Potential with Hypercubic Blocking,

    R. Hoffmann, “The Static Potential with Hypercubic Blocking,” diploma thesis (2002)

    2002

  60. [68]

    The determination of r0 and r1 in Nf=2+1 QCD,

    T. M. B. Asmussen, R. Höllwieser, F. Knechtli, and T. Korzec, “The determination of r0 and r1 in Nf=2+1 QCD,” PoS LATTICE2023 (2024) 296, arXiv:2312.14726 [hep-lat]. 31

    2024 arXiv

  61. [69]

    A new approach for delta form factors,

    C. Aubin, K. Orginos, D. Armstrong, V . Burkert, J.-P. Chen, W. Detmold, J. Dudek, W. Melnitchouk, and D. Richards, “A new approach for delta form factors,” inAIP Conference Proceedings, p. 621–624. AIP, 2011. http://dx.doi.org/10.1063/1.3647217

    2011 doi

  62. [70]

    An improved method for extracting matrix elements from lattice three-point functions,

    C. Aubin and K. Orginos, “An improved method for extracting matrix elements from lattice three-point functions,” PoS Lattice 2011 (2012) 148

    2012

  63. [71]

    Expanding the interpolator basis in the variational method to explicitly account for backward running states,

    R. W. Schiel, “Expanding the interpolator basis in the variational method to explicitly account for backward running states,” Phys. Rev. D 92 (Aug, 2015) 034512. https://link.aps.org/doi/10.1103/PhysRevD.92.034512

    2015 doi

  64. [72]

    Nucleon average quark momentum fraction with nf = 2+1 wilson fermions,

    K. Ottnad, T. Harris, H. Meyer, G. von Hippel, J. Wilhelm, and H. Wittig, “Nucleon average quark momentum fraction with nf = 2+1 wilson fermions,” EPJ Web of Conferences 175 (2018) 06026. http://dx.doi.org/10.1051/epjconf/201817506026

    2018

  65. [73]

    Fixed point gauge actions with fat links: Scaling and glueballs,

    F. Niedermayer, P. Rufenacht, and U. Wenger, “Fixed point gauge actions with fat links: Scaling and glueballs,” Nucl. Phys. B 597 (2001) 413–450, arXiv:hep-lat/0007007

    2001 arXiv

  66. [74]

    A new look at the statistical model identification,

    H. Akaike, “A new look at the statistical model identification,” IEEE Transactions on Automatic Control 19 no. 6, (1974) 716–723

    1974

  67. [75]

    Bayesian model averaging for analysis of lattice field theory results,

    W. I. Jay and E. T. Neil, “Bayesian model averaging for analysis of lattice field theory results,” Phys. Rev. D 103 (2021) 114502, arXiv:2008.01069 [stat.ME]

    2021 arXiv

  68. [76]

    Improved information criteria for Bayesian model averaging in lattice field theory,

    E. T. Neil and J. W. Sitison, “Improved information criteria for Bayesian model averaging in lattice field theory,” Phys. Rev. D 109 no. 1, (2024) 014510, arXiv:2208.14983 [stat.ME]

    2024 arXiv

  69. [77]

    Nonperturbative running of the tensor operator for Nf=3 QCD from the chirally rotated Schrödinger functional,

    ALPHA Collaboration, I. Campos Plasencia, M. Dalla Brida, G. M. de Divitiis, A. Lytle, M. Papinutto, L. Pirelli, and A. Vladikas, “Nonperturbative running of the tensor operator for Nf=3 QCD from the chirally rotated Schrödinger functional,” Phys. Rev. D 109 no. 5, (2024) 0545...

    2024 arXiv

  70. [78]

    Cutoff dependence in lattice ϕ4 4 theory,

    K. Symanzik, “Cutoff dependence in lattice ϕ4 4 theory,” NATO Sci. Ser . B59 (1980) 313–330

    1980

  71. [79]

    Logarithmic corrections to O(a**2) lattice artifacts,

    J. Balog, F. Niedermayer, and P. Weisz, “Logarithmic corrections to O(a**2) lattice artifacts,” Phys. Lett. B 676 (2009) 188–192, arXiv:0901.4033 [hep-lat]

    2009 arXiv

  72. [80]

    Asymptotic behavior of cutoff effects in Yang–Mills theory and in Wilson’s lattice QCD,

    N. Husung, P. Marquard, and R. Sommer, “Asymptotic behavior of cutoff effects in Yang–Mills theory and in Wilson’s lattice QCD,”Eur . Phys. J. C80 no. 3, (2020) 200, arXiv:1912.08498 [hep-lat]

    2020 arXiv

  73. [81]

    The asymptotic approach to the continuum of lattice QCD spectral observables,

    N. Husung, P. Marquard, and R. Sommer, “The asymptotic approach to the continuum of lattice QCD spectral observables,” Phys. Lett. B 829 (2022) 137069, arXiv:2111.02347 [hep-lat] . 32

    2022 arXiv

  74. [82]

    Up, down, strange and charm quark masses with Nf = 2+1+1 twisted mass lattice QCD,

    European Twisted Mass Collaboration, N. Carrasco et al., “Up, down, strange and charm quark masses with Nf = 2+1+1 twisted mass lattice QCD,” Nucl. Phys. B 887 (2014) 19–68, arXiv:1403.4504 [hep-lat]

    2014 arXiv

  75. [83]

    MILC results for light pseudoscalars,

    MILC Collaboration, A. Bazavov et al., “MILC results for light pseudoscalars,” PoS CD09 (2009) 007, arXiv:0910.2966 [hep-ph]

    2009 arXiv

  76. [84]

    Charm and strange quark masses and fDs from overlap fermions,

    Y .-B. Yanget al., “Charm and strange quark masses and fDs from overlap fermions,” Phys. Rev. D 92 no. 3, (2015) 034517, arXiv:1410.3343 [hep-lat]

    2015 arXiv

  77. [85]

    Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks,

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

    2013 arXiv

  78. [86]

    Results for light pseudoscalar mesons,

    MILC Collaboration, A. Bazavov et al., “Results for light pseudoscalar mesons,” PoS LATTICE2010 (2010) 074, arXiv:1012.0868 [hep-lat]

    2010 arXiv

  79. [87]

    Equation of state in ( 2+1 )-flavor QCD,

    HotQCD Collaboration, A. Bazavov et al., “Equation of state in ( 2+1 )-flavor QCD,” Phys. Rev. D 90 (2014) 094503, arXiv:1407.6387 [hep-lat]

    2014 arXiv

  80. [88]

    Continuum Limit Physics from 2+1 Flavor Domain Wall QCD,

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

    2011 arXiv

  81. [89]

    The Upsilon spectrum and m(b) from full lattice QCD,

    A. Gray, I. Allison, C. T. H. Davies, E. Dalgic, G. P. Lepage, J. Shigemitsu, and M. Wingate, “The Upsilon spectrum and m(b) from full lattice QCD,” Phys. Rev. D 72 (2005) 094507, arXiv:hep-lat/0507013

    2005 arXiv

  82. [90]

    Light hadrons with improved staggered quarks: Approaching the continuum limit,

    C. Aubin, C. Bernard, C. DeTar, J. Osborn, S. Gottlieb, E. B. Gregory, D. Toussaint, U. M. Heller, J. E. Hetrick, and R. Sugar, “Light hadrons with improved staggered quarks: Approaching the continuum limit,” Phys. Rev. D 70 (2004) 094505, arXiv:hep-lat/0402030

    2004 arXiv

  83. [91]

    Precise determination of the lattice spacing in full lattice QCD,

    HPQCD Collaboration, C. T. H. Davies, E. Follana, I. D. Kendall, G. P. Lepage, and C. McNeile, “Precise determination of the lattice spacing in full lattice QCD,” Phys. Rev. D 81 (2010) 034506, arXiv:0910.1229 [hep-lat]

    2010 arXiv

  84. [92]

    Nonperturbative QCD Simulations with 2+1 Flavors of Improved Staggered Quarks,

    MILC Collaboration, A. Bazavov et al., “Nonperturbative QCD Simulations with 2+1 Flavors of Improved Staggered Quarks,” Rev. Mod. Phys. 82 (2010) 1349–1417, arXiv:0903.3598 [hep-lat]

    2010 arXiv

  85. [93]

    2+1 Flavor Lattice QCD toward the Physical Point,

    PACS-CSCollaboration, S. Aoki et al., “2+1 Flavor Lattice QCD toward the Physical Point,” Phys. Rev. D 79 (2009) 034503, arXiv:0807.1661 [hep-lat]

    2009 arXiv

  86. [94]

    The Upsilon spectrum and the determination of the lattice spacing from lattice QCD including charm quarks in the sea,

    HPQCD Collaboration, R. J. Dowdall et al., “The Upsilon spectrum and the determination of the lattice spacing from lattice QCD including charm quarks in the sea,”Phys. Rev. D 85 (2012) 054509, arXiv:1110.6887 [hep-lat]

    2012 arXiv

  87. [95]

    The chiral and deconfinement aspects of the QCD transition,

    A. Bazavov et al., “The chiral and deconfinement aspects of the QCD transition,” Phys. Rev. D 85 (2012) 054503, arXiv:1111.1710 [hep-lat] . 33

    2012 arXiv

  88. [96]

    Static energy in (2 + 1 + 1)-flavor lattice QCD: Scale setting and charm effects,

    TUMQCD Collaboration, N. Brambilla, R. L. Delgado, A. S. Kronfeld, V . Leino, P. Petreczky, S. Steinbeißer, A. Vairo, and J. H. Weber, “Static energy in (2 + 1 + 1)-flavor lattice QCD: Scale setting and charm effects,” Phys. Rev. D 107 no. 7, (2023) 074503, arXiv:2206.03156 [hep-lat]

    2023 arXiv

  89. [97]

    Effects of Heavy Sea Quarks at Low Energies,

    ALPHA Collaboration, M. Bruno, J. Finkenrath, F. Knechtli, B. Leder, and R. Sommer, “Effects of Heavy Sea Quarks at Low Energies,”Phys. Rev. Lett. 114 no. 10, (2015) 102001, arXiv:1410.8374 [hep-lat]

    2015 arXiv

  90. [98]

    Power corrections from decoupling of the charm quark,

    ALPHA Collaboration, F. Knechtli, T. Korzec, B. Leder, and G. Moir, “Power corrections from decoupling of the charm quark,” Phys. Lett. B 774 (2017) 649–655, arXiv:1706.04982 [hep-lat]

    2017 arXiv

  91. [99]

    Past, present, and future of precision determinations of the QCD parameters from lattice QCD,

    M. Dalla Brida, “Past, present, and future of precision determinations of the QCD parameters from lattice QCD,” Eur . Phys. J. A57 no. 2, (2021) 66, arXiv:2012.01232 [hep-lat]

    2021 arXiv

  92. [100]

    QCD Coupling from a Nonperturbative Determination of the Three-Flavor Λ Parameter,

    ALPHA Collaboration, M. Bruno, M. Dalla Brida, P. Fritzsch, T. Korzec, A. Ramos, S. Schaefer, H. Simma, S. Sint, and R. Sommer, “QCD Coupling from a Nonperturbative Determination of the Three-Flavor Λ Parameter,” Phys. Rev. Lett. 119 no. 10, (2017) 102001, arXiv:1706.03821 [hep-lat]

    2017 arXiv

  93. [101]

    Determination of the QCD coupling from the static energy and the free energy,

    TUMQCD Collaboration, A. Bazavov, N. Brambilla, X. Garcia i Tormo, P. Petreczky, J. Soto, A. Vairo, and J. H. Weber, “Determination of the QCD coupling from the static energy and the free energy,” Phys. Rev. D 100 no. 11, (2019) 114511, arXiv:1907.11747 [hep-lat]

    2019 arXiv

  94. [102]

    Running coupling constant from position-space current-current correlation functions in three-flavor lattice QCD,

    S. Cali, K. Cichy, P. Korcyl, and J. Simeth, “Running coupling constant from position-space current-current correlation functions in three-flavor lattice QCD,” Phys. Rev. Lett. 125 (2020) 242002, arXiv:2003.05781 [hep-lat]

    2020 arXiv

  95. [103]

    Determination of α(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair,

    C. Ayala, X. Lobregat, and A. Pineda, “Determination of α(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair,” JHEP 09 (2020) 016, arXiv:2005.12301 [hep-ph]

    2020 arXiv

  96. [104]

    Precise determination of the strong coupling constant in Nf = 2+1 lattice QCD with the Schrodinger functional scheme,

    PACS-CSCollaboration, S. Aoki et al., “Precise determination of the strong coupling constant in Nf = 2+1 lattice QCD with the Schrodinger functional scheme,” JHEP 10 (2009) 053, arXiv:0906.3906 [hep-lat]

    2009 arXiv

  97. [105]

    The Realistic Lattice Determination of alpha(s)(M(Z)) Revisited,

    K. Maltman, D. Leinweber, P. Moran, and A. Sternbeck, “The Realistic Lattice Determination of alpha(s)(M(Z)) Revisited,” Phys. Rev. D 78 (2008) 114504, arXiv:0807.2020 [hep-lat]

    2008 arXiv

  98. [106]

    High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD,

    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 Lattice and Continuum QCD,” Phys. Rev. D 82 (2010) 034512, arXiv:1004.4285 [hep-lat]

    2010 arXiv

  99. [107]

    Domain decomposition, multi-level integration and exponential noise reduction in lattice QCD,

    M. Cè, L. Giusti, and S. Schaefer, “Domain decomposition, multi-level integration and exponential noise reduction in lattice QCD,” Phys. Rev. D 93 no. 9, (2016) 094507, arXiv:1601.04587 [hep-lat] . 34

    2016 arXiv

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