Pith. sign in

REVIEW 5 minor 5 cited by

Renormalising vector currents in lattice QCD using momentum-subtraction schemes

T0 review · 0 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The renormalisation factor for the nonconserved local HISQ vector current obtained in the RI-SMOM scheme is exact, free of nonperturbative condensate contamination, and differs from the charge-conservation determination only by…

desk verdict A careful and convincing lattice-QCD methods paper: the RI-SMOM exactness claim is carried by the Ward-Takahashi identity, the numerics are excellent, and the soft spots are minor. read the letter →

arxiv 1909.00756 v2 pith:NLCAFM66 submitted 2019-09-02 hep-lat

D. Hatton , C. T. H. Davies , G. P. Lepage , A. T. Lytle This is my paper · ORCID
classification hep-lat MSC 81T2581T8081V05 PACS 11.15.Ha12.38.Gc
keywords latticeQCDvectorcurrentrenormalisationRI-SMOMschemeRI-prime-MOMWard-TakahashiidentityHISQactioncondensatecontaminationquenchedQED
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

This paper establishes that the renormalisation factor for the nonconserved local HISQ vector current obtained in the RI-SMOM momentum-subtraction scheme is exact, in the sense that it carries no nonperturbative condensate contamination and therefore agrees with the charge-conservation form-factor determination up to cleanly removable discretisation effects. The same protection is shown to hold for the one-link point-split vector current. By contrast, the standard RI-prime-MOM scheme is shown to carry about one percent condensate contamination in both conserved and local currents, and a modified ratio version, called RI-prime-MOM Rc, is proposed and verified to be safe. The paper also provides a first nonperturbative study of quenched QED corrections to the vector current renormalisation in the RI-SMOM scheme, finding an effect below 0.1% for the HISQ action.

What carries the argument

The load-bearing mechanism is the exact lattice vector Ward-Takahashi identity, which in momentum space reads $-2i a^{-1}\sin(aq_\mu/2)\Lambda_\mu^+ = -S^{-1}(p_1)+S^{-1}(p_2)$ and holds configuration by configuration in any gauge. For the HISQ action the conserved current is a one-link-plus-three-link Naik-improved operator, and the RI-SMOM scheme, a momentum-subtraction scheme with symmetric kinematics $p_1^2=p_2^2=q^2=\mu^2$ and a projector constructed from this identity, therefore forces $Z_V=1$ for the conserved current. Any nonconserved current renormalised by a ratio to the conserved vertex is then protected from the condensate contaminations that would otherwise appear as $1/\mu^2$ terms; this Ward-Takahashi-protected ratio is the central object, and for the RI-prime-MOM scheme the same ratio, called RI-prime-MOM Rc, is what restores safety.

What would settle it

Examine the difference $Z_{\rm loc}^V({\rm SMOM})-Z_{\rm loc}^V(F(0))$ on a finer lattice or with a different quark action and check whether it extrapolates to exactly zero in the continuum limit, since a nonzero intercept would falsify the claim. Equivalently, measure the coefficient of the $1/\mu^2$ term in $Z_{\rm loc}^V({\rm SMOM})$ with higher statistics; the paper constrains it to $-0.020(44)$, so a value several standard deviations from zero would show contamination that the Ward-Takahashi protection was supposed to remove.

Watch

Extended reading notes

Core claim

Using the exact lattice vector Ward-Takahashi identity for the HISQ action, the authors show that any renormalisation procedure built on that identity must assign $Z_V=1$ to the conserved current; they verify this explicitly for RI-SMOM kinematics, with $Z_{\rm cons}^V({\rm SMOM})$ equal to 1 to better than 0.05% at every scale. Because the renormalised local current coincides with the conserved current up to $​O(a^2)$ discretisation effects, the RI-SMOM value $Z_{\rm loc}^V({\rm SMOM})$ inherits the same protection: its difference from the form-factor value $Z_{\rm loc}^V(F(0))$ extrapolates to zero in the continuum limit, and the fit constrains any $1/\mu^2$ condensate term to $-0.020(44)$, statistically consistent with zero. The standard RI-prime-MOM scheme does not use the identity, and its $Z_V$ for both the conserved and local currents shows a clear condensate contribution with leading coefficient $0.154(54)$, so that naive use brings roughly one percent systematic errors; defining $Z_V$ instead as the ratio of local to conserved vertex functions, the Rc variant, removes this contamination.

Load-bearing premise

The argument assumes that the form-factor benchmark used for comparison, fixed by charge conservation, is itself exactly free of nonperturbative contamination; any hidden error in that benchmark would shift the difference plots and be inherited by the claim that the momentum-subtraction results are clean.

Editorial extensions

If this is right

  • $Z_{\rm loc}^V({\rm SMOM})$ can be used at any momentum scale $\mu$ without fitting away condensate effects, so there is no need for a restricted window of $\mu$ values; the only trade-off is between statistical error and discretisation error.
  • Standard RI-prime-MOM determinations of $Z_V$ carry about one percent systematic error unless condensate terms are included in a multi-$\mu$, multi-$a$ fit, whereas the RI-prime-MOM Rc ratio removes that error at the cost of computing the conserved-current vertex.
  • For staggered quarks, the local axial current renormalisation $Z_A$ can be set equal to the local vector result $Z_V$, avoiding a separate momentum-subtraction calculation that would reintroduce chiral-symmetry-breaking condensate contamination.
  • Quenched QED corrections to $Z_V$ in the RI-SMOM scheme are below 0.1% for the HISQ action and are describable by the known perturbative coefficient, so QED effects can be included nonperturbatively in precision matrix-element calculations.
  • The conclusions are not specific to the HISQ action: any improved action with an exact lattice Ward-Takahashi identity should enjoy the same protection in RI-SMOM and in the Rc-type ratio schemes.

Reading between the lines

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

  • The paper's result that there is no lower limit on $\mu$ suggests a step-scaling strategy in which $Z_V$ is computed at low $\mu$, where discretisation effects are smallest, and then run to higher scales; the authors demonstrate a two-$\mu$ combination but do not pursue full step scaling.
  • The ratio-to-conserved-current construction generalises: any lattice current with an exactly conserved counterpart could be renormalised in any momentum-subtraction scheme by normalising to the conserved vertex, potentially extending the same protection to other operators with an exact Ward-Takahashi identity.
  • For actions whose pure-QCD $Z_V$ is far from 1, the quenched-QED shift in $Z_V$ should scale roughly as $(1-Z_V)\,\alpha_{\rm QED}$; if confirmed, this would let collaborations estimate QED corrections to renormalisation factors without a dedicated calculation.
  • A direct test of the Ward-Takahashi protection would be to compute the difference $Z_V({\rm SMOM})-Z_V(F(0))$ at $\mu$ values below 1 GeV on large volumes, where the paper's data show smaller discretisation effects and any hidden condensate term would first become visible.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 5 minor

Summary. The paper studies the renormalisation of flavour-diagonal vector currents in lattice QCD using the HISQ action on MILC n_f=2+1+1 ensembles, with emphasis on momentum-subtraction schemes. It derives the exact lattice vector Ward-Takahashi identity for the HISQ conserved current and verifies it on a single gauge configuration. It then shows that the RI-SMOM scheme gives Z_cons^V = 1 to better than 0.05% and that Z_loc^V from RI-SMOM differs from the form-factor value Z_loc^V(F(0)) only by discretisation effects, with the leading condensate coefficient constrained to -0.020(44). In contrast, the standard RI'-MOM scheme yields Z_cons^V and Z_loc^V with O(1%) condensate contamination, which can be removed by using ratios of conserved-to-local vertex functions in the RI'-MOMRc and SMOM-gamma_mu,Rc schemes. A first study of quenched QED effects in the RI-SMOM scheme shows the QED correction to Z_loc^V is below 0.1%.

Significance. If the conclusions hold, RI-SMOM provides an exact, fully nonperturbative Z_V that requires no momentum window and no condensate fit, which is practically valuable for precision calculations such as the hadronic vacuum polarisation contribution to the muon anomalous magnetic moment. The load-bearing argument is the exact Ward-Takahashi identity, not the external benchmark: the paper verifies Eq. (8) to double precision on a single configuration, confirms Z_cons^V(SMOM)=1 to 0.05%, and supports the local-current result with a controlled difference fit. The internal consistency across schemes and lattice spacings, and the explicit quantitative diagnosis of RI'-MOM contamination, are strengths. The main caveat is that parts of the comparison to the form-factor benchmark use values inferred from a fit in Ref. [11], but this does not undermine the Ward-Takahashi-based reasoning.

minor comments (5)
  1. [Section IV D] The comparison to Z_loc^V(F(0)) on fine and superfine ensembles uses benchmark values inferred from a fit in Ref. [11] rather than values measured directly on those ensembles. The text should state explicitly how the uncertainties of those benchmark values are propagated into Figs. 6, 9, and 15, and acknowledge that a common contamination in the benchmark would shift the difference plots. This does not affect the Ward-Takahashi-based argument for the SMOM result, but it is a limitation of the numerical demonstration.
  2. [Sections I and II] The name 'Ward-Takashashi' appears in the Introduction, Section II heading, and Section IV A; it should be 'Ward-Takahashi'.
  3. [Section IV F] The tree-level factor used for the conserved current in the RI-SMOM-gamma_mu scheme is only described verbally as a modification of Eq. (24) to the SMOM kinematics; writing the explicit analogue of Eq. (24) would make the scheme reproducible without guesswork.
  4. [Section IV D / Fig. 6] The lower panel of Fig. 6 labels the horizontal axis as 'a^2 [fm]', which is dimensionally inconsistent; it should be 'a^2 [fm^2]'.
  5. [Section III] The sentence 'This is not true configuration by configuration' in the discussion of Z_cons^V(SMOM) is slightly confusing because Eq. (8) is exact on every configuration; the statement should clarify that the ensemble average is needed for the replacement in Eq. (14), not for the Ward-Takahashi identity itself.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the RI-SMOM exactness claim follows from the exact lattice Ward-Takahashi identity and standard operator relations; the form-factor benchmark is a consistency check, not a fitted input.

full rationale

The central claim that ZlocV(SMOM) is free of nonperturbative condensate contamination is derived from the exact lattice vector Ward-Takahashi identity, Eq. (8), which the paper verifies explicitly in Fig. 1, together with the standard operator relation Eq. (9): J+_mu = ZlocV Vloc_mu + O(a^2). Equation (15) then shows that the RI-SMOM projector applied to the conserved current gives ZconsV(SMOM)=1; this is a consequence of the identity, not a fitted input. The numerical tests in Figs. 2 and 3 confirm that consequence rather than redefining the result. The comparison of ZlocV(SMOM) with ZlocV(F(0)) from Ref. [11] is used to demonstrate that the two determinations differ only by discretisation effects, but the exactness conclusion does not rest on the F(0) benchmark: it follows from the Ward-Takahashi identity and Eq. (9). The F(0) values in Ref. [11] are a same-collaboration benchmark, and the paper notes that on finer lattices they were inferred from a fit rather than directly measured; if that fitted benchmark carried an unrecognised condensate contribution, the difference plots in Figs. 6, 9 and 15 would shift, but the central derivation would remain intact. The RI'-MOM condensate coefficient in Eq. (27) is a fitted diagnostic illustrating a known contamination, not a parameter forced to produce the paper's conclusion. The quenched-QED leading-order coefficient is fixed from QCD perturbation theory and then tested against the lattice data, which is a genuine prediction check. No equation reduces by construction to its own inputs, and no load-bearing step is justified only by a self-citation.

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

The paper's conclusions rest on standard lattice QCD machinery (HISQ action, WTI, OPE) plus specific assumptions about the external benchmark and the fit forms. No new entities are introduced. The free parameters are nuisance coefficients in the fits used to separate discretisation and condensate effects.

free parameters (3)
  • Leading condensate coefficient c^(1)_cond in RI'-MOM fit = 0.154(54)
    Eq. (27). Fit to Z_cons^V(MOM)(a,mu) using Eq. (26); quantifies the nonperturbative contamination that is the paper's main negative result.
  • Coefficients of discretisation/condensate terms in Eq. (29) and Eq. (B7) difference fits = not quoted individually, priors 0±1
    Used to demonstrate that the SMOM-minus-form-factor difference is purely discretisation; the leading condensate coefficient is -0.020(44). These are nuisance parameters, but they are fitted to the data.
  • Coefficients c_i, d_ij in the quenched-QED ratio fit, Eq. (34) = not quoted, c0 fixed to -0.0388
    Fit to the Z_V ratio data in Table IV; c0 is fixed from QCD perturbation theory, higher coefficients are fitted.
assumptions (5)
  • domain assumption The lattice vector Ward-Takahashi identity, Eq. (8), holds exactly for the HISQ conserved current, including the 3-link terms.
    Section IV A verifies it on a single configuration, but the analytic derivation in Section II assumes the conserved current J_mu^+ of Eq. (A1) is the correct Noether current.
  • domain assumption Equation (14): Tr(S^-1(p1)/q) - Tr(S^-1(p2)/q) = Tr(S^-1(q)/q) holds on the lattice for HISQ with SMOM kinematics.
    Tested numerically in Fig. 2 to 0.05%, but used to derive Z_cons^V(SMOM)=1; it is a property of the HISQ action and the special momentum configuration, not a general identity.
  • domain assumption The vector form factor at zero momentum transfer, Z_V(F(0)) from Ref. [11], is an exact condensate-free renormalisation factor.
    Used as the external benchmark in Figs. 6, 8, 9, 10, 15. The paper does not re-derive it; it is taken from earlier HPQCD work.
  • domain assumption Nonperturbative condensate contributions appear as even powers of 1/mu^2 in the operator product expansion, as in Eq. (26) and Eq. (29).
    The conclusion that RI-SMOM has no contamination depends on the fit form capturing any contamination; if condensates took a different mu-dependence they would be missed.
  • domain assumption Quenched QED (valence quarks charged, sea quarks neutral) is an adequate approximation to quantify QED effects on Z_V.
    Section V states sea-quark QED contributions are O(alpha_s^2 alpha_QED) and unlikely to change the picture. The paper is explicit that this is quenched.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Renormalising vector currents in lattice QCD using momentum-subtraction schemes." pith.science (2026). https://pith.science/paper/NLCAFM66

@misc{pith2026190900756,
  author       = {Pith},
  title        = {Pith review of: Renormalising vector currents in lattice QCD using momentum-subtraction schemes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NLCAFM66}},
  note         = {Machine review of arXiv:1909.00756}
}
abstract

We examine the renormalisation of flavour-diagonal vector currents in lattice QCD with the aim of understanding and quantifying the systematic errors from nonperturbative artefacts associated with the use of intermediate momentum-subtraction schemes. Our study uses the Highly Improved Staggered Quark (HISQ) action on gluon field configurations that include $n_f=2+1+1$ flavours of sea quarks, but our results have applicability to other quark actions. Renormalisation schemes that make use of the exact lattice vector Ward-Takahashi identity for the conserved current also have renormalisation factors, $Z_V$, for nonconserved vector currents that are free of contamination by nonperturbative condensates. We show this by explicit comparison of two such schemes: that of the vector form factor at zero momentum transfer and the RI-SMOM momentum-subtraction scheme. The two determinations of $Z_V$ differ only by discretisation effects (for any value of momentum-transfer in the RI-SMOM case). The RI$^{\prime}$-MOM scheme, although widely used, does not share this property. We show that $Z_V$ determined in the standard way in this scheme has $\mathcal{O}(1\%)$ nonperturbative contamination that limits its accuracy. Instead we define an RI$^{\prime}$-MOM $Z_V$ from a ratio of local to conserved vector current vertex functions and show that this $Z_V$ is a safe one to use in lattice QCD calculations. We also perform a first study of vector current renormalisation with the inclusion of quenched QED effects on the lattice using the RI-SMOM scheme.

Figures

Figures reproduced from arXiv: 1909.00756 by the authors.

Figure 2
Figure 2. FIG. 2. A test of the expression for the difference of inverse [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Points labelled ‘MOM’ show the renormalisation fac [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figures from the paper (9 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Valence mass dependence of [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: (top plot) shows our results as a difference between Z loc V (SMOM) and Z loc V (F(0)). Z loc V (F(0)) values are from [11] and obtained on the same gluon field con￾figurations that we use here. We plot the difference for the multiple µ values used for the Z loc V (SMO…
Figure 7
Figure 7. Figure 7: FIG. 7. Valence mass dependence of our raw results for [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: shows our results given, following the discus￾sion in Section IV D, as a difference to the renormalisa￾tion constants obtained for the local current using the form factor method in [11]. This figure is very different from [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: , the values converge to zero as a → 0 as discretisa￾tion effects should. Discretisation effects are significantly larger here than in the previous schemes, however. We fit the results to the same functional form as used for the other schemes (i.e. Eq. (29)) and obtain…
Figure 11
Figure 11. Figure 11: FIG. 11. The difference between the vertex functions for the [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 13
Figure 13. Figure 13: FIG. 13. The impact of quenched QED (with quark charge [PITH_FULL_IMAGE:figures/full_fig_p015_13.png]
Figure 14
Figure 14. Figure 14: shows that the results for ZV behave as ex￾pected. The impact of quenched QED on the value of Z loc V is tiny and indeed negligible if we imagine working to an accuracy of 0.1%. Note that this follows directly from the analysis above in which we derive the O(αQED) coe…
Figure 15
Figure 15. Figure 15: FIG. 15 [PITH_FULL_IMAGE:figures/full_fig_p018_15.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Constraints on axion-like particles using lattice QCD calculations of the rate for $J/\psi \to \gamma a$

    hep-lat 2025-02 conditional novelty 8.0 of 10

    First lattice QCD calculation of the J/psi to gamma plus axion-like-particle form factor, with under 2% uncertainty, used to update ALP constraints.

  2. Heavy-light meson decay constants and hyperfine splittings with the heavy-HISQ method

    hep-lat 2025-02 conditional novelty 7.0 of 10

    A heavy-HISQ lattice QCD calculation yields vector, tensor, and pseudoscalar decay-constant ratios and hyperfine splittings for D(s) and B(s) mesons, including first lattice results for B*_(s) tensor decay constants.

  3. Update of HPQCD $B_c\to J/\psi$ Form Factors

    hep-lat 2025-01 conditional novelty 6.0 of 10

    A lattice QCD update determines B_c to J/psi vector, axial-vector, and new tensor form factors with roughly twice the previous precision.

  4. Hadronic vacuum polarization for the muon $g-2$ from lattice QCD: Long-distance and full light-quark connected contribution

    hep-lat 2024-12 conditional novelty 6.0 of 10

    The light-quark connected hadronic vacuum polarization contribution to muon g-2 is determined to 0.69% precision, 655.2(4.5) x 10^-10, from lattice QCD.

  5. Hadronic vacuum polarization for the muon $g-2$ from lattice QCD: Complete short and intermediate windows

    hep-lat 2024-11 conditional novelty 6.0 of 10

    The complete short- and intermediate-distance hadronic vacuum polarization contributions to the muon g-2 are computed on the lattice with 0.31% and 0.36% total errors.

Reference graph

Works this paper leans on

47 extracted references · 16 canonical work pages · cited by 5 Pith papers

  1. [11]

    Wilson’s Operator Expansion: Can It Fail?

    V. A. Novikov, Mikhail A. Shifman, A. I. Vainshtein, and Valentin I. Zakharov, “Wilson’s Operator Expansion: Can It Fail?” Nucl. Phys. B249, 445–471 (1985), [Yad. Fiz.41,1063(1985)]

    work page 1985

  2. [1]

    How to calculate these tree-level factors is dis- cussed in [21]

    We therefore need to divide by the tree-level matrix element for the conserved current that we denote here V cons γµ⊗I. How to calculate these tree-level factors is dis- cussed in [21]. We have V cons γ⊗I = ∏ µ (9 8cos(apµ(S−T )µ)− 1 8cos(3apµ(S−T )µ) ) . (24) The spin-taste 4-vector S−T is composed of 1s and 0s. For the taste-singlet vector it takes valu...

    work page

  3. [2]

    Column 3 gives results using the RI-SMOM scheme

    on gluon field configurations at different lattice spacing values (denoted by the set number in column 1). Column 3 gives results using the RI-SMOM scheme. Set µ [GeV] Z 1link V (SMOM) 1 1 0.9617(11) 2 1 0.9713(19) 1 2 0.93516(16) 2 2 0.94966(20) 6 2 0.96695(11) 7 2 0.97996(34) 2 2.5 0.94236(11) 2 3 0.939193(87) 6 3 0.954643(37) 7 3 0.97225(12) 6 4 0.948641(...

    work page

  4. [3]

    High-precision determination of the light-quark masses from realistic lattice QCD,

    Quentin Mason, Howard D. Trottier, Ron Horgan, Chris- tine T. H. Davies, and G. Peter Lepage (HPQCD), “High-precision determination of the light-quark masses from realistic lattice QCD,” Phys. Rev. D73, 114501 (2006), arXiv:hep-ph/0511160 [hep-ph]

    arXiv 2006

  5. [4]

    Determination of quark masses from nf = 4 lattice QCD and the RI-SMOM in- termediate scheme,

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

    arXiv 2018

  6. [5]

    On-shell Improved Lattice Action for QCD With Susskind Fermions and Asymptotic Free- dom Scale,

    Satchidananda Naik, “On-shell Improved Lattice Action for QCD With Susskind Fermions and Asymptotic Free- dom Scale,” Nucl. Phys. B316, 238–268 (1989)

    work page 1989

  7. [6]

    Highly improved staggered quarks on the lattice, with applications to charm physics,

    E. Follana, Q. Mason, C. Davies, K. Hornbostel, G. P. Lepage, J. Shigemitsu, H. Trottier, and K. Wong (HPQCD, UKQCD), “Highly improved staggered quarks on the lattice, with applications to charm physics,” Phys. Rev. D75, 054502 (2007), arXiv:hep-lat/0610092 [hep- lat]

    arXiv 2007

  8. [7]

    High Precision de- termination of the pi, K, D and D(s) decay constants from lattice QCD,

    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]

    arXiv 2008

Show all 47 references
  1. [8]

    Precision tests of theJ/ψ from full lat- tice QCD: mass, leptonic width and radiative decay rate toηc,

    G. C. Donald, C. T. H. Davies, R. J. Dowdall, E. Follana, K. Hornbostel, J. Koponen, G. P. Lepage, and C. Mc- Neile (HPQCD), “Precision tests of theJ/ψ from full lat- tice QCD: mass, leptonic width and radiative decay rate toηc,” Phys. Rev. D86, 094501 (2012), arXiv:1208.2855 ...

    2012 arXiv

  2. [9]

    Vcs from Ds → φ𝓁ν semileptonic decay and full lattice QCD,

    G. C. Donald, C. T. H. Davies, J. Koponen, and G. P. Lepage (HPQCD), “ Vcs from Ds → φ𝓁ν semileptonic decay and full lattice QCD,” Phys. Rev. D90, 074506 (2014), arXiv:1311.6669 [hep-lat]

    2014 arXiv

  3. [10]

    Prediction of the D∗ s width from a calculation of its radiative decay in full lattice QCD,

    G. C. Donald, C. T. H. Davies, J. Koponen, and G. P. Lepage (HPQCD), “Prediction of the D∗ s width from a calculation of its radiative decay in full lattice QCD,” Phys. Rev. Lett. 112, 212002 (2014), arXiv:1312.5264 [hep-lat]

    2014 arXiv

  4. [12]

    Three Topics in Renormaliza- tion and Improvement,

    Anastassios Vladikas, “Three Topics in Renormaliza- tion and Improvement,” in Modern perspectives in lattice QCD: Quantum field theory and high performance com- puting. Proceedings, International School, 93rd Session, Les Houches, France, August 3-28, 2009 (2011) pp. 161– 222, ...

    2011 arXiv

  5. [13]

    Nonperturba- tive comparison of clover and highly improved staggered quarks in lattice QCD and the properties of the φ me- son,

    Bipasha Chakraborty, C. T. H. Davies, G. C. Donald, J. Koponen, and G. P. Lepage (HPQCD), “Nonperturba- tive comparison of clover and highly improved staggered quarks in lattice QCD and the properties of the φ me- son,” Phys. Rev. D96, 074502 (2017), arXiv:1703.05552 [hep-lat]

    2017 arXiv

  6. [14]

    A general method for non- perturbative renormalization of lattice operators,

    G. Martinelli, C. Pittori, Christopher T. Sachrajda, M. Testa, and A. Vladikas, “A general method for non- perturbative renormalization of lattice operators,” Nucl. Phys. B445, 81–108 (1995), arXiv:hep-lat/9411010 [hep- lat]

    1995 arXiv

  7. [15]

    Renormalization and running of quark mass and field in the regulariza- tion invariant and MS-bar schemes at three loops and four loops,

    K. G. Chetyrkin and A. Retey, “Renormalization and running of quark mass and field in the regulariza- tion invariant and MS-bar schemes at three loops and four loops,” Nucl. Phys. B583, 3–34 (2000), arXiv:hep- ph/9910332 [hep-ph]

    2000

  8. [16]

    Non-perturbative renormalization of quark bilinear operators and B(K) using do- main wall fermions,

    Y. Aoki et al. , “Non-perturbative renormalization of quark bilinear operators and B(K) using do- main wall fermions,” Phys. Rev. D78, 054510 (2008), arXiv:0712.1061 [hep-lat]

    2008 arXiv

  9. [17]

    Renormalization of quark bi- linear operators in a momentum-subtraction scheme with a nonexceptional subtraction point,

    C. Sturm, Y. Aoki, N. H. Christ, T. Izubuchi, C. T. C. Sachrajda, and A. Soni, “Renormalization of quark bi- linear operators in a momentum-subtraction scheme with a nonexceptional subtraction point,” Phys. Rev. D80, 014501 (2009), arXiv:0901.2599 [hep-ph]

    2009 arXiv

  10. [18]

    Nonperturbative renormalization of compos- ite operators in lattice QCD,

    M. Gockeler, R. Horsley, H. Oelrich, H. Perlt, D. Pet- ters, Paul E. L. Rakow, A. Schafer, G. Schierholz, and A. Schiller, “Nonperturbative renormalization of compos- ite operators in lattice QCD,” Nucl. Phys. B544, 699– 733 (1999), arXiv:hep-lat/9807044 [hep-lat]

    1999 arXiv

  11. [19]

    Renormalization con- stants of quark operators for the nonperturbatively im- proved Wilson action,

    D. Becirevic, V. Gimenez, V. Lubicz, G. Martinelli, M. Papinutto, and J. Reyes, “Renormalization con- stants of quark operators for the nonperturbatively im- proved Wilson action,” JHEP 08, 022 (2004), arXiv:hep- lat/0401033 [hep-lat]

    2004

  12. [20]

    Non-perturbative renor- malization of quark bilinear operators with Nf = 2 20 (tmQCD) Wilson fermions and the tree-level improved gauge action,

    M. Constantinou et al. (ETM), “Non-perturbative renor- malization of quark bilinear operators with Nf = 2 20 (tmQCD) Wilson fermions and the tree-level improved gauge action,” JHEP 08, 068 (2010), arXiv:1004.1115 [hep-lat]

    2010 arXiv

  13. [21]

    Lattice Fermions: Species Doubling, Chiral Invariance, and the Triangle Anomaly,

    Luuk H. Karsten and Jan Smit, “Lattice Fermions: Species Doubling, Chiral Invariance, and the Triangle Anomaly,” Nucl. Phys. B183, 103 (1981), [,495(1980)]

    1981

  14. [22]

    Chiral Symme- try on the Lattice with Wilson Fermions,

    Marco Bochicchio, Luciano Maiani, Guido Martinelli, Gian Carlo Rossi, and Massimo Testa, “Chiral Symme- try on the Lattice with Wilson Fermions,” Asia Pacific Conf.1987:439, Trieste Electroweak 1985:25, Nucl. Phys. B262, 331 (1985)

    1985

  15. [23]

    Nonperturba- tive renormalization for improved staggered bilinears,

    Andrew T. Lytle and Stephen R. Sharpe, “Nonperturba- tive renormalization for improved staggered bilinears,” Phys. Rev. D88, 054506 (2013), arXiv:1306.3881 [hep- lat]

    2013 arXiv

  16. [24]

    Scaling studies of QCD with the dynamical HISQ action,

    A. Bazavov et al. (MILC), “Scaling studies of QCD with the dynamical HISQ action,” Phys. Rev. D82, 074501 (2010), arXiv:1004.0342 [hep-lat]

    2010 arXiv

  17. [25]

    Lattice QCD ensembles with four flavors of highly improved staggered quarks,

    A. Bazavov et al. (MILC), “Lattice QCD ensembles with four flavors of highly improved staggered quarks,” Phys. Rev. D87, 054505 (2013), arXiv:1212.4768 [hep-lat]

    2013 arXiv

  18. [26]

    Radiative corrections to the lattice gluon action for HISQ improved staggered quarks and the effect of such corrections on the static potential,

    A. Hart, G. M. von Hippel, and R. R. Horgan (HPQCD), “Radiative corrections to the lattice gluon action for HISQ improved staggered quarks and the effect of such corrections on the static potential,” Phys. Rev. D79, 074008 (2009), arXiv:0812.0503 [hep-lat]

    2009 arXiv

  19. [27]

    High-precision scale setting in lattice QCD,

    Szabolcs Borsanyi, Stephan Durr, Zoltan Fodor, Chris- tian Hoelbling, Sandor D. Katz, et al. , “High-precision scale setting in lattice QCD,” JHEP 1209, 010 (2012), arXiv:1203.4469 [hep-lat]

    2012 arXiv

  20. [28]

    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. Mc- Neile (HPQCD), “Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks,” Phys.Rev. D88, 074504 (2013), arXiv:1303.1670 [hep- lat]

    2013 arXiv

  21. [29]

    High-precision quark masses and QCD coupling from nf = 4 lattice QCD,

    Bipasha Chakraborty, C. T. H. Davies, B. Galloway, P. Knecht, J. Koponen, G. C. Donald, R. J. Dow- dall, G. P. Lepage, and C. McNeile (HPQCD), “High-precision quark masses and QCD coupling from nf = 4 lattice QCD,” Phys. Rev. D91, 054508 (2015), arXiv:1408.4169 [hep-lat]

    2015 arXiv

  22. [30]

    Lattice study of semileptonic form-factors with twisted boundary conditions,

    D. Guadagnoli, F. Mescia, and S. Simula, “Lattice study of semileptonic form-factors with twisted boundary conditions,” Phys.Rev. D73, 114504 (2006), arXiv:hep- lat/0512020 [hep-lat]

    2006

  23. [31]

    Step Scal- ing with off-shell renormalisation,

    R. Arthur and P. A. Boyle (RBC, UKQCD), “Step Scal- ing with off-shell renormalisation,” Phys. Rev. D83, 114511 (2011), arXiv:1006.0422 [hep-lat]

    2011 arXiv

  24. [32]

    Renormalization factors of quark bilin- ears using the DCI operator with dynamical quarks,

    Philipp Huber, “Renormalization factors of quark bilin- ears using the DCI operator with dynamical quarks,” JHEP 11, 107 (2010), arXiv:1003.3496 [hep-lat]

    2010 arXiv

  25. [33]

    Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three,

    K. G. Chetyrkin and A. Maier, “Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three,” JHEP 01, 092 (2010), arXiv:0911.0594 [hep-ph]

    2010 arXiv

  26. [34]

    Constrained curve fitting,

    G. P. Lepage, B. Clark, C. T. H. Davies, K. Horn- bostel, P. B. Mackenzie, C. Morningstar, and H. Trot- tier, “Constrained curve fitting,”Lattice field theory. Pro- ceedings, 19th International Symposium, Lattice 2001, Berlin, Germany, August 19-24, 2001 , Nucl. Phys. Proc. Supp...

    2002 arXiv

  27. [35]

    Strange and charm quark contributions to the anomalous magnetic moment of the muon,

    Bipasha Chakraborty, C. T. H. Davies, G. C. Donald, R. J. Dowdall, J. Koponen, G. P. Lepage, and T. Teub- ner (HPQCD), “Strange and charm quark contributions to the anomalous magnetic moment of the muon,” Phys. Rev. D89, 114501 (2014), arXiv:1403.1778 [hep-lat]

    2014 arXiv

  28. [36]

    Perturbative corrections for staggered four fermion operators,

    Stephen R. Sharpe and Apoorva Patel, “Perturbative corrections for staggered four fermion operators,” Nucl. Phys. B417, 307–356 (1994), arXiv:hep-lat/9310004 [hep-lat]

    1994 arXiv

  29. [37]

    Hadronic-vacuum-polarization contri- bution to the muon’s anomalous magnetic moment from four-flavor lattice QCD,

    C. T. H. Davies et al. (Fermilab Lattice, LATTICE- HPQCD, MILC), “Hadronic-vacuum-polarization contri- bution to the muon’s anomalous magnetic moment from four-flavor lattice QCD,” (2019), arXiv:1902.04223 [hep- lat]

    2019 arXiv

  30. [38]

    Isospin breaking cor- rections to meson masses and the hadronic vacuum po- larization: a comparative study,

    P. Boyle, V. G¨ ulpers, J. Harrison, A. J¨ uttner, C. Lehner, A. Portelli, and C. T. Sachrajda, “Isospin breaking cor- rections to meson masses and the hadronic vacuum po- larization: a comparative study,” JHEP 09, 153 (2017), arXiv:1706.05293 [hep-lat]

    2017 arXiv

  31. [39]

    Electromagnetic and strong isospin-breaking corrections to the muong−2 from Lattice QCD+QED,

    D. Giusti, V. Lubicz, G. Martinelli, F. Sanfilippo, and S. Simula, “Electromagnetic and strong isospin-breaking corrections to the muong−2 from Lattice QCD+QED,” Phys. Rev. D99, 114502 (2019), arXiv:1901.10462 [hep- lat]

    2019 arXiv

  32. [40]

    One loop calculation of the renormalized anisotropy for improved anisotropic gluon actions on a lattice,

    I. T. Drummond, A. Hart, R. R. Horgan, and L. C. Storoni, “One loop calculation of the renormalized anisotropy for improved anisotropic gluon actions on a lattice,” Phys. Rev. D66, 094509 (2002), arXiv:hep- lat/0208010 [hep-lat]

    2002

  33. [41]

    Electromag- netic splittings and light quark masses in lattice QCD,

    A. Duncan, E. Eichten, and H. Thacker, “Electromag- netic splittings and light quark masses in lattice QCD,” Phys. Rev. Lett. 76, 3894–3897 (1996), arXiv:hep- lat/9602005 [hep-lat]

    1996

  34. [42]

    QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons,

    Masashi Hayakawa and Shunpei Uno, “QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons,” Prog. Theor. Phys. 120, 413–441 (2008), arXiv:0804.2044 [hep-ph]

    2008 arXiv

  35. [43]

    QED Corrections to Hadronic Ob- servables,

    Agostino Patella, “QED Corrections to Hadronic Ob- servables,” Proceedings, 34th International Symposium on Lattice Field Theory (Lattice 2016): Southampton, UK, July 24-30, 2016 , PoS LA TTICE2016, 020 (2017), arXiv:1702.03857 [hep-lat]

    2017 arXiv

  36. [44]

    Elec- tromagnetic corrections to light hadron masses,

    A. Portelli et al. (Budapest-Marseille-Wuppertal), “Elec- tromagnetic corrections to light hadron masses,”Proceed- ings, 28th International Symposium on Lattice field the- ory (Lattice 2010): Villasimius, Italy, June 14-19, 2010 , PoS LA TTICE2010, 121 (2010), arXiv:1011.4189 [...

    2010 arXiv

  37. [45]

    Perturbation theory versus simulation for tadpole improvement factors in pure gauge theories,

    A. Hart, R. R. Horgan, and L. C. Storoni, “Perturbation theory versus simulation for tadpole improvement factors in pure gauge theories,” Phys. Rev. D70, 034501 (2004), arXiv:hep-lat/0402033 [hep-lat]

    2004 arXiv

  38. [46]

    Theoretical as- pects of quantum electrodynamics in a finite volume with periodic boundary conditions,

    Zohreh Davoudi, James Harrison, Andreas J¨ uttner, An- tonin Portelli, and Martin J. Savage, “Theoretical as- pects of quantum electrodynamics in a finite volume with periodic boundary conditions,” Phys. Rev. D99, 034510 (2019), arXiv:1810.05923 [hep-lat]

    2019 arXiv

  39. [47]

    On the via- bility of lattice perturbation theory,

    G. Peter Lepage and Paul B. Mackenzie, “On the via- bility of lattice perturbation theory,” Phys. Rev. D48, 2250–2264 (1993), arXiv:hep-lat/9209022 [hep-lat]

    1993 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.