Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD

Bazavov, A.; Bernard, C.; Brambilla, N.; Brown, N.; DeTar, C.; El-Khadra, A. X.; Gámiz, E.; Gottlieb, Steven; Heller, U. M.; Komijani, J.; Kronfeld, A. S.; Laiho, J.; Mackenzie, P. B.; Neil, E. T.; Simone, J. N.; Sugar, R. L.; Toussaint, D.; Vairo, A.; Van de Water, R. S.

doi:10.1103/PhysRevD.98.054517

Title: Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD

Abstract

Here, we calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice spacings ranging from a≈0.15 to 0.03 fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. Our results for the $$ \overline{MS}\ $$-renormalized masses are m_u(2 GeV)=2.130(41) MeV, m_d(2 GeV)=4.675(56) MeV, m_s(2 GeV)=92.47(69) MeV, m_c(3 GeV)=983.7(5.6) MeV, and m_c(m_c)=1273(10) MeV, with four active flavors; and m_b(m_b)=4195(14) MeV with five active flavors. We also obtain ratios of quark masses m_c/m_s=11.783(25), m_b/m_s=53.94(12), and m_b/m_c=4.578(8). The result for m_c matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of α $\frac{4}{s}$ . As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: $$ \overline{Λ}\ $$_MRS=555(31) MeV in the minimal renormalon-subtracted (MRS) scheme, μ $\frac{2}{π}$ =0.05(22) GeV², and μ $\frac{2}{G}$ (m_b)=0.38(2) GeV². The MRS scheme is the key new aspect of our method.

Publication Date:: Thu Sep 27 00:00:00 EDT 2018

Research Org.:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

Contributing Org.:: Fermilab Lattice, MILC, and TUMQCD Collaborations

OSTI Identifier:: 1474191

Alternate Identifier(s):: OSTI ID: 1422192

Report Number(s):: arXiv:1802.04248; FERMILAB-PUB-17-492-T; TUM-EFT-107-18; FERMILAB-PUB-17/492-T; TUM-EFT-107/18
Journal ID: ISSN 2470-0010; PRVDAQ; 054517

Grant/Contract Number:: AC02-05CH11231; AC02-06CH11357; FG02-91ER40628; FC02-12ER41879; SC0010120; FG02-91ER40661; FG02-13ER42001; SC0015655; SC0010005; FG02-13ER41976; SC0012704; AC02-07CH11359

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 5; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Bazavov, A., Bernard, C., Brambilla, N., Brown, N., DeTar, C., El-Khadra, A. X., Gámiz, E., Gottlieb, Steven, Heller, U. M., Komijani, J., Kronfeld, A. S., Laiho, J., Mackenzie, P. B., Neil, E. T., Simone, J. N., Sugar, R. L., Toussaint, D., Vairo, A., Van de Water, R. S., and Fermilab Lattice, MILC, and TUMQCD Collaborations. Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.98.054517.

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                    Bazavov, A., Bernard, C., Brambilla, N., Brown, N., DeTar, C., El-Khadra, A. X., Gámiz, E., Gottlieb, Steven, Heller, U. M., Komijani, J., Kronfeld, A. S., Laiho, J., Mackenzie, P. B., Neil, E. T., Simone, J. N., Sugar, R. L., Toussaint, D., Vairo, A., Van de Water, R. S., & Fermilab Lattice, MILC, and TUMQCD Collaborations. Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD.  United States.  https://doi.org/10.1103/PhysRevD.98.054517

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                    Bazavov, A., Bernard, C., Brambilla, N., Brown, N., DeTar, C., El-Khadra, A. X., Gámiz, E., Gottlieb, Steven, Heller, U. M., Komijani, J., Kronfeld, A. S., Laiho, J., Mackenzie, P. B., Neil, E. T., Simone, J. N., Sugar, R. L., Toussaint, D., Vairo, A., Van de Water, R. S., and Fermilab Lattice, MILC, and TUMQCD Collaborations. Thu .  
"Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD".  United States.  https://doi.org/10.1103/PhysRevD.98.054517.

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@article{osti_1474191,

  title        = {Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD},

  author       = {Bazavov, A. and Bernard, C. and Brambilla, N. and Brown, N. and DeTar, C. and El-Khadra, A. X. and Gámiz, E. and Gottlieb, Steven and Heller, U. M. and Komijani, J. and Kronfeld, A. S. and Laiho, J. and Mackenzie, P. B. and Neil, E. T. and Simone, J. N. and Sugar, R. L. and Toussaint, D. and Vairo, A. and Van de Water, R. S. and Fermilab Lattice, MILC, and TUMQCD Collaborations},

  abstractNote = {Here, we calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice spacings ranging from a≈0.15 to 0.03 fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. Our results for the $ \overline{MS}\ $-renormalized masses are mu(2 GeV)=2.130(41) MeV, md(2 GeV)=4.675(56) MeV, ms(2 GeV)=92.47(69) MeV, mc(3 GeV)=983.7(5.6) MeV, and mc(mc)=1273(10) MeV, with four active flavors; and mb(mb)=4195(14) MeV with five active flavors. We also obtain ratios of quark masses mc/ms=11.783(25), mb/ms=53.94(12), and mb/mc=4.578(8). The result for mc matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of α4s. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: $ \overline{Λ}\ $MRS=555(31) MeV in the minimal renormalon-subtracted (MRS) scheme, μ2π=0.05(22) GeV2, and μ2G(mb)=0.38(2) GeV2. The MRS scheme is the key new aspect of our method.},

  doi          = {10.1103/PhysRevD.98.054517},

  journal      = {Physical Review D},

  number       = 5,

  volume       = 98,

  place        = {United States},

  year         = {Thu Sep 27 00:00:00 EDT 2018},

  month        = {Thu Sep 27 00:00:00 EDT 2018}

}

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Highly improved staggered quarks on the lattice with applications to charm physics
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Charm and bottom quark masses: An update
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Boyd, C. Glenn; Grinstein, Benjamín
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Beneke, M.; Maier, A.; Piclum, J.
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Mass of the bottom quark from Upsilon(1S) at NNNLO: an update
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Index Theorem and Universality Properties of the Low-Lying Eigenvalues of Improved Staggered Quarks
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Continuum limit improved lattice action for pure Yang-Mills theory (II)
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Weisz, P.; Wohlert, R.
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Dürr, Stephan; Hoelbling, Christian
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Bussone, A.; Carrasco, N.; Dimopoulos, P.
Physical Review D, Vol. 93, Issue 11
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Blum, T.; Boyle, P. A.; Christ, N. H.
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Physical Review D, Vol. 47, Issue 1
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Works referencing / citing this record:

| V u s | from K ℓ 3 decay and four-flavor lattice QCD
journal, June 2019

Bazavov, A.; Bernard, C.; DeTar, C.
Physical Review D, Vol. 99, Issue 11
DOI: 10.1103/physrevd.99.114509

Determination of the quark condensate from heavy-light current-current correlators in full lattice QCD
journal, August 2019

Davies, C. T. H.; Hornbostel, K.; Komijani, J.
Physical Review D, Vol. 100, Issue 3
DOI: 10.1103/physrevd.100.034506

| V u s | from K ℓ 3 decay and four-flavor lattice QCD
journal, June 2019

Bazavov, A.; Bernard, C.; DeTar, C.
Physical Review D, Vol. 99, Issue 11
DOI: 10.1103/physrevd.99.114509

Status of isospin splittings in mesons and baryons
journal, October 2019

Karliner, Marek; Rosner, Jonathan L.
Physical Review D, Vol. 100, Issue 7
DOI: 10.1103/physrevd.100.073006

Hyperasymptotic approximation to the top, bottom, and charm pole mass
journal, February 2020

Ayala, Cesar; Lobregat, Xabier; Pineda, Antonio
Physical Review D, Vol. 101, Issue 3
DOI: 10.1103/physrevd.101.034002

Lattice computation of the electromagnetic contributions to kaon and pion masses
journal, February 2019

Basak, S.; Bazavov, A.; Bernard, C.
Physical Review D, Vol. 99, Issue 3
DOI: 10.1103/physrevd.99.034503

Electric dipole moment of ${}^{199}{Hg}$ atom from $P$ , $C P$ -odd electron-nucleon interaction
journal, April 2019

Yanase, K.; Yoshinaga, N.; Higashiyama, K.
Physical Review D, Vol. 99, Issue 7
DOI: 10.1103/physrevd.99.075021

$$b \rightarrow c \tau \nu _{\tau }$$ b → c τ ν τ Decays: a catalogue to compare, constrain, and correlate new physics effects
journal, March 2019

Bhattacharya, Srimoy; Nandi, Soumitra; Patra, Sunando Kumar
The European Physical Journal C, Vol. 79, Issue 3
DOI: 10.1140/epjc/s10052-019-6767-7

FLAG Review 2019
text, January 2019

Aoki, S.; Aoki, Y.; Becirevic, D.
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2020-00055

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Title: Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD

Abstract

Citation Formats

Non-perturbative quark mass renormalization in two-flavor QCD journal, November 2005

A ‘BPS expansion’ for B and D mesons journal, April 2004

Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks journal, October 2014

Review of Particle Physics journal, October 2016

Baryon spectrum with N f = 2 + 1 + 1 twisted mass fermions journal, October 2014

BLM resummation and OPE in heavy flavor transitions journal, April 1997

Short-distance charmonium correlator on the lattice with Möbius domain-wall fermion and a determination of charm quark mass journal, September 2016

Perturbative pole mass in QCD journal, July 1998

Determination of the bottom quark mass from the Υ(1 S ) system journal, May 2001

ϒ and ϒ ′ leptonic widths, a μ b , and m b from full lattice QCD journal, April 2015

High-precision quark masses and QCD coupling from n f = 4 lattice QCD journal, March 2015

The Nielsen identities for the two-point functions of QED and QCD journal, March 1995

Addendum to “Charm and bottom quark masses: An update” journal, December 2017

Relations between heavy-light meson and quark masses journal, February 2018

The bottom quark mass from the ϒ 1 S $$ \boldsymbol{\Upsilon} (1S) $$ system at NNNLO journal, September 2014

Heavy quark effective theory beyond perturbation theory: renormalons, the pole mass and the residual mass term journal, September 1994

Heavy Quark Physics book, January 2009

Strong and electromagnetic mass splittings in heavy mesons journal, June 2007

Fitting parton distribution data with multiplicative normalization uncertainties journal, May 2010

Computation of and λ1 with lattice QCD journal, October 2000

Inclusive semileptonic fits, heavy quark masses, and V c b journal, January 2014

Precision Determination of the Cabibbo-Kobayashi-Maskawa Element V c b journal, February 2015

Bottom quark mass from $ \varUpsilon $ sum rules to $ \mathcal{O}\left( {\alpha_s^3} \right) $ journal, April 2014

Corrigendum to “Determination of m and m from quarkonium 1S energy levels in perturbative QCD” [Phys. Lett. B 752 (2016) 122–127] journal, September 2017

Deep-inelastic scattering beyond the leading order in asymptotically free gauge theories journal, December 1978

Resummation of (ß0αs)n corrections in QCD: techniques and applications to the τ hadronic width and the heavy quark pole mass journal, October 1995

Nonperturbative QCD simulations with 2 + 1 flavors of improved staggered quarks journal, May 2010

Nonperturbative renormalization for improved staggered bilinears journal, September 2013

Locality of the fourth root of the staggered-fermion determinant: Renormalization-group approach journal, February 2005

Lattice QCD ensembles with four flavors of highly improved staggered quarks journal, March 2013

High-precision determination of the light-quark masses from realistic lattice QCD journal, June 2006

Staggered chiral perturbation theory and the fourth-root trick journal, June 2006

Staggered fermions, zero modes, and flavor-singlet mesons journal, September 2011

Charm- and bottom-quark masses from perturbative QCD journal, October 2006

Quarkonium spectroscopy and perturbative QCD: Massive quark-loop effects journal, January 2002

On-shell improved lattice gauge theories journal, September 1985

Observations on staggered fermions at nonzero lattice spacing journal, June 2006

Isospin Splittings in the Light-Baryon Octet from Lattice QCD and QED journal, December 2013

Quark masses and strong coupling constant in 2 + 1 flavor QCD journal, August 2016

Continuum limit and improved action in lattice theories journal, September 1983

Pole mass of the heavy quark: Perturbation theory and beyond journal, August 1994

Bottom and charm mass determinations from global fits to Q Q ¯ $$ Q\overline{Q} $$ bound states at N3LO journal, January 2018

High-precision c and b masses, and QCD coupling from current-current correlators in lattice and continuum QCD journal, August 2010

Determination of m c and m b from quarkonium 1 S energy levels in perturbative QCD journal, January 2016

Mass of the b quark from lattice NRQCD and lattice perturbation theory journal, April 2013

Lattice QCD at the physical point: Light quark masses journal, July 2011

Update: Precision D s decay constant from full lattice QCD using very fine lattices journal, December 2010

Exploring the invisible renormalon: Renormalization of the heavy-quark kinetic energy journal, February 1997

Non-perturbative quark mass renormalization in quenched lattice QCD journal, April 1999

Symanzik's improved lagrangian for lattice gauge theory journal, October 1983

Quark Mass Relations to Four-Loop Order in Perturbative QCD journal, April 2015

Erratum to: “Computation of and λ1 with lattice QCD” journal, December 2000

Staggered eigenvalue mimicry journal, November 2004

Five-Loop Running of the QCD Coupling Constant journal, February 2017

XSEDE: Accelerating Scientific Discovery journal, September 2014

High-precision charm-quark mass and QCD coupling from current-current correlators in lattice and continuum QCD journal, September 2008

Quark mass and field anomalous dimensions to O α s 5 $$ \mathcal{O}\left({\alpha}_s^5\right) $$ journal, October 2014

Scaling tests with dynamical overlap and rooted staggered fermions journal, March 2005

Scalar meson spectroscopy with lattice staggered fermions journal, November 2007

Three-loop chromomagnetic interaction in HQET journal, January 2008

A discussion on leading renormalon in the pole mass journal, August 2017

Radiative corrections to the lattice gluon action for highly improved staggered quarks and the effect of such corrections on the static potential journal, April 2009

MS ¯ -on-shell quark mass relation up to four loops in QCD and a general SU ( N ) gauge group journal, October 2016

B - and D -meson decay constants from three-flavor lattice QCD journal, June 2012

Bottom-quark mass from finite energy QCD sum rules journal, February 2012

Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe journal, March 2007

Highly improved staggered quarks on the lattice with applications to charm physics journal, March 2007

Charm and bottom quark masses: An update journal, October 2009

A general method for non-perturbative renormalization of lattice operators journal, July 1995

Monte Carlo simulation of the massive Schwinger model journal, December 1981

Chiral and heavy quark symmetry violation in B decays journal, May 1995

The bottom-quark mass from non-relativistic sum rules at NNNLO journal, February 2015

Mass of the bottom quark from Upsilon(1S) at NNNLO: an update journal, October 2016

Index Theorem and Universality Properties of the Low-Lying Eigenvalues of Improved Staggered Quarks journal, December 2004

More on ambiguities in the pole mass journal, January 1995

Constrained curve fitting journal, March 2002

Singlet versus nonsinglet perturbative renormalization of fermion bilinears journal, December 2016

Non-perturbative quark mass renormalization in two-flavor QCD
journal, November 2005

A ‘BPS expansion’ for B and D mesons
journal, April 2004

Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks
journal, October 2014

Review of Particle Physics
journal, October 2016

Baryon spectrum with $N_{f} = 2 + 1 + 1$ twisted mass fermions
journal, October 2014

BLM resummation and OPE in heavy flavor transitions
journal, April 1997

Short-distance charmonium correlator on the lattice with Möbius domain-wall fermion and a determination of charm quark mass
journal, September 2016

Perturbative pole mass in QCD
journal, July 1998

Determination of the bottom quark mass from the Υ(1 S ) system
journal, May 2001

$ϒ$ and $ϒ^{'}$ leptonic widths, $a_{μ}^{b}$ , and $m_{b}$ from full lattice QCD
journal, April 2015

High-precision quark masses and QCD coupling from $n_{f} = 4$ lattice QCD
journal, March 2015

The Nielsen identities for the two-point functions of QED and QCD
journal, March 1995

Addendum to “Charm and bottom quark masses: An update”
journal, December 2017

Relations between heavy-light meson and quark masses
journal, February 2018

The bottom quark mass from the ϒ 1 S $$ \boldsymbol{\Upsilon} (1S) $$ system at NNNLO
journal, September 2014

Heavy quark effective theory beyond perturbation theory: renormalons, the pole mass and the residual mass term
journal, September 1994

Heavy Quark Physics
book, January 2009

Strong and electromagnetic mass splittings in heavy mesons
journal, June 2007

Fitting parton distribution data with multiplicative normalization uncertainties
journal, May 2010

Computation of and λ1 with lattice QCD
journal, October 2000

Inclusive semileptonic fits, heavy quark masses, and $V_{c b}$
journal, January 2014

Precision Determination of the Cabibbo-Kobayashi-Maskawa Element $V_{c b}$
journal, February 2015

Bottom quark mass from $ \varUpsilon $ sum rules to $ \mathcal{O}\left( {\alpha_s^3} \right) $
journal, April 2014

Corrigendum to “Determination of m and m from quarkonium 1S energy levels in perturbative QCD” [Phys. Lett. B 752 (2016) 122–127]
journal, September 2017

Deep-inelastic scattering beyond the leading order in asymptotically free gauge theories
journal, December 1978

Resummation of (ß0αs)n corrections in QCD: techniques and applications to the τ hadronic width and the heavy quark pole mass
journal, October 1995

Nonperturbative QCD simulations with $2 + 1$ flavors of improved staggered quarks
journal, May 2010

Nonperturbative renormalization for improved staggered bilinears
journal, September 2013

Locality of the fourth root of the staggered-fermion determinant: Renormalization-group approach
journal, February 2005

Lattice QCD ensembles with four flavors of highly improved staggered quarks
journal, March 2013

High-precision determination of the light-quark masses from realistic lattice QCD
journal, June 2006

Staggered chiral perturbation theory and the fourth-root trick
journal, June 2006

Staggered fermions, zero modes, and flavor-singlet mesons
journal, September 2011

Charm- and bottom-quark masses from perturbative QCD
journal, October 2006

Quarkonium spectroscopy and perturbative QCD: Massive quark-loop effects
journal, January 2002

On-shell improved lattice gauge theories
journal, September 1985

Observations on staggered fermions at nonzero lattice spacing
journal, June 2006

Isospin Splittings in the Light-Baryon Octet from Lattice QCD and QED
journal, December 2013

Quark masses and strong coupling constant in $2 + 1$ flavor QCD
journal, August 2016

Continuum limit and improved action in lattice theories
journal, September 1983

Pole mass of the heavy quark: Perturbation theory and beyond
journal, August 1994

Bottom and charm mass determinations from global fits to Q Q ¯ $$ Q\overline{Q} $$ bound states at N3LO
journal, January 2018

High-precision $c$ and $b$ masses, and QCD coupling from current-current correlators in lattice and continuum QCD
journal, August 2010

Determination of m c and m b from quarkonium 1 S energy levels in perturbative QCD
journal, January 2016

Mass of the $b$ quark from lattice NRQCD and lattice perturbation theory
journal, April 2013

Lattice QCD at the physical point: Light quark masses
journal, July 2011

Update: Precision $D_{s}$ decay constant from full lattice QCD using very fine lattices
journal, December 2010

Exploring the invisible renormalon: Renormalization of the heavy-quark kinetic energy
journal, February 1997

Non-perturbative quark mass renormalization in quenched lattice QCD
journal, April 1999

Symanzik's improved lagrangian for lattice gauge theory
journal, October 1983

Quark Mass Relations to Four-Loop Order in Perturbative QCD
journal, April 2015

Erratum to: “Computation of and λ1 with lattice QCD”
journal, December 2000

Staggered eigenvalue mimicry
journal, November 2004

Five-Loop Running of the QCD Coupling Constant
journal, February 2017

XSEDE: Accelerating Scientific Discovery
journal, September 2014

High-precision charm-quark mass and QCD coupling from current-current correlators in lattice and continuum QCD
journal, September 2008

Quark mass and field anomalous dimensions to O α s 5 $$ \mathcal{O}\left({\alpha}_s^5\right) $$
journal, October 2014

Scaling tests with dynamical overlap and rooted staggered fermions
journal, March 2005

Scalar meson spectroscopy with lattice staggered fermions
journal, November 2007

Three-loop chromomagnetic interaction in HQET
journal, January 2008

A discussion on leading renormalon in the pole mass
journal, August 2017

Radiative corrections to the lattice gluon action for highly improved staggered quarks and the effect of such corrections on the static potential
journal, April 2009

$\bar{MS}$ -on-shell quark mass relation up to four loops in QCD and a general $SU (N)$ gauge group
journal, October 2016

$B$ - and $D$ -meson decay constants from three-flavor lattice QCD
journal, June 2012

Bottom-quark mass from finite energy QCD sum rules
journal, February 2012

Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe
journal, March 2007

Highly improved staggered quarks on the lattice with applications to charm physics
journal, March 2007

Charm and bottom quark masses: An update
journal, October 2009

A general method for non-perturbative renormalization of lattice operators
journal, July 1995

Monte Carlo simulation of the massive Schwinger model
journal, December 1981

Chiral and heavy quark symmetry violation in B decays
journal, May 1995

The bottom-quark mass from non-relativistic sum rules at NNNLO
journal, February 2015

Mass of the bottom quark from Upsilon(1S) at NNNLO: an update
journal, October 2016

Index Theorem and Universality Properties of the Low-Lying Eigenvalues of Improved Staggered Quarks
journal, December 2004

More on ambiguities in the pole mass
journal, January 1995

Constrained curve fitting
journal, March 2002

Singlet versus nonsinglet perturbative renormalization of fermion bilinears
journal, December 2016

Continuum limit improved lattice action for pure Yang-Mills theory (I)
journal, February 1983

On-shell improved lattice gauge theories
journal, March 1985

Effects of staggered fermions and mixed actions on the scalar correlator
journal, January 2006