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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 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 α 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 2 π =0.05(22) GeV2, and μ 2 G (mb)=0.38(2) GeV2. The MRS scheme is the key new aspect of our method.

Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (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.
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. doi:10.1103/PhysRevD.98.054517.
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. doi:10.1103/PhysRevD.98.054517.
@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 = {2018},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
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DOI: 10.1103/PhysRevD.98.054517

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Cited by: 8 works
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Works referenced in this record:

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

  • Breckenridge, J. C.; Lavelle, M. J.; Steele, T. G.
  • Zeitschrift für Physik C Particles and Fields, Vol. 65, Issue 1
  • DOI: 10.1007/BF01571316

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

  • Ayala, César; Cvetič, Gorazd; Pineda, Antonio
  • Journal of High Energy Physics, Vol. 2014, Issue 9
  • DOI: 10.1007/JHEP09(2014)045

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


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


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

  • Ball, Richard D.; Del Debbio, Luigi; Forte, Stefano
  • Journal of High Energy Physics, Vol. 2010, Issue 5
  • DOI: 10.1007/JHEP05(2010)075

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

  • Penin, Alexander A.; Zerf, Nikolai
  • Journal of High Energy Physics, Vol. 2014, Issue 4
  • DOI: 10.1007/JHEP04(2014)120

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


Gluon condensates and precise <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mover accent="true"><mml:mi>m</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mrow><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:math> from QCD-moments and their ratios to order <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msubsup><mml:mi>α</mml:mi><mml:mi>s</mml:mi><mml:mn>3</mml:mn></mml:msubsup></mml:math> and <mml:math altimg="si3.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mo stretchy="false">〈</mml:mo><mml:msup><mml:mi>G</mml:mi><mml:mn>4</mml:mn></mml:msup><mml:mo stretchy="false">〉</mml:mo></mml:math>
journal, January 2012


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

  • Donald, Gordon C.; Davies, Christine T. H.; Follana, Eduardo
  • Physical Review D, Vol. 84, Issue 5
  • DOI: 10.1103/PhysRevD.84.054504

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

  • Lüscher, M.; Weisz, P.
  • Communications in Mathematical Physics, Vol. 98, Issue 3
  • DOI: 10.1007/BF01205792

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


Bottom and charm mass determinations with a convergence test
journal, August 2015

  • Dehnadi, Bahman; Hoang, André H.; Mateu, Vicent
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)155

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


XSEDE: Accelerating Scientific Discovery
journal, September 2014

  • Towns, John; Cockerill, Timothy; Dahan, Maytal
  • Computing in Science & Engineering, Vol. 16, Issue 5
  • DOI: 10.1109/MCSE.2014.80

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

  • Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/JHEP10(2014)076

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


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

  • Marquard, Peter; Smirnov, Alexander V.; Smirnov, Vladimir A.
  • Physical Review D, Vol. 94, Issue 7
  • DOI: 10.1103/PhysRevD.94.074025

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


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

  • Lüscher, M.; Weisz, P.
  • Communications in Mathematical Physics, Vol. 97, Issue 1-2
  • DOI: 10.1007/BF01206178

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


Scaling studies of QCD with the dynamical highly improved staggered quark action
journal, October 2010


Second-order power corrections in the heavy-quark effective theory. I. Formalism and meson form factors
journal, April 1993


On the chromomagnetic expectation value μG2 and higher power corrections in heavy flavor mesons
journal, October 2002


Up, down, strange and charm quark masses with N f = 2 + 1 + 1 twisted mass lattice QCD
journal, October 2014


Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG)
journal, February 2017


Lattice QCD on small computers
journal, November 1995


Charm and strange quark masses and f D s from overlap fermions
journal, August 2015


Computation of the action for on-shell improved lattice gauge theories at weak coupling
journal, August 1985


Up and Down Quark Masses and Corrections to Dashen’s Theorem from Lattice QCD and Quenched QED
journal, August 2016


Erratum to “Non-perturbative quark mass renormalization in quenched lattice QCD” [Nucl. Phys. B 544 (1999) 669]
journal, August 2000


Systematics of staggered fermion spectral properties and topology
journal, May 2005


Effects of nonequilibrated topological charge distributions on pseudoscalar meson masses and decay constants
journal, April 2018


Continuum limit improved lattice action for pure Yang-Mills theory (II)
journal, April 1984


Lattice fermions with complex mass
journal, July 2006


Mass of the b quark and B -meson decay constants from N f = 2 + 1 + 1 twisted-mass lattice QCD
journal, June 2016


Chiral perturbation theory for all-staggered heavy-light mesons
journal, November 2013


Two-loop renormalization of vector, axial-vector, and tensor fermion bilinears on the lattice
journal, May 2009


QCD sum rule determination of the charm-quark mass
journal, April 2011


Domain wall QCD with physical quark masses
journal, April 2016


Decoupling of heavy quarks at four loops and effective Higgs-fermion coupling
journal, June 2015


Meson masses from SU(3) and heavy-quark symmetry
journal, January 1993


QCD phenomenology of static sources and gluonic excitations at short distances
journal, May 2004


    Works referencing / citing this record:

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


    Lattice QCD form factor for B s D s * l ν at zero recoil with nonperturbative current renormalization
    journal, June 2019


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


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


    Lattice QCD form factor for B s D s * l ν at zero recoil with nonperturbative current renormalization
    journal, June 2019


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


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


    B - and D -meson leptonic decay constants from four-flavor lattice QCD
    journal, October 2018


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


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


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


    FLAG Review 2019
    text, January 2019