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

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

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

Phys. Rev. D 98, 054517 – Published 27 September 2018

Abstract

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 $a \approx 0.15$ 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 $\bar{MS}$ -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 $α_{s}^{4}$ . As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: ${\bar{Λ}}_{MRS} = 555 (31) MeV$ in the minimal renormalon-subtracted (MRS) scheme, $μ_{π}^{2} = 0.05 (22) {GeV}^{2}$ , and $μ_{G}^{2} (m_{b}) = 0.38 (2) {GeV}^{2}$ . The MRS scheme [Phys. Rev. D 97, 034503 (2018)] is the key new aspect of our method.

Received 16 February 2018

DOI:https://doi.org/10.1103/PhysRevD.98.054517

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Mass

Particles & Fields

Authors & Affiliations

A. Bazavov¹, C. Bernard^2,*, N. Brambilla^3,4,†, N. Brown², C. DeTar⁵, A. X. El-Khadra^6,7, E. Gámiz⁸, Steven Gottlieb⁹, U. M. Heller¹⁰, J. Komijani^3,4,11,‡, A. S. Kronfeld^7,4,§, J. Laiho¹², P. B. Mackenzie⁷, E. T. Neil^13,14, J. N. Simone⁷, R. L. Sugar¹⁵, D. Toussaint^16,∥, A. Vairo^3,¶, and R. S. Van de Water⁷ (Fermilab Lattice, MILC, and TUMQCD Collaborations)

¹Department of Computational Mathematics, Science and Engineering, and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
²Department of Physics, Washington University, St. Louis, Missouri 63130, USA
³Physik-Department, Technische Universität München, 85748 Garching, Germany
⁴Institute for Advanced Study, Technische Universität München, 85748 Garching, Germany
⁵Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
⁶Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
⁷Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
⁸CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada, E-18071 Granada, Spain
⁹Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
¹⁰American Physical Society, One Research Road, Ridge, New York 11961, USA
¹¹School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
¹²Department of Physics, Syracuse University, Syracuse, New York 13244, USA
¹³Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
¹⁴RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA
¹⁵Department of Physics, University of California, Santa Barbara, California 93106, USA
¹⁶Physics Department, University of Arizona, Tucson, Arizona 85721, USA

^*cb@lump.wustl.edu
^†nora.brambilla@ph.tum.de
^‡javad.komijani@glasgow.ac.uk
^§ask@fnal.gov
^∥doug@physics.arizona.edu
^¶antonio.vairo@tum.de

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Issue

Vol. 98, Iss. 5 — 1 September 2018

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