Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD
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Fermilab Lattice, M. I. L. C., Collaborations, T. U. M. Q. C. D., Bazavov, A., Bernard, C., Brambilla, N., Brown, N., ... & Heller, U. M. (2018). Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD. Physical Review D, 98(5), 054517.
SponsorshipThis work was supported in part by the U.S. Department of Energy under Grants No. DEFG02- 91ER40628 (C. B., N. B.), No. DE-FC02- 12ER41879 (C. D.), No. DE-SC0010120 (S. G.), No. DE-FG02-91ER40661 (S. G.), No. DE-FG02- 13ER42001 (A. X. K.), No. DE-SC0015655 (A. X. K.), No. DE-SC0010005 (E. T. N.), No. DE-FG02- 13ER41976 (D. T.); by the U.S. National Science Foundation under Grants No. PHY14-14614 and No. PHY17-19626 (C. D.), PHY14-17805 (J. L.), and PHY13-16748 and PHY16-20625 (R. S.); by the MINECO (Spain) under Grants No. FPA2013-47836-C- 1-P and No. FPA2016-78220-C3-3-P (E. G.); by the Junta de Andalucía (Spain) under Grant No. FQM-101 (E. G.); by the DFG cluster of excellence “Origin and Structure of the Universe” (N. B., A. V.); by the UK Science and Technology Facilities Council (J. K.); by the German Excellence Initiative and the European Union Seventh Framework Program under Grant Agreement No. 291763 as well as the European Union’s Marie Curie COFUND program (J. K., A. S. K.). Brookhaven National Laboratory is supported by the United States Department of Energy, Office of Science, Office of High Energy Physics, under Contract No. DE-SC0012704. This document was prepared by the Fermilab Lattice, MILC, and TUMQCD Collaborations using the resources of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DEAC02- 07CH11359.
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 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 αs4. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: Λ¯MRS=555(31) MeV in the minimal renormalon-subtracted (MRS) scheme, μπ2=0.05(22) GeV2, and μG2(mb)=0.38(2) GeV2. The MRS scheme [Phys. Rev. D 97, 034503 (2018)PRVDAQ2470-001010.1103/PhysRevD.97.034503] is the key new aspect of our method.