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

Abstract

Three-flavor lattice QCD simulations and two-loop perturbation theory are used to make the most precise determination to date of the strange-, up-, and down-quark masses, m{sub s}, m{sub u}, and m{sub d}, respectively. Perturbative matching is required in order to connect the lattice-regularized bare-quark masses to the masses as defined in the MS scheme, and this is done here for the first time at next-to-next-to leading (or two-loop) order. The bare-quark masses required as input come from simulations by the MILC collaboration using so-called staggered quarks, with three flavors of light quarks in the Dirac sea; these simulations were previously analyzed in a joint study by the HPQCD and MILC collaborations, using degenerate u and d quarks, with masses as low as m{sub s}/8, and two values of the lattice spacing, with chiral extrapolation/interpolation to the physical masses. With the new perturbation theory presented here, the resulting MS masses are m{sub s}{sup MS}(2 GeV)=87(0)(4)(4)(0) MeV, and m-circumflex{sup MS}(2 GeV)=3.2(0)(2)(2)(0) MeV, where m-circumflex=(1/2)(m{sub u}+m{sub d}) is the average of the u and d masses. The respective uncertainties are from statistics, simulation systematics, perturbation theory, and electromagnetic/isospin effects. The perturbative errors are about a factor of 2 smaller than in an earliermore » study using only one-loop perturbation theory. Using a recent determination of the ratio m{sub u}/m{sub d}=0.43(0)(1)(0)(8) due to the MILC collaboration, these results also imply m{sub u}{sup MS}(2 GeV)=1.9(0)(1)(1)(2) MeV and m{sub d}{sup MS}(2 GeV)=4.4(0)(2)(2)(2) MeV. A technique for estimating the next order in the perturbative expansion is also presented, which uses input from simulations at more than one lattice spacing; this method is used here in the estimate of the systematic uncertainties.« less