Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2005-11-14
Phys.Rev.D73:114501,2006
Physics
High Energy Physics
High Energy Physics - Phenomenology
Scientific paper
10.1103/PhysRevD.73.114501
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, $m_s$, $m_u$, and $m_d$, respectively. Perturbative matching is required in order to connect the lattice-regularized bare- quark masses to the masses as defined in the \msbar 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 of a highly-efficient formalism (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 $m_s/8$, and two values of the lattice spacing, with chiral extrapolation/interpolation to the physical masses. With the new perturbation theory presented here, the resulting \msbar\ masses are $m^\msbar_s(2 {GeV}) = 87(0)(4)(4)(0)$ MeV, and $\hat m^\msbar(2 {GeV}) = 3.2(0)(2)(2)(0)$ MeV, where $\hat m = \sfrac12 (m_u + m_d)$ 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 two smaller than in an earlier study using only one-loop perturbation theory. Using a recent determination of the ratio $m_u/m_d = 0.43(0)(1)(0)(8)$ due to the MILC collaboration, these results also imply $m^\msbar_u(2 {GeV}) = 1.9(0)(1)(1)(2)$ MeV and $m^\msbar_d(2 {GeV}) = 4.4(0)(2)(2)(2)$ 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.
Davies Christine. T. H.
Horgan Ronald R.
Lepage Peter G.
Mason Quentin
Trottier Howard D.
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