Light-quark masses from unquenched lattice QCD

Abstract

We calculate the light meson spectrum and the light quark masses by lattice QCD simulation, treating all light quarks dynamically and employing the Iwasaki gluon action and the nonperturbatively O(a)-improved Wilson quark action. The calculations are made at the squared lattice spacings at an equal distance a 2 ≃ 0.005, 0.01 and 0.015 fm 2 , and the continuum limit is taken assuming an O(a 2 ) discretization error. The light meson spectrum is consistent with experiment. The up, down and strange quark masses in the MS scheme at 2 GeV are m = (mu + m d )/2 = 3.55 The masses of light quarks are fundamental parameters of QCD. They cannot be measured experimentally since quarks are confined in hadrons. Lattice QCD enables calculations of hadron masses as functions of quark masses, and hence allows a determination of the quark masses from the experimental hadron masses. This approach has been successfully applied, first in quenched QCD [1] and then in N f = 2 QCD where degenerate up (u) and down (d) quarks are treated dynamically [2]. These studies have revealed that the light quark mass values are significantly reduced by dynamical u and d quark effects. In this article, we present our attempt to determine the quark masses in N f = 2 + 1 QCD where the heavier strange (s) quark is also treated dynamically. We wish to examine to what extent the dynamical s quark affects the light quark masses. We determine the quark masses in the continuum limit and estimate all possible systematic errors. We also calculate the prerequisite light meson spectrum. A similar attempt has been made by the MILC Collaboration [3].We adopt the Iwasaki RG gauge action [4] and the clover quark action with the improvement coefficient c SW determined nonperturbatively for the RG action [5]. The choice of the gauge action is made to avoid a first-order phase transition (lattice artifact) observed for the plaquette gauge action [6]. We employed the Wilson quark formalism because we prefer an unambiguous quark-flavor interpretation over the computational ease of the staggered formalism adopted by the MILC collaboration [7].Configurations are generated at three values of the coupling β ≡ 6/g 2 = 2.05, 1.90 and 1.83 corresponding to the squared lattice spacing a 2 ≃ 0.005, 0.01 and 0.015 fm 2 , with the physical volume fixed to about (2.0fm) 3 . At each β, we perform simulations for 10 quark mass combinations using a combined algorithm [8] of the Hybrid Monte Carlo (HMC) for the degenerate u and d quarks and the polynomial Hybrid Monte Calro (PHMC) for the s quark. Table I summarizes the simulation parameters.The meson and quark masses at the simulation points are determined from single exponential correlated χ 2 fits to the correlators P (t)P (0) , V (t)V (0) and A 4 (t)P (0) , where P , V and A µ denote pseudoscalar, vector and nonperturbatively O(a)-improved [9] axialvector current operators, respectively. We use an exponentially smeared source and a point sink, and measurements are made at every 10 HMC trajectories in the Coulomb gauge. For the pse...

Precise determination of the strong coupling constant inNf= 2+1 lattice QCD with the Schrödinger functional scheme

“…1 These results agree with each other and we adopt the constant fit with three data points for our final results since there is almost no scaling violation. Our final results are where the first parenthesis is statistical error and the second is systematic error of perturbative matching of different flavors, which is estimated as a difference between results with three-and two-loop matching relation for (3.12) and may be overestimated.…”

“…A physical scale is introduced from the previous N f = 2 + 1 simulation of the CP-PACS/JL-QCD collaboration [1], which covered the up-down quark mass range heavier than m π ∼ 500 MeV. Our final result is α MS (M Z ) = 0.12047(81)(48)( +0 −173 ) and Λ (N f =5) MS …”

“…[18,21] and evaluate the strong coupling constant in N f = 2 + 1 QCD. For setting the physical scale we employ a recent large-scale N f = 2 + 1 lattice QCD simulation employing non-perturbatively O(a) improved Wilson quark action; the work of CP-PACS/JL-QCD Collaboration with relatively heavy pion mass with m π ∼ 500 MeV [1].…”

“…JHEP10 (2009) [1]. Three values of β, 1.83, 1.90 and 2.05 were adopted to take the continuum limit and the up-down quark mass covered a rather heavy region corresponding to m π /m ρ = 0.63 − 0.78.…”

“…The physical scale is introduced from the spectrum simulations of CP-PACS/JLQCD collaboration [1] through the hadron masses m π , m K , m Ω . From these inputs we evaluated (6.1) and (6.2), where all the statistical and systematic errors are included.…”