Light quark masses, chiral condensate and quark–gluon condensate in quenched lattice QCD with exact chiral symmetry

Abstract

We determine several quantities in quenched lattice QCD with exact chiral symmetry. For 100 gauge configurations generated with Wilson gauge action at β=6.0 on the 16 3×32 lattice, we compute quenched quark propagators for 13 bare quark masses. The pion decay constant is extracted from the pion propagator, and from which the inverse lattice spacing is determined to be a −1=1.979(6) GeV. The parameters ( δ, A, B) in the pseudoscalar meson mass formula in quenched chiral perturbation theory (q χPT) to one-loop order are determined. Further, we measure the index (topological) susceptibility of these 100 gauge configurations, χ t =(175±6 MeV) 4, from which we obtain an estimate of the mass of η′ in q χPT, and the coefficient of quenched chiral logarithm, both in good agreement with the values determined from the pion masses, as well as with the theoretical estimates. With our values of δ, A, B, the experimental inputs of pion and kaon masses, and the pion decay constant, we determine the light quark masses: m u, d =4.1±0.3 MeV, and m s =92±9 MeV, in the MS scheme at scale μ=2 GeV. Also, we determine the quark condensate 〈 q ̄ q〉=−(250±3 MeV) 3 , and the quark–gluon condensate g〈 q ̄ σ μνF μνq〉=−(434±4 MeV) 5 , in the MS scheme at scale 2 GeV.