Light quark masses, chiral condensate and quark-gluon condensate in quenched lattice QCD with exact chiral symmetry
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 \times 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 ($ C, δ, B $) in the pseudoscalar meson mass formula in quenched chiral perturbation theory (q$χ$PT) to one-loop order are determined. Further, we measure the index (topological) susceptibility of these 100 gauge configurations, $ χ_t = (175 \pm 6 {MeV})^4 $, from which we obtain an estimate of the mass of $ η' $ in q$χ$PT, 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 $ C, δ, 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 \pm 0.3 $ MeV, and $ m_s = 92 \pm 9 $ MeV, in the $ \bar{MS} $ scheme at scale $ μ= 2 $ GeV. Also, we determine the quark condensate $<\bar q q > = -(250 \pm 3 {MeV})^3 $, and the quark-gluon condensate $ g < \bar q σ_{μν} F_{μν} q > = -(434 \pm 4 {MeV})^5 $, in the $ \bar{MS} $ scheme at scale 2 GeV.