QCD condensates with flavor SU(3) symmetry breaking from the instanton vacuum

Abstract

Abstract We investigate the effects of flavor SU(3)-symmetry breaking on the quark, gluon, and mixed quark–gluon condensates, based on the nonlocal effective chiral action from the instanton vacuum. We take into account the effects of the flavor SU(3) symmetry breaking in the effective chiral action, so that the dynamical quark mass depends on the current quark mass ( m f ) . We compare the results of the present approach with those without the current quark mass dependence of the dynamical quark mass. It is found that the result of the quark condensate is decreased by about 30% as m f increases to 200 MeV, while that of the quark–gluon mixed condensates is diminished by about 15%. We obtain the ratios of the quark and quark–gluon mixed condensates, respectively: [ 〈 s ¯ s 〉 / 〈 u ¯ u 〉 ] 1 / 3 = 0.75 and [ 〈 s ¯ σ μ ν G μ ν s 〉 / 〈 u ¯ σ μ ν G μ ν u 〉 ] 1 / 5 = 0.87 . It turns out that the dimensional parameter m 0 2 = 〈 q ¯ σ μ ν G μ ν q 〉 / 〈 q ¯ q 〉 = 1.60 – 1.92 GeV 2 .