QCD topological susceptibility from the nonlocal chiral quark model

We investigate the quantum chromodynamics (QCD) topological susceptibility χ by using the semi-bosonized nonlocal chiral-quark model (SB-NLχQM) for the leading large-N c contributions. This model is based on the liquid-instanton QCD-vacuum configuration, in which SU(3) flavor symmetry is explicitly broken by the finite current-quark mass (m u,d,m s) ≈ (5, 135) MeV. To compute χ, we derive the local topological charge-density operator Q t(x) from the effective action of SB-NLχQM. We verify that the derived expression for χ in our model satisfies the Witten- Veneziano (WV) and the Leutwyler-Smilga (LS) formulae, and the Crewther theorem in the chiral limit by construction. Once the average instanton size and the inter-instanton distance are fixed with ρ = 1/3 fm and R = 1 fm, respectively, all the other parameters are determined self-consistently within the model. We obtain χ = (167.67MeV)4, which is comparable with the empirical value χ = (175±5MeV)4 whereas it turns out that χ QL = (194.30MeV)4 in the quenched limit. Thus, we conclude that the value of χ will be reduced around 10 ~ 20% by the dynamical-quark contribution.