QCD topological susceptibility from the nonlocal chiral quark model

Abstract

We investigate the QCD topological susceptibility χt by using the nonlocal chiral quark model (NLχQM). This model is based on the liquid instanton QCD-vacuum configuration in which SU(3) flavor symmetry is explicitly broken by the current quark mass (m u,d , ms) ≈ (5, 135) MeV. To compute χt, the local topological charge density operator Qt(x) is derived from the effective partition function of NLχQM. We take into account the contributions from the leading-order (LO) ones ∼ O(Nc) in the 1 Nc expansion. We also verify that the analytical expression of χt in NLχQM satisfy the Witten-Veneziano (WV) and the Leutwyler-Smilga (LS) formulae. Once the average instanton size and inter-instanton distance are fixed withρ = 1 3 fm andR = 1 fm, respectively, all the associated model parameters are all determined self-consistently within the model, including the η and η ′ weak decay constants. We obtain the results such as Fη = 96.77 MeV and F η ′ = 102.53 MeV for instance. Numerically we observe that χt = (165.57 MeV) 4 in our full calculation. This value is comparable with its empirical one χt = (175 ± 5 MeV)4 . We also find that our χ (194.30, MeV) 4 in the quenched limit and χ LS t = (162.54 MeV) 4 in the chiral limit. Consequently, we conclude that χt < χ QL t . Our result also implies that the (10 ∼ 20) % decrease with the dynamical quark contributions.