Nonlocal PNJL model beyond mean field and the QCD phase transition

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/Nc expansion scheme. The parameters of the nonlocal model are refitted so that the physical values of the pion mass and the weak pion decay constant are obtained. The size of the 1/Nc correction to the quark condensate is carefully studied and compared with the usual local Nambu-Jona-Lasinio model. It is found that even the sign of the corrections can be different. This can be attributed to the mesonic cut-off of the local model. The model is also applied to finite temperature. We find that the 1/Nc corrections dominate the melting of the chiral condensate at low temperatures, T<100 MeV, in agreement with chiral perturbation theory. On the other hand, the relative importance of the 1/Nc corrections in the cross-over regime depends on the parameter T0 of the Polyakov loop potential. For T0=270 MeV, corresponding to a fit of lattice data for pure gluodynamics, the correction terms are large and lead to a lowering of the chiral phase transition temperature in comparison with the mean-field result. Near the phase transition the 1/Nc expansion breaks down and a non-perturbative scheme is needed to include mesonic correlations in that regime. Lowering T0 leads to a more rapid cross-over even at the mean-field level and the unstable region for the 1/Nc corrections shrinks. For T0< 220 MeV the temperatures of deconfinement and chiral restoration are practically synchronized.