A nonlocal chiral quark model is consistently extended beyond mean field using a strict $1/N_c$ 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 $1/N_c$ 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 cutoff of the local model. The model is also applied to finite temperature. We find that the $1/N_c$ corrections dominate the melting of the chiral condensate at low temperatures, $T\lesssim 100\mathrm{MeV}$, in agreement with chiral perturbation theory. On the other hand, the relative importance of the $1/N_c$ corrections in the crossover regime depends on the parameter $T_0$ of the Polyakov-loop potential. For $T_0=270\mathrm{MeV}$, 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 $1/N_c$ expansion breaks down and a nonperturbative scheme is needed to include mesonic correlations in that regime. Lowering $T_0$ leads to a more rapid crossover even at the mean-field level and the unstable region for the $1/N_c$ corrections shrinks. For $T_0\lesssim 220\mathrm{MeV}$ the temperatures of deconfinement and chiral restoration are practically synchronized.

• Received 3 February 2011

DOI:https://doi.org/10.1103/PhysRevD.83.116004