Mass dependence of the deconfinement and chiral restoration critical temperatures in nonlocal SU(2) Polyakov-Nambu-Jona-Lasinio models

In the framework of nonlocal SU(2) chiral quark models with Polyakov loop, we analyze the dependence of the deconfinement and chiral restoration critical temperatures on the explicit chiral symmetry breaking driven by the current quark mass. Our results are compared with those obtained within the standard local Polyakov-Nambu-Jona-Lasinio model and with lattice QCD calculations. For a wide range of pion masses, it is found that both deconfinement and chiral restoration critical temperatures turn out to be strongly entangled, in contrast with the corresponding results within the Polyakov-Nambu-Jona-Lasinio model. In addition, it is seen that the growth of the critical temperatures with the pion mass above the physical point is basically linear, with a slope parameter that is close to the existing lattice QCD estimates. On the other hand, we find a tendency to favor an early onset of the first order transition expected in the large quark mass limit.

Figure 1

Pion properties at $T=0$ as functions of the pion mass in local and nonlocal chiral quark models. Upper and lower panels correspond to the ratio $m_{\pi }^2/m_c$ and the pion decay constant $f_{\pi }$, respectively. Lattice results are taken from Ref. 41, and the NJL model parametrization is that in Refs. 14, 31.

Figure 2

Order parameters (upper panels) and the corresponding susceptibilities (lower panels) as functions of the temperature for some representative values of the pion mass. Left (right) panels correspond to the polynomic (logarithmic) Polyakov potential.

Figure 3

Critical temperatures as functions of the pion mass for PNJL and nlPNJL models, considering polynomic (upper panel) and logarithmic (lower panel) Polyakov loop potentials. Dashed and dotted lines correspond to chiral restoration and deconfinement transition temperatures, respectively. For the nlPNJL models with a logarithmic potential (lower panel), both transitions occur at the same temperature, and they can be of first order (solid lines) or proceed as a smooth crossover (dash-dotted lines).