Nonlocal Polyakov–Nambu–Jona-Lasinio model beyond mean field and the QCD phase transition

Abstract

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 & 100 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 ¼ 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=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 & 220 MeV the temperatures of deconfinement and chiral restoration are practically synchronized.

Thermal nonlocal Nambu–Jona-Lasinio model in the real time formalism

“…(50) can produce an unstable thermodynamical potential [11]. However, the inclusion of the Polyakov loop should fix this problem [25,31]. Note that now, we can also obtain other relevant quantities directly from the thermodynamical potential already calculated in the real time formalism.…”

“…Nonlocal extensions of the NJL model are designed to regularize the model in such a way that UV divergences are controlled, internal symmetries are preserved, and quark confinement is incorporated. The nNJL model has been extended to a finite temperature and density scenario [22][23][24][25][26][27][28][29][30][31][32] through the usual Matsubara formalism [33,34]. Here, nevertheless, the exact summation of Matsubara frequencies turns out to be cumbersome, due to the complicated shape of the regulators.…”

From chiral quark dynamics with Polyakov loop to the hadron resonance gas model

“…An effective and phenomenologically successful approach to the physics of the phase transition is provided by chiral quark models coupled to gluon fields in the form of a Polyakov loop [19,20,21,22,23,24,25,26,27,28,29,30,31,32]. Because most often the venerable Nambu-Jona-Lasinio model has been used, these models are referred to as PNJL models.…”

Chiral transition in a magnetic field and at finite baryon density

“…[14][15][16][17][18][19][20][21][22], and the PNJL model in Refs. [16,[23][24][25][26][27][28][29] Using the QM model, it is a common approximation to omit the quantum and thermal fluctuations of the * Electronic address: andersen@tf.phys.no † Electronic address: rashid.khan@ntnu.no bosonic degrees of freedom, i.e. treating them at tree level.…”