Phenomenological improvement of the linear-$\sigma$ model in the large-N_c limit

Abstract

The linear-$\sigma$ model has been widely used to describe the chiral phase transition. Numerically, the critical temperature $T_c$ of the chiral phase transition is in agreement with other effective theories of QCD. However, in the large-$N_c$ limit $T_c$ scales as $\sqrt{N_c}$ which is not in line with the NJL model and with basic expectations of QCD, according to which $T_c$ is --just as the deconfinement phase transition- $N_c$-independent. This mismatch can be corrected by a phenomenologically motivated temperature dependent parameter.