$\pi$ and $\sigma$ mesons at finite temperature and density in the NJL model with dimensional regularization

Dynamical Symmetry breaking and meson masses are studied in the Nambu-Jona-Lasinio (NJL) model at finite temperature and chemical potential using the dimensional regularization. Since the model is not renormalizable in four space-time dimensions, physical results and parameters depend on the regularization method. Following the imaginary time formalism, we introduce the temperature, $T$ and the chemical potential, $\mu$. The parameters in the model are fixed by calculating the pion mass and decay constant in the dimensional regularization at $T=\mu=0$.