Massive Meson Fluctuation in NJL Model

Based on the self-consistent scheme beyond mean-field approximation in the large $N_c$ expansion, including current quark mass explicitly, a general scheme of SU(2) NJL model is developed. To ensure the quark self-energy expanded in the proper order of $N_c$, an approximate internal meson propagator is deduced, which is in order of $O(1/N_c)$. In our scheme, adopting the method of external momentum expansion, all the Feynman diagrams are calculated in a unified way by only expanding the quark propagator. Our numerical results show, that different from the mean field approximation in which the explicitly chiral symmetry breaking is invisible, the effect of finite pion mass can be seen clearly when beyond mean-field approximation.