EFFICIENT DESCRIPTION FOR π AND σ MESONS BY RESONATING MEAN-FIELD APPROXIMATION TO TWO-FLAVOR NAMBU-JONA-LASINIO MODEL

Abstract

We have applied the resonating (Res-) mean-field approximation (MFA) to fermion systems with large quantum fluctuations over the usual MFA to a naive Nambu-Jona-Lasinio (NJL) model involving no current quark mass term. In our approach, as part of the model the normalization volume is kept finite, which plays an important role. This attempt has been quite successful in explaining the pion and sigma-meson masses, but the values of the order parameter for quark condensate and the pion decay constant are too small. This fact suggests us that the Res-MFA including no isospin causes such a problem. To avoid the serious drawback, if we naturally extend the NJL model to include two-flavor degrees of freedom and make an SU(2)f resonating Hartree-Fock (Res-HF) approximation, it is expected that the magnitudes of the order parameter and the pion decay constant are much improved. Using this extended NJL model, they are calculated again and both the numerical values [Formula: see text] and fπ reach good agreements with their experimental ones.