Meson loop effect on high density chiral phase transition

Abstract

We test the stability of the mean-field solution in the Nambu--Jona-Lasinio model. For stable solutions with respect to both the \sigma and \pi directions, we investigate effects of the mesonic loop corrections of 1/N_c, which correspond to the next-to-leading order in the 1/N_c expansion, on the high density chiral phase transition. The corrections weaken the first order phase transition and shift the critical chemical potential to a lower value. At N_c=3, however, instability of the mean field effective potential prevents us from determining the minimum of the corrected one.