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According to the generally accepted phase diagram of QCD, at low temperatureand high baryon number density the chiral phase transition of QCD is of firstorder and the co-existence of the Nambu-Goldstone phase and the Wigner phaseshould appear. This is in conflict with the usual claim that the quark gapequation has no Wigner solution in the case of nonzero current quark mass. Inthis paper we analyze the reason why the Wigner solution does not exist in theusual treatment and try to propose a new approach to discuss this question. Asa first step, we adopt a modified Nambu-Jona-Lasinio (NJL) model to study theWigner solution at finite current quark mass. We then generalize this approachto the case of finite chemical potential and discuss partial restoration ofchiral symmetry at finite chemical potential and compare our results with thosein the normal NJL model.

The Wigner solution of quark gap equation at nonzero current quark mass and partial restoration of chiral symmetry at finite chemical potential