Axial Anomaly, Mismatched Fermi Surfaces and Vector Interaction in Dense Neutral Quark Matter

We report on effects of the q-(q) over bar vector interaction and/or the U(1)(A)-anomaly-induced chiral-diquark coupling on the charge-neutral quark matter in beta-equilibrium. We show that when the vector coupling is absent, there can appear a cross-over region sandwiched by two critical points in the intermediate temperature (T) region, while the phase transition in the low-T region including zero temperature keeps being first order until the strength of the anomaly term is increased to have a critical value. On the other hand, when the vector coupling is also present, there appears a crossover region in the low-T area including zero temperature with a new critical point, as was first demonstrated by Kitazawa et al. and the present authors without and with the charge-neutral condition, respectively. We remark that the possible chromomagnetic instability is suppressed and can be even completely absent owing to the enhanced diquark coupling due to the anomaly term and/or by the vector interaction.