Effect of an imaginary part of the Schwinger-Dyson equation at finite temperature and density

We examined the effect of an imaginary part of the ladder approximation Schwinger-Dyson equation. We show that the imaginary part enhances the effect of the first-order transition and affects a tricritical point. In particular, a chemical potential at the tricritical point is displaced about 200 MeV. Thus, one should not ignore the imaginary part. However, because the imaginary part is small away from the tricritical point, one should be able to ignore the imaginary part. In addition, we also examined the contribution of the wave-function renormalization constant.