A new algorithm towards a quasi-Wigner solution of the gap equation beyond the chiral limit

Abstract

We propose a new algorithm to solve the quasi-Wigner solution of the gap equation beyond the chiral limit. Employing a Gaussian gluon model and rainbow truncation, we find that the quasi-Wigner solution exists in a limited region of quark mass, m < 43.1 MeV, at zero temperature T and zero chemical potential μ. The difference between Cornwall–Jackiw–Tomboulis (CJT) effective actions of quasi-Wigner and Nambu–Goldstone solutions shows that the Nambu–Goldstone solution is more stable. Moreover, the quasi-Wigner solution is studied at finite temperature and chemical potential, the infrared mass function of the quasi-Wigner solution is negative and decreases along with T at μ = 0. Its susceptibility is divergent at certain temperatures with small m, and this temperature decreases along with m. Taking T = 80 MeV as an example, the quasi-Wigner solution is shown at finite chemical potential up to μ = 350 MeV as well as Nambu solution, the coexistence of these two solutions is used to analyze the properties of phase transition. The first order chiral phase transition line is determined by the difference of CJT effective actions.