Pion and σ-meson Properties in a Strong Magnetic Field**Supported by the National Natural Science Foundation of China under Grant Nos. 10935001, 11175004, and 11435001, and the National Key Basic Research Program of China under Grant Nos. G2013CB834400 and G2015CB856900

Abstract

With the Nambu–Jona-Lasinio (NJL) model we calculate the properties of pion and σ-meson at finite temperature and finite magnetic field. The obtained temperature and magnetic field strength dependence of the constituent quark mass M, the pion and σ-meson masses and the neutral pion decay constant indicates that, in the simple four fermion interaction model, there exists the magnetic catalysis effect. It also shows that the Gell-Mann–Oakes–Renner relation is violated obviously with the increasing of the temperature, and the effect of the magnetic field becomes pronounced only around the critical temperature. The deviation of the critical temperatures obtained with different criteria indicates that the chiral phase transition driven by the temperature in the magnetic field strength region we have considered is in fact a crossover.