Inverse magnetic catalysis effect and current quark mass effect on mass spectra and Mott transitions of pions under external magnetic field

Mass spectra and Mott transitions of pions (pi(0), pi(+/-)) at finite temperature and magnetic field are investigated in a two-flavor Nambu-Jona-Lasinio model, and we focus on the inverse magnetic catalysis (IMC) effect and current quark mass (CQM) effect. Due to the dimension reduction of the constituent quarks, the pion masses jump at their Mott transitions, which is independent of the IMC effect and CQM effect. We consider the IMC effect by using a magnetic-field-dependent coupling constant, which is a monotonic decreasing function of magnetic field. With the IMC effect, the Mott transition temperature of pi(0) mesons, T-m(0), is a monotonic decreasing function of magnetic field. For charged pions, pi(+/-), the Mott transition temperature T-m(+) increases quickly in the weak magnetic field region and then decreases with increasing magnetic field, which is accompanied with some oscillations. Comparing with the case without IMC, T-m(0) and T-m(+) are lower when including the IMC effect. The CQM effect is considered by varying parameter m(0) in the nonchiral limit. For pi(0) mesons, T-m(0) is not a monotonic function of magnetic field with low m(0), but it is a monotonic decreasing function with larger m(0). In the weak magnetic field region, T-m(0) is higher for larger m(0), but in the strong magnetic field region, it is lower for larger m(0). For pi(+) mesons, T-m(+) is only quantitatively modified by the current quark mass effect, and it becomes higher with larger m(0).