Mass Spectra and Decay of Mesons under Strong External Magnetic Field

We study the mass spectra and decay process of $\sigma$ and $\pi_0$ mesons under strong external magnetic field. For this purpose, we deduce the thermodynamic potential in a two-flavor, hot and magnetized Nambu-Jona-Lasinio model. We calculate the energy gap equation through the random phase approximation(RPA). Then we use Ritus method to calculate the decay triangle diagram and self-energy in the presence of a constant magnetic field B. Our results indicate that the magnetic field has little influence on the mass of $\pi_0$ at low temperatures. While for quarks and $\sigma$ mesons, their mass changes obviously, which reflects the influence of magnetic catalysis(MC). The presence of magnetic field accelerates the decay of the meson while the presence of chemical potential will decrease the decay process.