Mass spectra and decay of mesons under strong external magnetic field

We study the mass spectra and decay process of σ and π_(0) mesons under a strong external magnetic field.To achieve this goal,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 the 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 π_(0) at low temperatures.However,for quarks andσmesons,their mass clearly changes,which reflects the influence of magnetic catalysis(MC).The presence of a magnetic field accelerates the decay of the meson while the presence of a chemical potential will decrease the decay process.