Mass spectra and decay of mesons under strong external magnetic field

We study the mass spectra and decay process of σ and begin{document}$ pi_0 $end{document} mesons under a strong external magnetic field. To achieve this goal, we deduce the thermodynamic potential in a two-flavor, hot and magnetized Nambu–Jona-Lasinio model. We calculate the energy gap equation through the random phase approximation (RPA). Then we use the Ritus method to calculate the decay triangle diagram and self-energy in the presence of a constant magnetic field B. Our results indicate that the magnetic field has little influence on the mass of begin{document}$ pi_0 $end{document} at low temperatures. However, for quarks and σ mesons, 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.