Neutral and charged pion properties under strong magnetic fields in the NJL model

In the framework of the Nambu--Jona-Lasino (NJL) model, we study the effect of an intense external uniform magnetic field on neutral and charged pion masses and decay form factors. In particular, the treatment of charged pions is carried out on the basis of the Ritus eigenfunction approach to magnetized relativistic systems. Our analysis shows that in the presence of the magnetic field three and four nonvanishing pion-to-vacuum hadronic form factors can be obtained for the case of the neutral and charged pions, respectively. As expected, it is seen that for nonzero magnetic field the $\pi^0$ meson can still be treated as a pseudo Nambu-Goldstone boson, and consequently the corresponding form factors are shown to satisfy various chiral relations. For definite parametrizations of the model, numerical results for $\pi^0$ and $\pi^\pm$ masses and decay constants are obtained and compared with previous calculations given in the literature.