Charged pseudoscalar and vector meson masses in strong magnetic fields in an extended NJL model

The mass spectrum of ${\pi }^{+}$ and ${\rho }^{+}$ mesons in the presence of a static uniform magnetic field $\overrightarrow{B}$ is studied within a two-flavor Nambu-Jona-Lasinio-like model. We improve previous calculations, taking into account the effect of Schwinger phases carried by quark propagators and using an expansion of meson fields in terms of the solutions of the corresponding equations of motion for nonzero $B$. It is shown that the meson polarization functions are diagonal in this basis. Our numerical results for the ${\rho }^{+}$ meson spectrum are found to disfavor the existence of a meson condensate induced by the magnetic field. In the case of the ${\pi }^{+}$ meson, $\pi$—$\rho$ mixing effects are analyzed for the meson lowest-energy state. The predictions of the model are compared with available lattice QCD results.