Masses of magnetized pseudoscalar and vector mesons in an extended NJL model: the role of axial vector mesons

We study the mass spectrum of light pseudoscalar and vector mesons in the presence of an external uniform magnetic field $\vec B$, considering the effects of the mixing with the axial vector meson sector. The analysis is performed within a two-flavor NJL-like model which includes isoscalar and isovector couplings together with a flavor mixing 't Hooft-like term. The effect of the magnetic field on charged particles is taken into account by retaining the Schwinger phases carried by quark propagators, and expanding the corresponding meson fields in proper Ritus-like bases. The spin-isospin and spin-flavor decomposition of meson mass states is also analyzed. For neutral pion masses it is shown that the mixing with axial vector mesons improves previous theoretical results, leading to a monotonic decreasing behavior with $B$ that is in good qualitative agreement with LQCD calculations, both for the case of constant or $B$-dependent couplings. Regarding charged pions, it is seen that the mixing softens the enhancement of their mass with $B$. As a consequence, the energy becomes lower than the one corresponding to a pointlike pion, improving the agreement with LQCD results. The agreement is also improved for the magnetic behavior of the lowest $\rho^+$ energy state, which does not vanish for the considered range of values of $B$ -- a fact that can be relevant in connection with the occurrence of meson condensation for strong magnetic fields.