The behavior of charged and neutral pion masses in the presence of a static uniform magnetic field is studied in the framework of the two-flavor Nambu-Jona-Lasinio (NJL) model. Analytical calculations are carried out employing the Ritus eigenfunction method. Numerical results are obtained for definite model parameters, comparing the predictions of the model with present lattice QCD (LQCD) results.The study of the behavior of strongly interacting matter under intense external magnetic fields has gained increasing interest in the last few years, especially due to its applications to the analysis of relativistic heavy ion collisions and the description of compact objects like magnetars [1]. In this work we concentrate on the effect of an intense external magnetic field on π meson properties. This issue has been studied in the last years following various theoretical approaches for low-energy QCD, such as NJL-like models, chiral perturbation theory, path integral Hamiltonians and LQCD calculations (see e.g.[1] and refs therein). In the framework of the NJL model, mesons are usually described as quantum fluctuations in the random phase approximation (RPA) [2]. In the presence of a magnetic field, the corresponding calculations require some special care, due to the appearance of Schwinger phases [3] associated with quark propagators. For the neutral pion these phases cancel out, and as a consequence the usual momentum basis can be used to diagonalize the corresponding polarization function [4][5][6][7]. On the other hand, for charged pions Schwinger phases do not cancel, leading to a breakdown of translational invariance that prevents to proceed as in the neutral case. In this contribution we present a method based on the Ritus eigenfunction approach [8] to magnetized relativistic systems, which allows us to fully diagonalize the charged pion polarization function. Further details of this work can be found in Ref. [9].We start by considering the Euclidean Lagrangian density for the NJL two-flavor model in the presence of an electromagnetic field. One haswhere ψ = (u d) T , τ i are the Pauli matrices, and m 0 is the current quark mass, which is assumed to be equal for u and d quarks. The interaction between the fermions and the electromagnetic field A µ is driven by the covariant derivative D µ = ∂ µ − iQA µ whereQ = diag(q u , q d ), with q u = 2e/3 and q d = −e/3, e being the proton electric charge. We consider here an homogeneous stationary magnetic field along the 3 axis in the Landau gauge, A µ = B x 1 δ µ2 .

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 π 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 π 0 and π AE masses and decay constants are obtained and compared with previous calculations given in the literature.

We propose a model-independent parametrization for the one-pion-to-vacuum matrix elements of the vector and axial vector hadronic currents in the presence of an external uniform magnetic field. It is shown that, in general, these hadronic matrix elements can be written in terms of several gauge covariant Lorentz structures and form factors. Within this framework we obtain a general expression for the weak decay π − → lν l and discuss the corresponding limits of strong and weak external magnetic fields.