We study the behavior of neutral meson properties in the presence of a static uniform external magnetic field in the context of nonlocal chiral quark models. The formalism is worked out introducing Ritus transforms of Dirac fields, which allow to obtain closed analytical expressions for ${\pi }^0$ and $\sigma$ meson masses and for the ${\pi }^0$ decay constant. Numerical results for these observables are quoted for various parametrizations. In particular, the behavior of the ${\pi }^0$ meson mass with the magnetic field is found to be in good agreement with lattice QCD results. It is also seen that the Goldberger-Treiman and Gell-Mann-Oakes-Renner chiral relations remain valid within these models in the presence of the external magnetic field.

We study the behavior of strongly interacting matter under a uniform intense external magnetic field in the context of nonlocal extensions of the Polyakov–Nambu–Jona-Lasinio model. A detailed description of the formalism is presented, considering the cases of zero and finite temperature. In particular, we analyze the effect of the magnetic field on the chiral restoration and deconfinement transitions, which are found to occur at approximately the same critical temperatures. Our results show that these models offer a natural framework to account for the phenomenon of inverse magnetic catalysis found in lattice QCD calculations.

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.

Basic features of nonstrange vector and axial vector mesons are analyzed in the framework of a chiral quark model that includes nonlocal four-fermion couplings. Unknown model parameters are determined from some input values of masses and decay constants, while nonlocal form factors are taken from a fit to lattice QCD results for effective quark propagators. Numerical results show a good agreement with the observed meson phenomenology.

The behavior of ${\pi }^0$ meson properties in the presence of a uniform external magnetic field is studied in the context of a nonlocal extension of the Polyakov-Nambu-Jona-Lasinio model. The analysis includes the ${\pi }^0$ mass, the effective ${\pi }^0$-quark coupling and the pion-to-vacuum hadronic form factors, both at zero and finite temperature. Numerical results are compared with previous calculations carried out within the local NJL model, when available. The validity of chiral relations and the features of deconfinement and chiral symmetry restoration transitions are discussed.

We study the features of a SU(2) Polyakov-Nambu-Jona-Lasinio model that includes wave function renormalization and nonlocal vector interactions. Within this framework we analyze, among other properties, the masses, width, and decay constants of light vector and axial-vector mesons at finite temperature. Then we obtain the corresponding phase diagram in a finite density scenario, after characterizing the deconfinement and chiral restoration transitions.