Properties of neutral mesons in a hot and magnetized quark matter: Size-dependent effects

In this work we investigate the combined finite-size and thermomagnetic effects on the properties of neutral mesons in a hot medium, in the context of the Nambu--Jona-Lasinio model. In particular, by using the mean-field approximation and the Schwinger proper time method in a toroidal topology with periodic and antiperiodic conditions, we evaluate the chiral phase transition, the critical coupling, the constituent quark mass and meson observables like the π⁰ and σ meson masses and pion decay constant under the change of the size, temperature and strength of external magnetic field. The results indicate that the observables are strongly affected by the conjoint effects of relevant variables and also by the periodicity of the boundary conditions chosen, and the net result will depend on the balance of these competing phenomena.