In medium properties of $K^0$ and $\phi$ mesons under an external magnetic field

The one loop polarization insertions for the kaon and the $\phi$ mesons are evaluated in a hadronic medium as functions of the field intensity and the baryonic density. For this purpose an effective chiral model of the hadronic interaction is used, supplemented with a phenomenological $K-\phi$ interaction. The propagators of the charged particles include the full effect of the coupling to the magnetic field which induces the quantum Landau levels. Consequently, the vacuum diagrams are defined within a zeta function regularization scheme. The effective masses as well as the decay widths are introduced and examined as functions of matter density and the magnetic intensity.