Effective Neutrino Photon Interaction in a Magnetized Medium

Neutrino-photon processes, forbidden in vacuum, can take place in presence of a thermal medium or an external electro-magnetic field, mediated by the corresponding charged leptons (real or virtual). The effect of a medium or an electromagnetic field is two-fold - to induce an effective $\nu -\gamma$ vertex and to modify the dispersion relations of all the particles involved to render the processes kinematically viable. It has already been noted that in presence of a thermal medium such an electromagnetic interaction translates into the neutrino acquiring a small effective charge. In this work, we extend this concept to the case of a thermal medium in presence of an external magnetic field and calculate the effective charge of a neutrino in the limit of a weak magnetic field. We find that the effective charge is direction dependent which is a direct effect of magnetic field breaking the isotropy of the space.