Dilepton production from hot and magnetized hadronic matter

The rate of dilepton emission from a magnetized hot hadronic medium is calculated in the framework of real time formalism of finite temperature field theory. We evaluate the one loop self-energy of neutral rho-meson containing thermo-magnetic propagators for the charged pions in the loop. The in-medium thermo-magnetic spectral function of rho obtained by solving the Dyson-Schwinger equation is shown to be proportional to the dilepton production rate. The study of the analytic structure of the neutral rho-meson spectral function in such a medium shows that in addition to the usual contribution coming from the Unitary cut beyond the two-pion threshold there is a non-trivial yield in the low invariant mass region originating due to the fact that the charged pions occupy different Landau levels before and after scattering with the neutral rho-meson and is purely a finite magnetic field effect.