Spectral function and dilepton rate from a strongly magnetised hot and dense medium in the light of mean field models

Abstract: We have calculated the electromagnetic spectral function (SF) vis-`{a}-vis the dilepton rate (DR) by evaluating the one-loop photon polarisation tensor for a strongly magnetised hot and dense medium. The calculation is performed in the ambit of mean field models namely Nambu\textendash Jona-Lasinio (NJL) and its Polyakov loop extended version (PNJL) in the lowest Landau level approximation. These models allow for a dynamical generation of quark mass which, evidently, gets affected in the presence of a magnetised medium. We have shown that the strength of the SF gets boosted because of the presence of dynamical quarks in lieu of the current quarks. It increases as we increase the magnetic field for a given value of temperature in both NJL and PNJL models. This increment is further reflected in the DR which is enhanced as compared to the Born rate for certain values of invariant masses. We also discuss the impact of chemical potential on DR within the present scenario.