Lepton pair production from a hot and dense QCD medium in the presence of an arbitrary magnetic field

In this article, we have explored the very important quantity of lepton pair production from a hot and dense QCD medium in presence of an arbitrary external magnetic field for simultaneous nonzero values of both the parallel (along the direction of the external field) and perpendicular (lying on the transverse plane to the external field) components of the dilepton momentum. As opposed to the zero magnetic field case (the so-called Born rate) or the lowest Landau level approximated rate, where only the annihilation process contributes, here we observe contributions also arising out of the quark and antiquark decay processes. We found the encouraging result of considerable enhancement of lepton pair production in presence of an arbitrary magnetic field. We decompose the total rate into different physical processes and discuss their behaviors for both zero and nonzero baryon density. The whole analysis is then subjected to an effective model treatment, where we have incorporated the magnetic field induced novel effects of magnetic catalysis (MC) and inverse MC (IMC) through a medium dependent scalar coupling, which leads to some further interesting observations.