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Dilepton production rate (DPR) from hot and dense quark matter is studied inthe presence of an arbitrary external magnetic field using the 2-flavourNambu--Jona-Lasinio (NJL) model. The anomalous magnetic moment (AMM) of thequarks is taken into consideration while calculating the constituent quark massas well as the DPR from the thermo-magnetic medium. An infinite number of quarkLandau levels is incorporated so that no approximations are made on thestrength of the background magnetic field. The analytic structure of the twopoint vector current correlation function in the complex energy plane revealsthat, in addition to the usual Unitary cut, a non-trival Landau cut appears inthe physical kinematic domains solely due to the external magnetic field.Moreover, these kinematic domains of the Unitary and Landau cuts are found tobe significantly modified due to the AMM of the quarks. With finite AMM of thequarks, for certain values of the external magnetic field, the kinematicallyforbidden gap between the Unitary and Landau cuts are shown to vanish leadingto the generation of a continuous spectrum of dilepton emission over the wholeinvariant mass region not observed earlier.

Effects of anomalous magnetic moment of quarks on the dilepton production from hot and dense magnetized quark matter using the NJL model