Electromagnetic spectral function and dilepton rate in a hot magnetized QCD medium

The dilepton production rate in a hot QCD medium is studied within an effective description of the medium in the presence of a magnetic field. This could be done by obtaining the one-loop self-energy of the photon due to the effective (quasi)quark loop at a finite temperature under an arbitrary external magnetic field while employing the real time formalism of thermal field theory. The effective quarks and gluons encode a hot QCD medium effective in terms of their respective effective fugacities. The magnetic field enters in the form of Landau level quantization, in the matter sector (quarks, antiquarks). The full Schwinger proper time propagator including all the Landau levels is considered for the quasiquarks while calculating the photon self-energy. The electromagnetic Debye screening (in terms of the self-energy) has been influenced by both the hot QCD medium effects and the magnetic field. Analogous results are also obtained from the semiclassical transport theory. The imaginary part of the photon self-energy function is obtained from the discontinuities of the self-energy across the unitary cuts that are also present at the zero magnetic field and the Landau cuts that are purely due to the magnetic field. The dilepton production rate is then obtained in terms of the product of electromagnetic spectral functions due to the quark loop and the lepton loop. The modifications of both the quarks/antiquarks as well as leptons in the presence of an arbitrary external magnetic field have been considered in the formalism. Significant enhancement of the low invariant mass dileptons due to the appearance of the Landau cuts in the electromagnetic spectral function at the finite external magnetic field has been observed. A substantial enhancement of the dilepton rate is also found when the equation of state effects are considered through the effective quarks/antiquraks.