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

Abstract

The dilepton production rate in hot QCD medium is studied within a effective description of the medium in the presence of magnetic field. This could be done by obtaining the one-loop self energy of photon due to the effective (quasi-) quark loop at finite temperature under an arbitrary external magnetic field while employing the real time formalism of Thermal Field Theory. The effective quarks and gluons encode 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 quasi quarks while calculating the photon self energy. The electromagnetic Debye screening (in terms of the self-energy) has seen to be influenced both by the hot QCD medium effects and magnetic field. Analogous results are also obtained from the semi classical transport theory. The imaginary part of the photon self energy function is obtained from the discontinuities of the self energy across the Unitary cuts which are also present at zero magnetic field and the Landau cuts which 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 quark loop and lepton loop. The modifications of both the quarks/antiquarks as well as leptons in presence of an arbitrary external magnetic field have been considered in the formalism. Significant enhancement of the low invariant mass dileptons due the appearance of the Landau cuts in the electromagnetic spectral function at finite external magnetic field has been observed. A substantial enhancement of dilepton rate is also found when the EOS effects are considered through the effective quarks/antiquraks.