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Register a new userSoft contribution to the damping rate of a hard photon in a weakly magnetized hot medium
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We consider weakly magnetized hot QED plasma comprising electrons and positrons. There are three distinct dispersive (longitudinal and two transverse) modes of a photon in a thermo-magnetic medium. At lowest order in coupling constant, photon is damped in this medium via Compton scattering and pair creation process. We evaluate the damping rate of hard photon by calculating the imaginary part of the each transverse dispersive modes in a thermo-magnetic QED medium. We note that one of the fermions in the loop of one-loop photon self-energy is considered as soft and the other one is hard. Considering the resummed fermion propagator in a weakly magnetized medium for the soft fermion and the Schwinger propagator for hard fermion, we calculate the soft contribution to the damping rate of hard photon. In weak field approximation the thermal and thermo-magnetic contributions to damping rate get separated out for each transverse dispersive mode. The total damping rate for each dispersive mode in presence of magnetic field is found to be reduced than that of the thermal one. This formalism can easily be extended to QCD plasma.
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We consider our recently obtained general structure of two point (self-energy and propagator) functions of quarks and gluons in a nontrivial background like a heat bath and an external magnetic field. Based on this, here we have computed free energy and pressure of quarks and gluons for a magnetized hot and dense deconfined QCD matter in weak field approximation. For heat bath we have used hard thermal loop perturbation theory (HTLpt) in presence of finite chemical potential. For weak field approximations we have obtained the pressure of QCD matter, both with and without the high temperature expansion. The results with high $T$ expansions are completely analytic and gauge independent but depends on the renormalization scale in addition to the temperature, chemical potential and the external magnetic field. We also discuss the modification of QCD Debye mass of such matter for an arbitrary magnetic field. Analytic expressions for Debye mass are also obtained for both strong and weak field approximation. It is found to exhibit some interesting features depending upon the three different scales, i.e, the quark mass, temperature and the strength of the magnetic field. The various divergences appearing in the quark and gluon free energies are regulated through appropriate counter terms. In weak field approximation, the low temperature behavior of the pressure is found to strongly depend on the magnetic field than that at high temperature. We also discuss the specific problem with one-loop HTLpt associated with the over-counting of certain orders in coupling.
We have computed the hard dilepton production rate from a weakly magnetized deconfined QCD medium within one-loop photon self-energy by considering one hard and one thermomagnetic resummed quark propagator in the loop. In the presence of the magnetic field, the resummed propagator leads to four quasiparticle modes. The production of hard dileptons consists of rates when all four quasiquarks originating from the poles of the propagator individually annihilate with a hard quark coming from a bare propagator in the loop. Besides these, there are also contributions from a mixture of pole and Landau cut part. In weak field approximation, the magnetic field appears as a perturbative correction to the thermal contribution. Since the calculation is very involved, for a first effort as well as for simplicity, we obtained the rate up to first order in the magnetic field, i.e., ${cal O}[(eB)]$, which causes a marginal improvement over that in the absence of magnetic field.
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