Electromagnetic spectral properties and Debye screening of a strongly magnetized hot medium

We evaluate the electromagnetic spectral function and its spectral properties by computing the one-loop photon polarization tensor involving quarks in the loop, particularly in a strong-field approximation compared to the thermal scale. When the magnetic scale is higher than the thermal scale the lowest Landau level (LLL) becomes an effectively (1 + 1)-dimensional strongly correlated system that provides a kinematical threshold based on the quark mass scale. Beyond this threshold the photon strikes the LLL and the spectral strength starts with a high value due to the dimensional reduction and then falls off with the increase of the photon energy due to LLL dynamics in a strong-field approximation. We obtain analytically the dilepton production rates from the LLL considering the lepton pair remains unaffected by the magnetic field when produced at the edge of a hot magnetized medium or it is affected by the magnetic field if produced inside a hot magnetized medium. For the latter case the production rate is of O[|eB|(2)] along with an additional kinematical threshold due to the lepton mass. We also investigate the electromagnetic screening by computing the Debye screening mass and it depends distinctively on three different scales (mass of the quasiquark, temperature and the magnetic field strength) of a hot magnetized system. The mass dependence of the Debye screening supports the occurrence of a magnetic catalysis effect in the strong-field approximation.