Dilepton production rate in a hot and magnetized quark-gluon plasma

The differential multiplicity of dileptons in a hot and magnetized quark-gluon plasma, Delta(B) dN(B)/d(4)xd(4)q, is derived from first principles. The constant magnetic field B is assumed to be aligned in a fixed spatial direction. It is shown that the anisotropy induced by the B field is mainly reflected in the general structure of photon spectral density function. This is related to the imaginary part of the vacuum polarization tensor, Im[Pi(mu nu)], which is derived in a first order perturbative approximation. As expected, the final analytical expression for Delta(B) includes a trace over the product of a photonic part, Im[Pi(mu nu)], and a leptonic part, L-mu nu. It is shown that Delta(B) consists of two parts, Delta(parallel to)(B) and Delta(perpendicular to)(B), arising from the components (mu, nu) = (parallel to,parallel to) and (mu,nu) = (perpendicular to,perpendicular to) of Im[Pi(mu nu]) and L-mu nu. Here, the transverse and longitudinal directions are defined with respect to the direction of the B field. Combining Delta(parallel to)(B) and Delta(perpendicular to)(B), a novel anisotropy factor nu(B) is introduced. Using the final analytical expression of Delta(B), the possible interplay between the temperature T and the magnetic field strength eB on the ratio Delta(B)/Delta(0) and nu(B) is numerically studied. Here, Delta(0) is the Born approximated dilepton multiplicity in the absence of external magnetic fields. It is, in particular, shown that for each fixed T and B, in the vicinity of certain threshold energies of virtual photons, Delta(B) >> Delta(0) and Delta(perpendicular to)(B) >> Delta(parallel to)(B). The latter anisotropy may be interpreted as one of the microscopic sources of the macroscopic anisotropies, reflecting themselves, e.g., in the elliptic asymmetry factor nu(2) of dileptons. (C) 2016 Elsevier Inc. All rights reserved.