Dilepton production by dynamical quasi-particles in the strongly interacting quark–gluon plasma

Abstract

We address the dilepton production by the constituents of the strongly interacting quark–gluon plasma (sQGP). In order to make quantitative predictions for dilepton rates at experimentally relevant low dilepton mass (O(1GeV)) and strong coupling (αS ∼ 0.5–1), we take into account non-perturbative spectral functions and self-energies of the quarks, antiquarks and gluons. For this purpose, we use parametrizations of the quark and gluon propagators provided by the dynamical quasi-particle model (DQPM) matched to reproduce lattice quantum chromodynamics (QCD) data. The DQPM describes QCD properties in terms of the single-particle Green's functions and leads to the notion of the constituents of the sQGP being effective quasi-particles, which are massive and have broad spectral functions (due to large interaction rates). By ‘dressing’ the quark and gluon lines with the effective propagators, we derive the off-shell cross sections for dilepton production in the reactions (Born mechanism), (quark annihilation with the gluon bremsstrahlung in the final state), (gluon–Compton scattering), and (virtual gluon decay, virtual quark decay). In contrast to previous calculations of these cross sections, we account for virtualities of all the quarks and gluons. We find that finite masses of the effective quasi-particles not only screen the singularities typical of the perturbative cross sections with massless quarks, but also modify the shape of the dilepton production cross sections, especially at low dilepton mass Q and at the edges of the phase space. Finally, we use the calculated mass-dependent cross sections to identify the dependence of the dilepton rates on the spectral function widths of the initial and final quarks and gluons, which has not been estimated so far. The results demonstrate that the multiple partonic scatterings encoded in the broad spectral functions of the dynamical quasi-particles have considerable effect on the dilepton rates.