Monte Carlo Calculations of Lepton-Pair Production in Relativistic Heavy-Ion Collisions

The main goal of the Relativistic Heavy-Ion Collider (RHIC) is to create a so-called quark-gluon plasma and to study the physics associated with it. It is expected that ultra-relativistic heavy-ions can provide this form of matter in the central, or near-central collisions. In these central collisions, thermodynamic conditions are sufficient enough to deconfine the constituent quarks and gluons of baryons and mesons in a short-lived plasma state. Lepton pairs especially electron and muon-pair production from hadronic interactions can help us to understand the formation and the decay of the quark-gluon plasma phase of matter. Here we study the electromagnetic lepton pair production from heavy-ion fields by using perturbative methods. We start with quantum-field theory deriving a classical-field method based on Feynman perturbation theory. Our derivation based on the limit that the momentum transfer of the photons is much smaller than the momentum carried by the nuclei which is basically true for the coherent production of particles through two-photon processes in relativistic heavy-ion collisions. These lowest-order Feynman diagrams have been evaluated exactly using Monte Carlo and analytical techniques and predict cross sections consistent with experiments. In this present work, we also generalize the Monte Carlo methods in order to calculate the impact-parameter dependence of the two-photon diagrams which has implications for the description of the electromagnetic background for hadronic interactions, the study of strong-field effect(e.g., pair multiplicities), and the study of the validity of the equivalent-photon approximation.