Production of Low Mass Electron Pairs Due to the Photon-Photon Mechanism in Central Collisions

We calculate the probability for dilepton production in central relativistic heavy ion collisions due to the gg mechanism. This is a potential background to more interesting mechanisms. We find that this mechanism is negligible in the CERES experiments. Generally, the contribution due to this mechanism is small in the central region, while it can be large for small invariant masses and forward or backward rapidities. A simple formula based on the equivalent photon approximation and applications to a possible scenario at the Relativistic Heavy Ion Collider are also given. PACS number~s!: 25.75.2q, 12.20.2m, 34.50.2s In peripheral relativistic heavy ion collisions there are huge effects due to the strong electromagnetic fields, while strong interactions among the colliding ions can be virtually neglected, due to their short range @1,2#. In central collisions, on the other hand, the strong interactions between the colliding ions completely overwhelm the effects due to the electromagnetic interaction. It is the purpose of this paper to study the effects due to the interactions of the very strong ~coherent! electromagnetic fields in the central collisions, see Fig. 1. The modification of the fields during the collision due to the strong interactions will be neglected for simplicity. We are mainly interested in the order of magnitude of the effects. Not unexpectedly, the production of strongly interacting particles ~like p 0) via the gg mechanism is negligible. On the other hand, the photon-photon mechanism could play a role in the production of e 1 e 2 pairs ~and also muon pairs! .I n recent experiments @3# low mass electron pairs are measured in p-Be, p-Au, and S-Au collisions. Even heavier systems like Au-Pb have recently been studied @4#. For the proton induced interactions, the spectra are explained essentially by electron pairs from hadronic decays, whereas for the heavier systems an enhancement is obtained, which is suggested to come from two-pion annihilation. In this paper we are going to calculate the contribution of the gg mechanism to the electron pairs. First the general theoretical framework is presented. Calculations within the framework of lowest order QED @5# are then given and compared to order of magnitude estimates using the equivalent photon approximation. In these calculations we have used the same kinematical constraints as are used in the CERES experiment. We also present calculations for a possible scenario at the Relativistic Heavy Ion Collider ~RHIC!. The vector potential of the combined electromagnetic field of two heavy ions, which travel with constant four velocities u (1,2) and with an impact parameter b between them is given by