Bremsstrahlung Dileptons in Ultra-relativistic Heavy Ion Collisions

We consider production of dilepton pairs through coherent electro-magnetic radiation during nuclear collisions. We show that the number of pairs produced through bremsstrahlung is about two orders of magnitude smaller than the yield measured by the CERES collaboration. Therefore, coherent bremsstrahlung can be ruled out as an explanation for the observed enhancement of low mass dileptons in CERES and HELIOS. Production of low mass dileptons in ultra-relativistic heavy ion collisions is considered a useful probe of possible in-medium changes of hadrons due to the onset of chiral restoration (see [1] for a recent review). Dilepton are penetrating probes, i.e. once produced they do not re-interact with the hadronic environment and thus, provide information about the early stages of the collision where high temperatures and densities are reached. Since vector mesons such as ρ, ω and Φ have direct decay channels into dileptons, possible in-medium changes of the vector mesons masses can be observed in the dilepton invariant mass spectrum. There has been a major surge of interest in dilepton mass spectrum due to a recent experimental observation of an enhanced dilepton yield at invariant masses of about 400MeV in S + Au and Pb + Au collisions in SPS compared to proton induced collisions as reported by CERES collaboration [2]. There is also a similar enhancement reported by HELIOS collaboration at more forward rapidities [3]. Although the decay of the final state hadrons explain the data well in proton induced collisions, they can not explain the current SPS data for S + Au and Pb + Au in the mass region around ∼ 400 MeV . A major source of this enhancement is simply pion annihilation which is not present in the proton-nucleus system. Including pion annihilation and contributions from other hadronic reactions the calculations reach the lower end of the sum of statistical and systematic errors of the CERES data (see [4] for a compilation of different calculations). An additional enhancement can be achieved [5, 6] if one assumes that the mass of the ρ is lowered according to the conjectures of [7]. Another possible enhancement arises from an in-medium modified pion dispersion relation. While this effect is small if one considers the modification of the pion dispersion in a pion gas [8], it is considerably larger if, in addition, one takes the effect of baryons into account [9]. Consistency of the latter scenario with the observed pion to baryon ratio is presently debated. Another source of dilepton production is simply the bremsstrahlung due to the deceleration of the incoming nuclei during the collision. Motivated by a recent result of Mishustin et.al. [10], we investigate whether this source could account for part of the observed enhancement of dilepton numbers as reported by CERES collaboration. In reference [10] only the production of ω mesons due to the deceleration and their subsequent decay into dileptons has been taken into account. This corresponds to considering the iso-scalar part of the electro-magnetic current. However, one also has to take into account the iso-vector part, i.e. production of ρ-mesons and their subsequent decay into dileptons. These two amplitudes, iso-scalar and iso-vector, interfere destructively and as a result the dilepton production cross section from the coherent deceleration scales like the square of the charge and not the square of the baryon number, as assumed in [10]. We should also note that the point like limit of this process addressed here has been