Dilepton bremsstrahlung from pion-pion scattering in a relativistic OBE model

Abstract

We have made a detailed and quantitative study of dilepton production via bremsstrahlung of a virtual photon during pion-pion collisions. Most calculations of electromagnetic radiation from strong interaction processes rely on the soft photon approximation (SPA). The conditions underlying this approximation are generally violated when dilepton spectra are calculated in terms of their invariant mass, so that an approach going beyond the SPA becomes necessary. Superseding previous derivations, we derive an exact formula for the bremsstrahlung cross section. The resulting formulation is compared to various forms based on the SPA, the two-particle phase space approximation and Rückl's formula using a relativistic One Boson Exchange (OBE) model. Within the OBE approach, we show that approximations to the bremsstrahlung dilepton cross sections often differ greatly from the exact result; discrepancies become greater both with rising temperature and with invariant mass. Integrated dilepton production rates are overestimated by Rückl-based approximations by factors 1.5--8.0. The largest discrepancies occur for the reaction $π^+π^+ \to π^+π^+\ell^+\ell^-$, where such approximations overestimate the exact rate by factors ranging from 2 to 30 for invariant masses between 10 and 500 MeV. Our findings, combined with recent estimates of the Landau-Pomeranchuk effect, indicate that bremsstrahlung dileptons rates in ultrarelativistic heavy ion collisions should be even more suppressed than had been thought before.