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We have made a detailed and quantitative study of dilepton production viabremsstrahlung of a virtual photon during pion-pion collisions. Mostcalculations of electromagnetic radiation from strong interaction processesrely on the soft photon approximation (SPA). The conditions underlying thisapproximation are generally violated when dilepton spectra are calculated interms of their invariant mass, so that an approach going beyond the SPA becomesnecessary. Superseding previous derivations, we derive an exact formula for thebremsstrahlung cross section. The resulting formulation is compared to variousforms based on the SPA, the two-particle phase space approximation andR\"uckl's formula using a relativistic One Boson Exchange (OBE) model. Withinthe OBE approach, we show that approximations to the bremsstrahlung dileptoncross sections often differ greatly from the exact result; discrepancies becomegreater both with rising temperature and with invariant mass. Integrateddilepton production rates are overestimated by R\"uckl-based approximations byfactors 1.5--8.0. The largest discrepancies occur for the reaction $\pi^+\pi^+\to \pi^+\pi^+\ell^+\ell^-$, where such approximations overestimate the exactrate by factors ranging from 2 to 30 for invariant masses between 10 and 500MeV. Our findings, combined with recent estimates of the Landau-Pomeranchukeffect, indicate that bremsstrahlung dileptons rates in ultrarelativistic heavyion collisions should be even more suppressed than had been thought before.Comment: REVTeX 3.0, 26 pages plus 15 figures in uuencoded PostScrip

Dilepton bremsstrahlung from pion-pion scattering in a relativistic one boson exchange model