Dileptons from bremsstrahlung: going beyond the soft photon approximation

The traditional calculation of dilepton yields from bremsstrahlung relies on the assumption that electromagnetic and strong processes factorize. We argue that this assumption, embodied by the soft photon approximation, cannot hold true for invariant mass spectra on very general grounds. Deriving a formula for the dilepton cross section for pion-pion scattering that does not rely on such factorization, we formulate the problem exactly in terms of three-particle phase space invariants. Using a simple one boson exchange model for comparison, we find that dilepton cross sections and yields are generally overestimated by the soft photon approximation by factors 2--8. In extreme cases, overestimation up to a factor 40 is possible.