Two - Loop N F = 1 QED Bhabha Scattering : Soft Emission and Numerical Evaluation of the Differential Cross - section

Recently, we evaluated the virtual cross-section for Bhabha scattering in pure QED, up to corrections of order α 4 (N F = 1). This calculation is valid for arbitrary values of the squared center of mass energy s and momentum transfer t; the electron and positron mass m was considered a finite, non vanishing quantity. In the present work, we supplement the previous calculation by considering the contribution of the soft photon emission diagrams to the differential cross-section, up to and including terms of order α 4 (N F = 1). Adding the contribution of the real corrections to the renormalized virtual ones, we obtain an UV and IR finite differential cross-section; we evaluate this quantity numerically for a significant set of values of the squared center of mass energy s.