Two-loop NF=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 α4(NF=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, nonvanishing 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 α4(NF=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.