Exact results on O(α) corrections to the single hard bremsstrahlung process in low angle Bhabha scattering in the SLC/LEP energy regime

We present the exact O(α) correction to the process e+e− → e+e− + γ in the low angle luminosity regime at SLC/LEP energies. We give explicit formulas for the completely differential cross section. As an important application, we illustrate the size of the respective corrections of O (α2) to the SLC/LEP luminosity cross section. We show explicitly that our results have the correct infrared limit, as a cross-check. Some comments are made about the implementation of our results in the framework of a Monte Carlo event generator. This latter implementation will appear elsewhere.