Exact Results on O(alpha^2) Single Bremsstrahlung Corrections to Low   Angle Bhabha Scattering at LEP/SLC Energies
  In this thesis exact results on O(alpha^2) single bremsstrahlung corrections to low angle Bhabha scattering at LEP/SLC energies are given. The calculation represents the last outstanding theoretical second order subleading electroweak contribution for that process, needed to determine the experimental luminosity at second generation LEP detectors below the 0.1% precision threshold. The exact, fully differential result is obtained by employing analytical as well as computer-algebraic methods and includes terms up to O(0.05%) relative to the Born cross section. The initial output of over 20,000 terms could be reduced to 90, only 18 of which are shown to be numerically relevant and for which a simple logarithmic ansatz is derived, that is in remarkable agreement with the complete answer. Strong consistency checks are performed, including Ward-Takahashi identities and tests on the right infrared limit according to the Yennie, Frautschi and Suura program. Monte Carlo results for the integrated cross section are compared with existing calculations in the leading logarithmic approximation for a chosen set of experimental cuts. The size of the missing subleading terms is found to be small but non negligible in the context of setting stringent limits on Standard Model predictions and thus its realm of validity. 
Michael Melles (SLAC)