HIGHER-ORDER QED CORRECTIONS TO BHABHA SCATTERING AT LOW ANGLES

We calculate the QED bremsstrahlung corrections beyond O(alpha) for small-angle Bhabha scattering. These corrections are of vital importance for measuring the luminosity and consequently the total cross sections in LEP experiments. They are dominated by the second order leading-logarithmic contributions. We calculate them with the high technical precision 0.02% and we show that they depend strongly of the details of experimental cut-offs. We propose a practical method of introducing the O(alpha-2) correction calculated in this paper into current procedures of the luminosity measurement at LEP. The remaining overall QED uncertainty is estimated to be 0.3%. This estimate includes 0.2% due to pure bremsstrahlung and 0.1% due to light pair production but does not include hadronic uncertainty in the photon vacuum polarization.