Small Angle Bhabha Scattering for LEP

Abstract

We present the results of our calculations to a one, two, and three loop approximation of the e$^+$e$^-$$\rightarrow$e$^+$e$^-$ Bhabha scattering cross-section at small angles. All terms contributing to the radiatively corrected cross-section, within an accuracy of $\delta\sigma/ \sigma = 0.1 \% $, are explicitely evaluated and presented in an analytic form. $O(\alpha)$ and $O(\alpha^2)$ contributions are kept up to next-to-leading logarithmic accuracy, and $O(\alpha^3)$ terms are taken into account to the leading logarithmic approximation. We define an experimentally measurable cross-section by integrating the calculated distributions over a given range of final-state energies and angles. The cross-sections for exclusive channels as well as for the totally integrated distributions are also given.