First order radiative corrections to Bhabha scattering in $d$ dimensions

Abstract

The luminosity measurement at the projected International Linear $e^{+}{e}^{-}$ Collider ILC is planned to be performed with forward Bhabha scattering with an accuracy of the order of $10^{-4}$. A theoretical prediction of the differential cross-section has to include one-loop weak corrections, with leading higher order terms, and the complete two-loop QED corrections. Here, we present the weak part and the virtual one-loop photonic corrections. For the photonic corrections, the expansions in $\hat{I}\mu =(4-d)/2$ are derived with inclusion of the terms of order $\hat{I}\mu$ in order to match the two-loop accuracy. For the photonic box master integral in $d$ dimensions we compare several different methods of evaluation.

35 pages, 3 figures, 2 tables, uses feynmp.sty, references updated