Eur. Phys. J. C (2006) 48: 35-52
https://doi.org/10.1140/epjc/s10052-006-0008-6

Theoretical Physics

One-loop photonic corrections to Bhabha scattering in d=4-2ε dimensions

¹ Fakultät für Physik, Universität Bielefeld, Universitätsstr. 25, 33615, Bielefeld, Germany
² Department of Field Theory and Particle Physics, Institute of Physics, University of Silesia, Uniwersytecka 4, 40007, Katowice, Poland
³ Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, 79104, Freiburg, Germany
⁴ Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, 15738, Zeuthen, Germany

^* e-mail: Tord.Riemann@desy.de

Received: 22 June 2006
Revised: 14 July 2006
Published online: 28 September 2006

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 ε=(4-d)/2 are derived with inclusion of the terms of order ε in order to match the two-loop accuracy. For the photonic box master integral in d dimensions we compare several different methods of evaluation.