Planar two-loop master integrals for massive Bhabha scattering: N_f=1 and N_f=2

Abstract

Recent developments in the computation of two-loop master integrals for massive Bhabha scattering are briefly reviewed. We apply a method based on expansions of exact Mellin-Barnes representations and evaluate all planar four-point master integrals in the approximation of small electron mass at fixed scattering angle for the one-flavor case. The same technique is employed to derive and evaluate also all two-loop masters generated by additional fermion flavors. The approximation is sufficient for the determination of QED two-loop corrections for Bhabha scattering in the kinematics planned to be used for the luminosity determination at the ILC.

Comments: 10 pages, 3 figures, 1 table, to appear in the proceedings of 8th DESY Workshop on Elementary Particle Theory: Loops and Legs in Quantum Field Theory, Eisenach, Germany, 23-28 Apr 2006; eqns. 22 and 23 corrected