Two-loop QED operator matrix elements with massive external fermion lines

Abstract

The two-loop massive operator matrix elements for the fermionic local twist-2 operators with external massive fermion lines in Quantum Electrodynamics (QED) are calculated up to the constant terms in the dimensional parameter ε = D − 4 . We investigate the hypothesis of Berends et al. (1988) [1] that the 2-loop QED initial state corrections to e + e − annihilation into a virtual neutral gauge boson, except power corrections of O ( ( m f 2 / s ) k ) , k ⩾ 1 , can be represented in terms of these matrix elements and the massless 2-loop Wilson coefficients of the Drell–Yan process.