Two-loop operator matrix elements for massive fermionic local twist-2 operators in QED

Abstract

We describe the calculation of the two--loop massive operator matrix elements with massive external fermions in QED. We investigate the factorization of the $O({\alpha }^2)$ initial state corrections to $e^{+}{e}^{-}$ annihilation into a virtual boson for large cms energies $s\gg m_e^2$ into massive operator matrix elements and the massless Wilson coefficients of the Drell-Yan process adapting the color coefficients to the case of QED, as proposed by Berends et. al. in Ref. [1]. Our calculations show explicitly that the representation proposed in Ref. [1] works at one-loop order and up to terms linear in $\ln (s/m_e^2)$ at two-loop order. However, the two-loop constant part contains a few structural terms, which have not been obtained in previous direct calculations.

Comments: 8 pages, Proceedings: RADCOR 2011