Two-loop QED Operator Matrix Elements with Massive External Fermion Lines

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 Ref. \cite{BBN} that the 2–loop QED initial state corrections to $e^{+}{e}^{-}$ annihilation into a virtual neutral gauge boson, except power corrections of $O((m_f^2\mathrm{/}s{)}^k),k\ge 1$, can be represented in terms of these matrix elements and the massless 2-loop Wilson coefficients of the Drell-Yan process.