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

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