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

TL;DR

This paper computes two-loop massive operator matrix elements in QED with external massive fermions and explores their role in initial state corrections for electron-positron annihilation, providing insights into higher-order effects.

Contribution

It presents the first calculation of two-loop massive operator matrix elements with external fermions in QED, extending previous massless results and testing their applicability to initial state corrections.

Findings

Calculated two-loop massive operator matrix elements in QED.

Supported the hypothesis relating these matrix elements to initial state corrections.

Provided results up to constant terms in dimensional regularization parameter.

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 $\epsilon = D - 4$. 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 $O((m_f^2/s)^k), k \geq 1$, can be represented in terms of these matrix elements and the massless 2-loop Wilson coefficients of the Drell-Yan process.