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

TL;DR

This paper calculates two-loop massive operator matrix elements in QED for massive fermions, confirming the factorization of initial state corrections in high-energy electron-positron annihilation and revealing new structural terms at two-loop order.

Contribution

It provides the first explicit two-loop calculation of massive operator matrix elements in QED, extending the factorization framework and identifying new structural terms.

Findings

Validation of the factorization approach at two-loop order

Explicit two-loop operator matrix elements for massive fermions in QED

Identification of new structural terms in the two-loop constant part

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 $\ln(s/m^2_e)$ at two-loop order. However, the two-loop constant part contains a few structural terms, which have not been obtained in previous direct calculations.