Planar two-loop integrals for $\mathbf{\mu e}$ scattering in QED with finite lepton masses

TL;DR

This paper provides exact analytic expressions for planar two-loop QED integrals involving muon-electron scattering with finite lepton masses, enabling accurate calculations across all mass regimes.

Contribution

It introduces comprehensive analytic formulas for two-loop integrals in muon-electron scattering without mass approximations, facilitating precise numerical evaluations.

Findings

Results valid for all electron mass regimes

Expressions in terms of multiple polylogarithms

Enables fast numerical evaluation in physical phase-space

Abstract

We present analytic results for one of two types of planar QED two-loop integrals for $\mu e$ scattering including finite lepton masses. No approximations are made, such that the results are valid not only in the limit of a small electron mass. The results are expressed in terms of multiple polylogarithms with algebraic function arguments in a representation which allows for fast numerical evaluation in the physical phase-space.