Two-loop master integrals for $e^{+}e^{-}\rightarrow\mu^+\mu^-$ process with account of electron mass

TL;DR

This paper computes specific two-loop master integrals for the electron-positron to muon-antimuon scattering process, incorporating electron mass effects, and expresses results as Frobenius series with polylogarithmic coefficients.

Contribution

It introduces a method to evaluate two-loop integrals with electron mass dependence using Frobenius series and Goncharov's polylogarithms, advancing precision in theoretical predictions.

Findings

Derived Frobenius series expansions for relevant integrals

Expressed results using Goncharov's polylogarithms

Enhanced understanding of mass effects in scattering amplitudes

Abstract

We calculate a subset of two-loop master integrals relevant for the differential cross section of $e^+e^-\to \mu^+\mu^-$ process. We consider only those families for which the account of the electron mass $m$ is necessary. Our results have the form of the Frobenius series in $m$ with coefficients expressed via Goncharov's polylogarithms.