Three-loop massive form factors: complete light-fermion corrections for the vector current

TL;DR

This paper presents a comprehensive three-loop QCD calculation of massive quark form factors involving light-fermion corrections, providing analytic results for master integrals including non-planar contributions.

Contribution

It offers the first complete analytic computation of three-loop light-fermion corrections to massive quark form factors, including non-planar diagrams, using differential equations and Goncharov polylogarithms.

Findings

Analytic expressions for all master integrals obtained.

Includes non-planar contributions not in previous large-$N_c$ results.

Enhances precision of QCD form factor calculations.

Abstract

We compute the three-loop QCD corrections to the massive quark-anti-quark-photon form factors $F_1$ and $F_2$ involving a closed loop of massless fermions. This subset is gauge invariant and contains both planar and non-planar contributions. We perform the reduction using FIRE and compute the master integrals with the help of differential equations. Our analytic results can be expressed in terms of Goncharov polylogarithms. We provide analytic results for all master integrals which are not present in the large-$N_c$ calculation considered in Refs. [1,2].