Massive three-loop form factor in the planar limit

TL;DR

This paper calculates the three-loop quantum chromodynamics corrections to form factors involving massive quarks in the planar limit, providing analytic expressions and series expansions for different kinematic regimes.

Contribution

It presents the first complete three-loop results for massive quark form factors in the large-N_c limit, expressed via Goncharov polylogarithms, with detailed series expansions.

Findings

Analytic three-loop form factors in terms of Goncharov polylogarithms

Series expansions for various kinematic regions including small and large invariant masses

Results facilitate precise numerical evaluations of heavy quark processes

Abstract

We compute the three-loop QCD corrections to the massive quark-anti-quark-photon form factors $F_1$ and $F_2$ in the large-$N_c$ limit. The analytic results are expressed in terms of Goncharov polylogarithms. This allows for a straightforward numerical evaluation. We also derive series expansions, including power suppressed terms, for three kinematic regions corresponding to small and large invariant masses of the photon momentum, and small velocities of the heavy quarks.