Fermionic contributions to the three-loop static potential

TL;DR

This paper calculates three-loop fermionic corrections to the static potential, revealing their significance for different quark systems and employing advanced integral reduction and evaluation techniques.

Contribution

It provides the first detailed computation of fermionic three-loop corrections to the static potential using Gr"obner, Laporta, and Mellin-Barnes methods.

Findings

Fermionic corrections are 2% for top quarks

8% for bottom quarks

27% for charm quarks

Abstract

We consider the three-loop corrections to the static potential which are induced by a closed fermion loop. For the reduction of the occurring integrals a combination of the Gr\"obner and Laporta algorithm has been used and the evaluation of the master integrals has been performed with the help of the Mellin-Barnes technique. The fermionic three-loop corrections amount to 2% of the tree-level result for top quarks, 8% for bottom quarks and 27% for the charm quark system.