Applying Mellin-Barnes technique and Groebner bases to the three-loop static potential

TL;DR

This paper combines Mellin-Barnes integrals and Groebner bases via FIRE to evaluate three-loop static QCD potentials, presenting initial results for specific quark number coefficients.

Contribution

It introduces a novel combination of Mellin-Barnes technique and Groebner bases with FIRE for three-loop static potential calculations.

Findings

Computed coefficients of n_l^3 and n_l^2 terms.

Demonstrated the effectiveness of the combined techniques.

Provided first results for three-loop static potential corrections.

Abstract

The Mellin-Barnes technique to evaluate master integrals and the algorithm called FIRE to solve IBP relations with the help of Groebner bases are briefly reviewed. In FIRE, an extension of the classical Buchberger algorithm to construct Groebner bases is combined with the well-known Laporta algorithm. It is explained how both techniques are used when evaluating the three-loop correction to the static QCD quark potential. First results are presented: the coefficients of n_l^3 and n_l^2, where n_l is the number of light quarks.