Evaluating the three-loop static quark potential

TL;DR

This paper reports on the progress of calculating three-loop corrections to the static quark-antiquark potential in QCD, using advanced integral reduction and evaluation techniques, providing initial results for specific coefficients.

Contribution

It introduces a systematic approach to evaluate three-loop corrections in the static QCD potential using FIRE and Mellin-Barnes methods, advancing precision in theoretical predictions.

Findings

Calculated coefficients of n_l^3 and n_l^2 terms in the potential

Applied FIRE for integral reduction in three-loop calculations

Used Mellin-Barnes technique for master integral evaluation

Abstract

This is a status report of the evaluation of the three-loop corrections to the static QCD potential of a heavy quark and an antiquark. The families of Feynman integrals that appear in the evaluation are described. To reduce any integral of the families to master integrals we solve integration-by-parts relations by the algorithm called FIRE. To evaluate the corresponding master integrals we apply the Mellin-Barnes technique. First results are presented: the coefficients of n_l^3 and n_l^2, where n_l is the number of light quarks.