From perturbative calculations of the QCD static potential towards four-loop pole-running heavy quarks masses relation

TL;DR

This paper reviews semi-analytical three-loop results for the QCD static potential and heavy quark mass ratios, discusses a method to determine four-loop contributions, and highlights discrepancies in numerical uncertainties.

Contribution

It introduces a procedure to analyze four-loop contributions to heavy quark mass ratios using least squares, addressing uncertainties and discrepancies in existing calculations.

Findings

Presented semi-analytical three-loop results for QCD static potential.

Described a method to determine four-loop mass ratio contributions based on least squares.

Highlighted the need to clarify discrepancies in numerical uncertainties of four-loop coefficients.

Abstract

The summary of the available semi-analytical results for the three-loop corrections to the QCD static potential and for the $\mathcal{O}(\alpha_s^4)$ contributions to the ratio of the running and pole heavy quark masses are presented. The procedure of the determination of the dependence of the four-loop contribution to the pole-running heavy quarks mass ratio on the number of quarks flavours, based on application of the least squares method is described. The necessity of clarifying the reason of discrepancy between the numerical uncertainties of the $\alpha_s^4$ coefficients in the mass ratio, obtained by this mathematical method by the direct numerical calculations is emphasised.