Least Squares Method: Application to Analysis of the Flavor Dependence of the QCD Relation Between Pole and Scheme Running Heavy Quark Masses

Abstract

We consider the ordinary least squares method, which allows solving overdetermined systems of algebraic equations and estimating the error of the obtained solutions. As an important physical example, we determine the four-loop QCD coefficients in the dependence of the relation between poles and running heavy quarks masses on the number of light flavors. For this, we use the existing results of supercomputer calculations of the corresponding four-loop contributions with different fixed numbers of light flavors. We demonstrate the stability of the found solutions under changing the number of considered equations and unknowns.