The least squares method: application to analysis of the flavor dependence of the QCD relation between pole and $\overline{\mathrm{MS}}$-scheme running heavy quark masses

Abstract

The features of the ordinary least squares method, which gives a possible way to a solution of the overdetermined systems of algebraic equations and allows to estimate the uncertainties of the obtained solutions, are considered. As the important physical example we define four-loop QCD coefficients in the dependence of the relation between pole and running heavy quarks masses on the number of light flavors, using the existing results of numerical supercomputer based calculations of the corresponding four-loop contributions at different fixed numbers of light flavors. Stability of the found solutions to the number of the considered equations and unknowns is demonstrated and supported by the Pearsons's $\chi$-squared test.

arXiv comment9 pages, 1 Table

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• Precise determination of the bottom-quark on-shell mass using its four-loop relation to the $\overline{\mathrm{MS}}$-scheme running mass
• Higgs Boson Mass Corrections at Three-Loops in the Top-Yukawa Sector of the Standard Model