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

## TL;DR

This paper applies the least squares method to analyze the flavor dependence of the relation between pole and MS-bar scheme heavy quark masses in QCD, demonstrating stability and uncertainty estimation of the solutions.

## Contribution

It introduces a novel application of the least squares method to determine four-loop QCD coefficients for heavy quark masses across different flavor numbers.

## Key findings

- Successfully estimated four-loop QCD coefficients for various flavors.
- Demonstrated the stability of solutions using statistical tests.
- Provided uncertainty estimates for the calculated coefficients.

## 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.