On the flavour dependence of the $O(\alpha_{s}^{4})$ correction to the relation between running and pole heavy quark masses

Abstract

Recently the four-loop perturbative QCD contributions to the relations between pole and running masses of charm, bottom and top quarks were evaluated in the $ \overline{MS}$ scheme with identical numerical error bars. In this work the flavour dependence of the $O(\alpha_{s}^{4})$ correction to these asymptotic series is obtained in the semi-analytical form with the help of the least squares method. The numerical structure of the corresponding asymptotic perturbative relations between pole and running c -, b - and t -quark masses is considered and the theoretical errors of the $O(\alpha_{s}^{4})$ contributions are discussed. The explicit dependence for these relations on the renormalization scale $ \mu^{2}$ and the flavour number nl is presented.