On the flavour dependence of the O(αs4) correction to the relation between running and pole heavy quark masses

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 scheme with identical numerical error bars. In this work the flavour dependence of the 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 contributions are discussed. The explicit dependence for these relations on the renormalization scale and the flavour number n(l) is presented.