Peculiar features of the relations between pole and running heavy quark masses and estimates of the O(\alpha_s^4) contributions

Abstract

Perturbative relations between pole and running heavy quark masses, defined in the Minkowski regions, are considered. Special attention is paid to the appearance of the kinematic ${\pi }^2$-effects, which exist in the coefficients of these series. The estimates of order $O({\alpha }_s^4)$ QCD corrections are presented.

Comments: Presented at the Conference "Problems of Theoretical and Mathematical Physics", dedicated to 100th anniversary of the birth of N.N. Bogolyubov, Dubna,August 23-27, 2009 and 9th Symposium on RADCOR-2009, October 25-30, 2009, Ascona; typos corrected,results unchanged