Author:
Kataev A. L.,Molokoedov V. S.
Abstract
AbstractThe asymptotic structure of the QCD perturbative relation between the on-shell and $$\overline{{\mathrm{MS}}}$$
MS
¯
heavy quark masses is studied. We estimate the five and six-loop contributions to this relation by three different techniques. First, the effective charges motivated approach in two variants is used. Second, the results following from the large-$$\beta _0$$
β
0
approximation are analyzed. Finally, the consequences of applying the asymptotic renormalon-based formula are investigated. We show that all approaches lead to corrections which are qualitatively consistent in order of magnitude. Their sign-alternating character in powers of the number of massless quarks is demonstrated. We emphasize that there is no contradiction in the behavior of the fine structure of the renormalon-based estimates with other approaches if one use the detailed information about the normalization factor included in the renormalon asymptotic formula. The obtained five- and six-loop estimates indicate that in the case of the b-quark the asymptotic character of the studied relation manifests itself above the fourth order of PT, whereas for the t-quark it starts to reveal itself after the seventh order. This allows to conclude that like the running masses, the pole masses of the b and especially t-quark in principle may be used in the phenomenologically-oriented studies.
Funder
Foundation for the Advancement of Theoretical Physics and Mathematics
Publisher
Springer Science and Business Media LLC
Subject
Physics and Astronomy (miscellaneous),Engineering (miscellaneous)
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