https://doi.org/10.1140/epjc/s10052-020-08673-6
Regular Article - Theoretical Physics
Multiloop contributions to the on-shell-
heavy quark mass relation in QCD and the asymptotic structure of the corresponding series: the updated consideration
1
Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect 7a, 117312, Moscow, Russia
2
Moscow Institute of Physics and Technology, Institusky per. 9, 141700, Dolgoprudny, Moscow Region, Russia
Received:
11
December
2019
Accepted:
14
November
2020
Published online:
16
December
2020
The asymptotic structure of the QCD perturbative relation between the on-shell and 
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-
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.
© The Author(s) 2020
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