English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The asymptotic structure of the QCD perturbative relation between theon-shell and $\overline{\rm{MS}}$ heavy quark masses is studied. We estimatethe five and six-loop contributions to this relation by three differenttechniques. First, the effective charges motivated approach in two variants isused. Second, the results following from the large-$\beta_0$ approximation areanalyzed. Finally, the consequences of applying the asymptotic renormalon-basedformula are investigated. We show that all approaches lead to corrections whichare qualitatively consistent in order of magnitude. Their sign-alternatingcharacter in powers of the number of massless quarks is demonstrated. Weemphasize that there is no contradiction in the behavior of the fine structureof the renormalon-based estimates with other approaches if one use the detailedinformation about the normalization factor included in the renormalonasymptotic formula. The obtained five- and six-loop estimates indicate that inthe case of the $b$-quark the asymptotic character of the studied relationmanifests itself above the fourth order of PT, whereas for the $t$-quark itstarts to reveal itself after the seventh order. This allows to conclude thatlike the running masses, the pole masses of the $b$ and especially $t$-quark inprinciple may be used in the phenomenologically-oriented studies.

Multiloop contributions to the on-shell-$ \overline{\rm{MS}}$ heavy  quark mass relation in QCD and the asymptotic structure of the corresponding  series: the updated consideration