Dependence of five and six-loop estimated QCD corrections to the relation between pole and running masses of heavy quarks on the number of light flavours

Abstract

In this paper various theoretical approaches are used to define the dependence of the estimated $\mathcal{O}({\alpha }_s^5)$ and $\mathcal{O}({\alpha }_s^6)$-corrections to the QCD relation between pole and $\overline{\mathrm{MS}}$ running masses of heavy quarks on the number of light flavours. It is found that recently studied asymptotic formula for the coefficients of this relation, based on the infared-renormalon method, does not reproduce sign-alternating structure in the flavour-dependence of the five and six-loop corrections, which holds in three other used by us approaches.

arXiv comment6 pages, 1 Table. Accepted for publication in JETP Letters

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• Renormalon-motivated evaluation of QCD observables
• Hyperasymptotic approximation to the top, bottom and charm pole mass
• Determination of the top-quark $\overline{\mathrm{MS}}$ running mass via its perturbative relation to the on-shell mass with the help of principle of maximum conformality
• Notes on interplay of the QCD and EW perturbative corrections to the pole-running top-quark mass ratio
• Renormalons beyond the Borel plane
• Precise determination of the top-quark on-shell mass $M_t$ via its scale-invariant perturbative relation to the top-quark $\overline{\mathrm{MS}}$ mass ${\overline{m}}_t({\overline{m}}_t)$
• Precise determination of the bottom-quark on-shell mass using its four-loop relation to the $\overline{\mathrm{MS}}$-scheme running mass