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

Understand

The asymptotic structure of the QCD perturbative relation between the on-shell and $\overline{\rm{MS}}$ 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-$\beta_0$ approximation are analyzed.