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 flavors

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