Top quark mass determination andO(αS5m)correction to the toponium1Senergy level

Abstract

Recently the full $O({\ensuremath{\alpha}}_{S}^{5}m,{\ensuremath{\alpha}}_{S}^{5}m\mathrm{log}{\ensuremath{\alpha}}_{S})$ correction to the heavy quarkonium $1S$ energy level has been computed (except the ${a}_{3}$ term in the QCD potential). We point out that the full correction (including the $\mathrm{log}{\ensuremath{\alpha}}_{S}$ term) is approximated well by the large-${\ensuremath{\beta}}_{0}$ approximation. Based on the assumption that this feature holds up to higher orders, we discuss why the top quark pole mass cannot be determined to better than $O({\ensuremath{\Lambda}}_{\mathrm{QCD}})$ accuracy at a future ${e}^{+}{e}^{\ensuremath{-}}$ collider, while the modified minimal-subtraction $(\overline{\mathrm{MS}})$ mass can be determined to about 40 MeV accuracy (provided the 4-loop $\overline{\mathrm{MS}}$-pole mass relation will be computed in due time).