Top quark mass determination and O(α_S⁵m) correction to the toponium 1S energy level

Recently the full O(α_S⁵m, α _S⁵ log α_S) correction to the heavy quarkonium 1S energy level has been computed (except the a₃ term in the QCD potential). We point out that the full correction (including the log α_S term) is approximated well by the large-β₀ 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(Λ_QCD) accuracy at a future e⁺e^- collider, while the modified minimal-subtraction (MS̄) mass can be determined to about 40 MeV accuracy (provided the 4-loop MS̄-pole mass relation will be computed in due time).