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Strong IR Cancellation in Heavy Quarkonium and Precise Top Mass Determination

Combining recent perturbative analyses on the static QCD potential and the quark pole mass, we find that, for the heavy quarkonium states $c\bar{c}$, $b\bar{b}$ and $t\bar{t}$, (1) ultra-soft (US) corrections in the binding energies are small, and (2) there is a stronger cancellation of IR contributions than what has been predicted by renormalon dominance hypothesis. By contrast, for a hypothetical heavy quarkonium system with a small number of active quark flavors ($n_l\approx 0$), we observe evidence that renormalon dominance holds accurately and that non-negligible contributions from US corrections exist. In addition, we examine contributions of renormalons at $u=- 1$. As an important consequence, we improve on a previous prediction for possible achievable accuracy of top quark $\overline{\rm MS}$--mass measurement at a future linear collider and estimate that in principle 20--30~MeV accuracy is reachable.