Perturbative heavy quarkonium spectrum at next-to-next-to-next-to-leading order

We compute the energy levels of some of the lower-lying heavy quarkonium states perturbatively up to O(alpha_s^5*m) and O(alpha_s^5*m*log[alpha_s]). Stability of the predictions depends crucially on the unknown 4-loop pole-MSbar mass relation. We discuss the current status of the predictions with respect to the observed bottomonium spectrum.Comment: Short review on non-perturbative contributions included at the end; version to appear in Phys.Lett.; 7 pages, 2 figure

Top mass determination and O (alpha_S^5 m) correction to toponium 1S energy level

Recently the full O(alpha_S^5 m, alpha_S^5 m log(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 log(alpha_S)-term) is approximated well by the large-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(Lambda_{QCD}) accuracy at a future e^+e^- collider, while the MS-bar mass can be determined to about 40 MeV accuracy (provided the 4-loop MSbar-pole mass relation will be computed in due time).Comment: LaTeX, 10 pages, 4 eps-figures; Version to appear in Phys. Rev. D, Rapid Communicatio

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.Comment: 17 pages, 7 figures, 3 tables; Revisions in ver.2: We added (i) a more conservative error estimate of m_t determination, (ii) discussion on u=+1 and u=-1 renormalons, (iii) interpretation of PS-schem

Third order Coulomb correction to ttbar threshold cross section

We report on our result of third order Coulomb correction to the cross section sigma(ee -> ttbar) near threshold. Analytic expression for the Coulomb energy and wave function at the origin are obtained. We discuss the significance of the Coulomb correction to the threshold cross section and heavy quarkonium phenomenology.Comment: To appear in the proceedings of the 7th International Symposium on Radiative Corrections(RADCOR05), Shonan Village, Japana Oct. 200

Off-shell Suppression of Renormalons in Non-relativistic QCD Boundstates

We study an effect of the off-shellness of the quark and antiquark inside a heavy quarkonium system on IR renormalons contained in the perturbative computations of the quarkonium energy levels. We demonstrate that, when the off-shellness p_Q^2 -m_Q^2 \sim alpha_S^2 m_Q^2 is larger than m_Q Lambda_QCD, renormalons in the energy levels as calculated in perturbative QCD are suppressed by a factor Lambda_QCD/alpha_S^2 m_Q as compared to those in 2 m_pole + V_QCD(r). In this case the residual O(Lambda_QCD^4) renormalon has the same dimension as that of the leading gluon-condensate contribution.Comment: Version to appear in Phys. Lett. B. 12 pages, 1 figur