We describe the QQbar_threshold library for computing the production cross section of heavy quark-antiquark pairs near threshold at electron-positron colliders. The prediction includes all presently known QCD, electroweak, Higgs, and nonresonant corr
ections in the combined nonrelativistic and weak-coupling expansion.
Combining recent perturbative analyses on the static QCD potential and the quark pole mass, we find that, for the heavy quarkonium states $cbar{c}$, $bbar{b}$ and $tbar{t}$, (1) ultra-soft (US) corrections in the binding energies are small, and (2) t
here 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 ($n_lapprox 0$), 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.
We derive a full formula for the energy level of a heavy quarkonium state identified by the quantum numbers $n$, $ell$, $s$ and $j$, up to ${cal O}(alpha_s^5 m)$ and ${cal O}(alpha_s^5 m log alpha_s)$ in perturbative QCD. The QCD Bethe logarithm is g
iven in a one-parameter integral form. The rest of the formula is given as a combination of rational numbers, transcendental numbers ($pi$, $zeta(3)$, $zeta(5)$) and finite sums (besides the 3-loop constant $bar{a}_3$ of the static potential whose full analytic form is still unknown). A derivation of the formula is given.
We compute the third-order correction to the heavy-quark current correlation function due to the emission and absorption of an ultrasoft gluon. Our result supplies a missing contribution to top-quark pair production near threshold and the determination of the bottom quark mass from QCD sum rules.
We compute the third-order correction to the S-wave quarkonium wave functions |psi_n(0)|^2 at the origin from non-Coulomb potentials in the effective non-relativistic Lagrangian. Together with previous results on the Coulomb correction and the ultras
oft correction computed in a companion paper, this completes the third-order calculation up to a few unknown matching coefficients. Numerical estimates of the new correction for bottomonium and toponium are given.
We present new results on the NNNLO top-antitop production cross section near threshold from potential and ultrasoft gluon corrections. The new non-logarithmic third-order terms are in the 10% range and lead to a significant reduction in the theoretical error.
We compute the third-order correction to electromagnetic S-wave quarkonium production and annihilation rates due to the emission and absorption of an ultrasoft gluon. Our result completes the analysis of the non-relativistic quarkonium bound-state
dynamics in the next-to-next-to-next-to-leading order. The impact of the ultrasoft correction on the Upsilon(1S) leptonic width and the top quark-antiquark threshold production cross section is estimated.
