New results on heavy quarks near threshold
M. Beneke
TL;DR
This paper reviews the threshold expansion approach to heavy-quark systems near threshold and its connection to the effective theories NRQCD and PNQRQCD. It discusses the four-scale separation (hard, soft, potential, ultrasoft) and how to perform systematic expansions, including Coulomb resummation and matching. The authors summarize NNLO results for $J/\psi\to l^+ l^-$, bottom quark mass determinations from Upsilon sum rules, and the near-threshold $t\bar t$ production cross section, highlighting issues with mass schemes and long-distance sensitivity. The work demonstrates significant progress in perturbative determinations of heavy-quark masses and threshold observables while acknowledging ongoing challenges in non-perturbative effects and scheme dependence.
Abstract
We review in brief the threshold expansion, a method to perform the expansion of Feynman integrals near the heavy quark-antiquark threshold, and its relation to the construction of two effective theories, non-relativistic QCD (NRQCD) and potential-NRQCD. We then summarize recent next-to-next-to-leading order results on the decay $J/Ψ\to l^+ l^-$, the bottom quark mass from $Υ$ sum rules and the top-anti-top production cross section near threshold in $e^+ e^-$ collisions.