Review of heavy quarkonium at weak coupling

Abstract

We review weakly-bound heavy quarkonium systems using effective field theories of QCD. We concentrate on potential Non-Relativistic QCD, which provides with a well founded connection between QCD and descriptions of the heavy quarkonium dynamics in terms of Schrödinger-like equations. This connection is obtained using standard quantum field theory techniques such as dimensional regularization, which is used throughout, and renormalization. Renormalization group equations naturally follow. Certain effort is made to illustrate how computations are performed and the necessary techniques, providing some examples. Finally, we briefly review a selected set of applications, which include spectroscopy, radiative transitions, non-relativistic sum rules, inclusive decays, and electromagnetic threshold production.

Relativistic corrections to the static energy in terms of Wilson loops at weak coupling

“…Such equation can be derived from first principles using effective field theories (EFTs) like potential NRQCD (pNRQCD) [1,2] (for reviews see [3,4]). This EFT systematically exploits the nonrelativistic scale hierarchy m mv mv 2 .…”

Improved determination of heavy quarkonium magnetic dipole transitions in potential nonrelativistic QCD

“…[3,4]) disentangle the dynamics of the heavy quarks from the dynamics of the light degrees of freedom efficiently and in a model-independent way. They profit from the fact that the dynamics of the bound state system is characterized by, at least, three widely separated scales: hard (the mass m of the heavy quarks), soft (the relative momentum | p| ∼ mv ≪ m of the heavy-quark-antiquark pair in the center-of-mass frame), and ultrasoft (the typical kinetic energy E ∼ mv 2 of the heavy quark in the bound state system).…”

Spectator effects in the HQET renormalization group improved Lagrangian at O(1/m3) with leading logarithmic accuracy: Spin-dependent case

“…(27)-(34), and that complement those that can be found in Refs. [7,18]. The conventions are shown in Fig.…”

“…The latter, is a theory optimized for the description of heavy quarkonium near threshold (for reviews see Refs. [6,7]). …”