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

Abstract

We consider the $\mathcal{O}(1/m)$ and the spin-independent momentum-dependent $\mathcal{O}(1/m^2)$ quasi-static energies of heavy quarkonium (with unequal masses). They are defined nonperturbatively in terms of Wilson loops. We determine their short-distance behavior through $\mathcal{O}({\alpha }^3)$ and $\mathcal{O}({\alpha }^2)$, respectively. In particular, we calculate the ultrasoft contributions to the quasi-static energies, which requires the resummation of potential interactions. Our results can be directly compared to lattice simulations. In addition, we also compare the available lattice data with the expectations from effective string models for the long-distance behavior of the quasi-static energies.

32 pages, 12 figures; v2: journal version

References in corpus (7)

• Nonperturbative determination of the QCD potential at O(1/m)
• The QCD static energy at NNNLL
• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
• Effective string theory and the long-range relativistic corrections to the quark-antiquark potential
• The static potential in {\cal N}=4 supersymmetric Yang-Mills at weak coupling
• Two-Loop Ultrasoft Running of the O(v^2) QCD Quark Potentials
• NLL resummation for the static potential in N=4 SYM theory

Cited by in corpus (2)

• 50 Years of Quantum Chromodynamics
• Heavy meson thresholds in Born-Oppenheimer Effective field theory