Eur. Phys. J. C (2017) 77: 681
https://doi.org/10.1140/epjc/s10052-017-5250-6

Regular Article - Theoretical Physics

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

¹ Physik Department T31, Technische Universität München, James Franck Straße 1, 85748, Garching, Germany
² Grup de Física Teòrica, Dept. Física and IFAE-BIST, Universitat Autònoma de Barcelona, Bellaterra, 08193, Barcelona, Spain
³ PRISMA Cluster of Excellence, Institute of Physics, Johannes Gutenberg University, Staudingerweg 7, 55128, Mainz, Germany

^* e-mail: pineda@ifae.es

Received: 27 June 2017
Accepted: 22 September 2017
Published online: 14 October 2017

Abstract

We consider the and the spin-independent momentum-dependent 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 and , 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.