Heavy quarkonia: Wilson area law, stochastic vacuum model, and dual QCD

Abstract

The $Q \bar{Q}$ semirelativistic interaction in QCD can be simply expressed in terms of the Wilson loop and its functional derivatives. In this approach we present the $Q \bar{Q}$ potential up to order $1/m^2$ using the expressions for the Wilson loop given by the Wilson Minimal Area Law (MAL), the Stochastic Vacuum Model (SVM) and Dual QCD (DQCD). We confirm the original results given in the different frameworks and obtain new contributions. In particular we calculate up to order $1/m^2$ the complete velocity dependent potential in the SVM. This allows us to show that the MAL model is entirely contained in the SVM. We compare and discuss also the SVM and the DQCD potentials. It turns out that in these two very different models the spin-orbit potentials show up the same leading non-perturbative contributions and 1/r corrections in the long-range limit.