We obtain the short-distance limit behavior of the nonperturbative definitions, in terms of Wilson loops, of the $1/m$ potential and of the $1/m^2$ spin-independent velocity-dependent heavy quarkonium potentials, with ${\cal O}(\alpha^3)$ and ${\cal O}(\alpha^2)$ accuracy, respectively. These results require a non-perturbative evaluation of ultrasoft effects. The outcome can be compared with lattice simulations. We also compare the lattice data with the expectations from effective string models.

Hadron Spectroscopy and Interactions