Phenomenology of renormalons and the OPE from lattice regularization: the gluon condensate and the heavy quark pole mass

We study the operator product expansion of the plaquette (gluon condensate) and the self-energy of an infinitely heavy quark. We first compute their perturbative expansions to order $\alpha^{35}$ and $\alpha^{20}$, respectively, in the lattice scheme. In both cases we reach the asymptotic regime where the renormalon behavior sets in. Subtracting the perturbative series, we obtain the leading non-perturbative corrections of their respective operator product expansions. In the first case we obtain the gluon condensate and in the second the binding energy of the heavy quark in the infinite mass limit. The results are fully consistent with the expectations from renormalons and the operator product expansion.