Lattice and renormalons in heavy quark physics

Perturbative expansions of QCD observables in powers of $\alpha_s$ are believed to be asymptotic and non-Borel summable due to the existence of singularities in the Borel plane (renormalons). This fact is connected with the factorization of scales (which is inherent to QCD and asymptotic freedom) and jeopardizes the convergence of the perturbative expansion and the accurate determination of power-suppressed corrections. This problem is more acute for physical systems composed by one or more heavy quarks. In lattice regulations, it reflects on the appearance of power-like divergences in the inverse of the lattice spacing for a series of quantities ($\bar \Lambda$, gluelump masses, the singlet and hybrid potentials, ...) making that the continuum limit can not be reached for them. Nevertheless, all these problems are solved within the framework of effective field theories with renormalon substraction. This allows us to obtain convergent perturbative series and to unambiguously define power corrections. In particular, one can connect with lattice results. Remarkably enough the dependence on the lattice spacing can be predicted by perturbation theory. This framework has been applied to the prediction of the gluelump masses and the singlet and octet (hybrid) potentials at short distances, as well as to their comparison with lattice simulations. Overall, very good agreement with data is obtained.