Heavy quarks, renormalons and lattices

I review the non-perturbative method, developed with Martinelli, for defining the higher dimensional operators which appear in the Heavy Quark Effective Theory (HQET), such that their matrix elements are free of renormalon singularities, and diverge at most logarithmically with the ultra-violet cut-off. Matrix elements of these operators can be computed numerically in lattice simulations of the HQET. The procedures are illustrated by presenting physical definitions of the binding energy (Λ) and of the kinetic energy (-λ1 /2mQ ) of the heavy quark in a hadron. This allows for a definitions of a ''subtracted pole mass'', whose inverse can be used as the expansion parameter in applications of the HQET. I also present some numerical results for the binding energy (Λ=190±30 MeV), and the kinetic energy (/λ1/ ///(2MB) < 1.0 GeV2), obtained with Crisafulli, Gimenez and Martinelli. (author). 33 refs, 2 figs