Renormalons and the heavy quark effective theory

We propose a non-perturbative method 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. We illustrate our procedures by presenting physical definitions of the binding energy (Λ and of the kinetic energy (−λ12mQ) of the heavy quark in a hadron. This allows us to define a “subtracted pole mass”, whose inverse can be used as the expansion parameter in applications of the HQET. We also discuss the determination of the Wilson coefficients of the subtracted operators, necessary for predictions of physical quantities, such as the running quark mass mQ in the MS scheme.