Cancellation of Renormalon Ambiguities in the Heavy Quark Effective Theory

Recently, it has been shown that the concept of the pole mass of a heavy quark becomes ambiguous beyond perturbation theory, because of the presence of infrared renormalons. We argue that the predictions of heavy quark effective theory, whose construction is based on the pole mass, are free of such ambiguities. In the $1/m_Q$ expansion of physical quantities, infrared and ultraviolet renormalons compensate each other between coefficient functions and matrix elements. We trace the appearance of these compensations for current-induced exclusive heavy-to-heavy and heavy-to-light transitions, and for inclusive decays of heavy hadrons. In particular, we show that the structure of the heavy quark expansion is not obscured by renormalons, and none of the predictions of heavy quark effective theory are invalidated.