Heavy quark effective theory beyond perturbation theory: renormalons, the pole mass and the residual mass term

Abstract

We study the asymptotic behaviour of the perturbative series in the heavy\nquark effective theory (HQET) using the $1/N_f$ expansion. We find that this\ntheory suffers from an {\\it ultraviolet} renormalon problem, corresponding to a\nnon-Borel-summable behaviour of perturbation series in large orders, and\nleading to a principal nonperturbative ambiguity in its definition. This\nambiguity is related to an {\\it infrared} renormalon in the pole mass and can\nbe understood as the necessity to include the residual mass term $\\delta m$ in\nthe definition of HQET, which must be considered as ambiguous (and possibly\ncomplex), and is required to cancel the ultraviolet renormalon singularity\ngenerated by the perturbative expansion. The formal status of $\\delta m$ is\nthus identical to that of condensates in the conventional short-distance\nexpansion of correlation functions in QCD. The status of the pole mass of a\nheavy quark, the operator product expansion for inclusive decays, and QCD sum\nrules in the HQET are discussed in this context.\n