HEAVY-QUARK EFFECTIVE THEORY BEYOND PERTURBATION-THEORY - RENORMALONS, THE POLE MASS AND THE RESIDUAL MASS TERM

We study the asymptotic behaviour of the perturbative series in the he avy quark effective theory (HQET) using the 1/N-f expansion. We find t hat this theory suffers from an ultraviolet renormalon problem, corres ponding to a non-Borel-summable behaviour of perturbation series in la rge orders, and leading to a principal nonperturbative ambiguity in it s definition. This ambiguity is related to an infrared renormalon in t he pole mass and can be understood as the necessity to include the res idual mass term delta m in the definition of HQET, which must be consi dered as ambiguous (and possibly complex), and is required to cancel t he ultraviolet renormalon singularity generated by the perturbative ex pansion. The formal status of delta m is thus identical to that of con densates in the conventional short-distance expansion of correlation f unctions in QCD. The status of the pole mass of a heavy quark, the ope rator product expansion for inclusive decays, and QCD sum rules in the HQET are discussed in this context.