POLE MASS OF THE HEAVY-QUARK - PERTURBATION-THEORY AND BEYOND

The key quantity of the heavy quark theory is the quark mass m(Q). Sin ce quarks are unobservable one can suggest different definitions of m( Q). One of the most popular choices is the pole quark routinely used i n perturbative calculations and in some analyses based on heavy quark expansions. We show that no precise definition of the pole mass can be given in the full theory once nonperturbative effects are included. A ny definition of this quantity suffers from an intrinsic uncertainty o f order LAMBDA(QCD)/m(Q). This fact is succinctly described by the exi stence of an infrared renormalon generating a factorial divergence in the high-order coefficients of the alpha(s) series; the corresponding singularity in the Borel plane is situated at 2pi/b. A peculiar featur e is that this renormalon is not associated with the matrix element of a local operator. The difference LAMBDABAR = M(HQ) - m(Q)pole can sti ll be defined by heavy quark effective theory, but only at the price o f introducing an explicit dependence on a normalization point mu: LAMB DA(mu)BAR. Fortunately the pole mass mQ(0) per se does not appear in c alculable observable quantities.