OPERATOR PRODUCT EXPANSION, HEAVY QUARKS, QCD DUALITY AND ITS VIOLATIONS

The quark(gluon)-hadron duality constitutes a basis for the theoretica l treatment of a wide range of inclusive processes - from hadronic tau decays and R(e+e-) to semileptonic and nonleptonic decay rates of hea vy flavor hadrons. A theoretical analysis of these processes is carrie d out by using the operator product expansion in the Euclidean domain, with subsequent analytic continuation to the Minkowski domain. We for mulate the notion of the quark(gluon)-hadron duality in quantitative t erms, then classify various contributions leading to violations of dua lity. A prominent role in the violations of duality seems to belong to the so-called exponential terms which, conceptually, may represent th e (truncated) tail of the power series. A qualitative model, relying o n an instanton background field, is developed, allowing one to get an estimate of the exponential terms. We then discuss a number of applica tions, mostly from heavy quark physics.