On the ambiguity of composite operators, IR renormalons and the status of the operator product expansion

Abstract

It is not possible in general to define in an unambiguous way the vacuum expectation value of local operators such that 〈0|Tr G μν G μν |0〉 used in the QCD sum rules formalism. This phenomenon is exhibited via the 1/ N expansion of some two-dimensional models and explains the existence of IR singularities (renormalons) in the Borel plane. Such ambiguities are present in the general definition of composite operators in any UV free theory. The consequences for the status of the operator product expansion are discussed.