Reshuffling the OPE Delocalized Operator Expansion.pdf

a r X i v : h e p - p h / 0 2 0 7 3 4 1 v 1 2 9 J u l 2 0 0 2 RESHUFFLING THE OPE: DELOCALIZED OPERATOR EXPANSION R. HOFMANN Max-Planck-Institut fu?r Physik, Werner-Heisenberg-Institut Fo?hringer Ring 6 80805 Mu?nchen, Germany E-mail: ralfh@mppmu.mpg.de A generalization of the operator product expansion for Euclidean correlators of gauge invariant QCD currents is presented. Each contribution to the modified expansion, which is based on a delocalized multipole expansion of a perturbatively determined coefficient function, sums up an infinite series of local operators. On a more formal level the delocalized operator expansion corresponds to an optimal choice of basis sets in the dual spaces which are associated with the interplay of perturbative and nonperturbative N-point correlations in a distorted vacuum. A consequence of the delocalized expansion is the running of condensates with the external momentum. Phenomenological evidence is gathered that the gluon condensate, often being the leading nonperturbative parameter in the OPE, is indeed a function of resolution. Within a model calculation of the nonperturbative corrections to the ground state energy of a heavy quarkonium system it is shown exemplarily that the convergence properties are better than those of the OPE. Potential applications of the delocalized operator expansion in view of estimates of the violation of local quark-hadron duality are discussed. 1. Introduction 1.1. Some historical remarks Once again: Happy Birthday, Arkady! This is a very lively conference that I am happy to attend. In this talk I would like to report about work done jointly with Andre? Hoang. The subject is to formulate a framework for a generalization of Wil- son’s operator product expansion (OPE), to confront this framework with experiment, and to demonstrate its usefulness in some model calculations. As a warm-up I remind you of some of the OPE applications. The OPE is a powerful tool for the treatment of conformally invaria