Reshuffling the OPE: Delocalized Operator Expansion

Abstract

A prescription for the short-distance expansion of Euclidean current correlators based on a delocalized modification of the multipole expansion of perturbative short-distance coefficient functions is proposed that appreciates the presence of nonlocal physics in the nonperturbative QCD vacuum. This expansion converges better than the local Wilson OPE, which is recovered in the limit of infinite resolution. As a consequence, the usual local condensates in the Wilson OPE become condensates that depend on a resolution parameter and that can be expressed as an infinite series of local condensates with increasing dimension. In a calculation of the nonperturbative correction to the ground state energy level of heavy quarkonia the improved convergence properties of the delocalized expansion are demonstrated. Phenomenological evidence is gathered that the gluon condensate, often being the leading nonperturbative parameter of the Wilson OPE, is indeed a function of resolution. The delocalized expansion is applied to derive a leading order scaling relation for $f_D/f_B$ in the heavy mass expansion.