General approach to the computation of instanton effects

Abstract

A systematic approach is developed for the computation of physical effects associated with nonperturbative vacuum structure generated by instantons. The new feature of this approach is that the size of instantons which naturally contribute to the effect in question is governed by the momentum q of the experimental probe. In that sense, nonperturbative vacuum structure can be controlled in the same way as perturbative short-distance corrections. The contribution of an instanton of size rho to certain measurable quantities falls as e/sup -rhoq/. Consequently, since the instanton density function decreases with decreasing rho, by making q large enough the effects due to a single instanton can be isolated. No ad hoc cutoff or assumption about the behavior of large, overlapping instantons need be introduced. The exponential falloff (essential to cutoff-independent calculations) emerges only in momentum space and is seen to depend on a set of smoothness and integrability properties of the instanton contribution to the effect in coordinate space. An analysis of these properties provides a characterization of the quantities which may be reliably computed in momentum space. The general approach is illustrated by two specific computations: instanton contributions to the static interaction of a heavy QQ-bar pair and to themore » correlation function of two electromagnetic currents, which is related to sigma/sub tot/ (e/sup +/e/sup -/ ..-->.. hadrons).« less