A Systematic Study of the Single Instanton Approximation in QCD

The single-instanton approximation (SIA) is often used to evaluate analytically instanton contributions to the Euclidean correlation function in QCD at small distances. We discuss how this approximation can be consistently derived from the theory of instanton ensemble and give precise definitions to a number of different "quark effective masses," generalizing the parameter m*, which was introduced long ago to account for the collective contribution of the whole ensemble. We test numerically the range of applicability of the SIA for different quantities. Furthermore, we determine all the effective masses (for random and interacting instanton liquid models) as well as from phenomenology, and discuss to what extent those are universal.