Instanton contributions to the $τ$ decay widths

Abstract

Contrary to some previous claims, we find a sizable instanton contribution to the finite energy sum rule used to extract the value of the strong coupling from the measured $τ$ decay widths. It is of the same order of magnitude as standard nonperturbative corrections induced by vacuum quark and gluon condensates. Our result indicates that there might be no hierarchy of power corrections in finite energy sum rules at the scale of $τ$ mass. Therefore, the standard nonperturbative corrections do not necessarily improve the accuracy of the theoretical predicition, but can rather be used to estimate an intrinsic accuracy of the pure perturbative calculation, which turns out to be rather high on this evidence, of order one percent.