The Problem of Asymptotic Freedom

Abstract

There is a growing body of evidence that the running of $\alpha_s$ predicted by perturbation (PT) theory is not correctly describing the accelerator experiments at the highest energies. A natural explanation is provided by the authors' 1992 proposal that in fact the true running predicted by the nonperturbatively defined lattice QCD is different, leading to an ultraviolet fixed point near $\alpha_s=.1$. It is explained how this can be understood from the fact that the conventional perturbative method is ambiguous and does not provide the correct asymptotic expansion. It is pointed out that there is a large amount of lattice data that are supporting this scenario rather than the conventional one.