The Problem of Asymptotic Freedom

TL;DR

This paper suggests that nonperturbative lattice QCD predicts a different running of the strong coupling constant than perturbation theory, potentially explaining discrepancies in high-energy accelerator experiments.

Contribution

It introduces the idea that the true running of $oldsymbol{ ext{α}_s}$ differs from perturbative predictions, proposing an ultraviolet fixed point near 0.1 based on lattice QCD data.

Findings

Lattice data supports a different running of $ ext{α}_s$ than perturbative theory.

Perturbation theory may be ambiguous and inadequate at high energies.

A nonperturbative fixed point near 0.1 is proposed.

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.