Anti-Screening by Quarks and the Structure of the Inter-Quark Potential

TL;DR

This paper investigates the anti-screening effects in the inter-quark potential, calculating higher-order contributions, revealing non-local divergences, and discussing implications for renormalisation and the beta function in quantum chromodynamics.

Contribution

It provides a detailed calculation of the order g^6 anti-screening contribution and analyzes the non-local divergences affecting renormalisation schemes.

Findings

Anti-screening effects dominate the inter-quark potential.

Non-local divergences prevent defining a coupling renormalisation scheme.

Renormalisation can be performed using the anti-screening potential.

Abstract

The inter-quark potential is dominated by anti-screening effects which underly asymptotic freedom. We calculate the order g^6 anti-screening contribution from light fermions and demonstrate that these effects introduce a non-local divergence. These divergences are shown to make it impossible to define a coupling renormalisation scheme that renormalises this minimal, anti-screening potential. Hence the beta function cannot be divided into screening and anti-screening parts beyond lowest order. However, we then demonstrate that renormalisation can be carried out in terms of the anti-screening potential.