Coulomb Potential Is Not a Part of The QCD Potential

TL;DR

This paper argues that the commonly used Coulomb plus linear potential in QCD is theoretically incorrect because the Coulomb term does not accurately represent the QCD potential at short or long distances due to scale dependence and the nature of color charge.

Contribution

It clarifies that the Coulomb potential is not part of the QCD potential, challenging a common assumption in modeling quark interactions.

Findings

Coulomb potential form is not part of QCD potential.

QCD potential's short-distance behavior involves scale-dependent coupling.

Long-distance QCD potential differs from Coulomb due to time-dependent color charge.

Abstract

The Coulomb plus linear potential is widely used in QCD. However, in this paper we show that the Coulomb potential of the form $\frac{1}{r}$ is not a part of the QCD potential. This is because the form $\frac{g^2}{r}$ is for abelian theory (not QCD) and the form $\frac{g^2(\mu)}{r}$ in QCD at short distance is not of the Coulomb form $\frac{1}{r}$ because $g(\mu)$ depends on the mass/length scale $\mu$. Similarly at long distance the QCD potential corresponds to the potential in the classical Yang-Mills theory which does not have the Coulomb form $\frac{1}{r}$ because the fundamental color charge of the quark is time dependent in the classical Yang-Mills theory. This is unlike the QED potential which reduces to Coulomb potential at long distance.