Confining potential under the gauge field condensation in the SU(2) Yang-Mills theory

TL;DR

This paper investigates the $Qar{Q}$ potential in SU(2) gauge theory, proposing that gluon condensation leads to a linear confining potential, with detailed analysis of its structure and relation to the Cornell potential.

Contribution

It introduces a gluon condensation mechanism in SU(2) Yang-Mills theory that results in a confining potential, expanding understanding beyond magnetic monopole condensation.

Findings

The potential includes Coulomb and linear parts plus an additional component.

Two implicit scales, $r_c$ and $ ilde{R}_0$, characterize the potential.

The Cornell potential is derived by incorporating these scales.

Abstract

$Q\bar{Q}$ potential is studied in the SU(2) gauge theory. Based on the nonlinear gauge of the Curci-Ferrari type, the possibility of a gluon condensation $\langle A_{\mu}^+A_{\mu}^-\rangle$ in low-energy region has been considered at the one-loop level. Instead of the magnetic monopole condensation, this condensation makes classical gluons massive, and can yield a linear potential. We show this potential consists of the Coulomb plus linear part and an additional part. Comparing with the Cornell potential, we study this confining potential in detail, and find that the potential has two implicit scales $r_c$ and $\tilde{R}_0$. The meanings of these scales are clarified. We also show that the Cornell potential that fits well to this confining potential is obtained by taking these scales into account.