Beyond one-gluon exchange in the infrared limit of Yang-Mills theory

TL;DR

This paper investigates the infrared behavior of Yang-Mills theory using Wilson loops, revealing that next-to-leading order corrections induce a linear confining potential consistent with Gribov's confinement picture.

Contribution

It demonstrates that higher-order corrections in the gluon propagator lead to a linear confining potential, advancing understanding of confinement in Yang-Mills theory.

Findings

One-gluon exchange does not produce a linear potential.

Next-to-leading order correction yields a linear confining term.

Infrared regularization is naturally determined by classical equations.

Abstract

We analyze the Wilson loop for a pure Yang-Mills theory, using a decoupling solution in close agreement with lattice computations. At one-gluon exchange level it is seen that the potential cannot yield a linear rising contribution as expected for a confining theory. Next-to-leading order correction gives rise to a quartic term for momenta in the gluon propagator that, in agreement with Gribov's view, yields a linear confining term. This correction is due to a two-loop or sunrise integral that we need to evaluate in the low-momenta limit. In the infrared regime, the physical consistency of the theory is determined by a natural cut-off, arising from the integration of the classical equations of the theory, fixing in this way the regularization scheme.