Decoupling and scaling solutions in Yang-Mills theory with the Gribov horizon

TL;DR

This paper introduces a method to incorporate the Gribov horizon into the Schwinger-Dyson equations in Yang-Mills theory, revealing a family of solutions that include both scaling and decoupling types, with implications for color confinement.

Contribution

It presents a novel approach to include the Gribov horizon in the equations, uncovering a continuous family of solutions previously overlooked, and discusses their physical significance.

Findings

Identified a one-parameter family of solutions including scaling and decoupling types.

Discovered that the parameter choice distinguishes between different solution behaviors.

Proposed a decoupling solution consistent with the Kugo-Ojima confinement criterion.

Abstract

We propose a trick which enables one to incorporate the Gribov horizon into the Schwinger-Dyson equation in Landau and Coulomb gauge Yang-Mills theory, using the Gribov-Zwanziger framework with the horizon term. We find a family of solutions parameterized by one-parameter $w_R(0)$ which was overlooked so far by assuming to be zero implicitly. The family includes both the scaling and decoupling solutions, and specification of the parameter discriminates between them. In the Landau gauge we discuss a possible decoupling solution satisfying the Kugo-Ojima criterion for color confinement.