Gribov-Zwanziger horizon condition, ghost and gluon propagators and Kugo-Ojima confinement criterion

TL;DR

This paper revisits the ghost and gluon propagator solutions in Landau gauge Yang-Mills theory, introducing a new method to incorporate the Gribov horizon into Schwinger-Dyson equations, revealing a family of solutions including both scaling and decoupling types.

Contribution

It proposes a novel trick to include the Gribov horizon directly into the Schwinger-Dyson equations, unifying scaling and decoupling solutions and showing horizon effects cancel ultraviolet divergences.

Findings

Identifies a family of solutions parameterized by $w_R(0)$ including both known types.

Shows horizon term cancels UV divergence in ghost propagator equations.

Demonstrates the horizon condition links infrared and ultraviolet behaviors.

Abstract

We reexamine the conventional arguments concerned with the scaling and decoupling solutions for the ghost and gluon propagators in the Landau gauge Yang-Mills theory. We point out a few issues to be clarified, which seems to be overlooked in the previous investigations in this field, in the fully non-perturbative treatment. We propose a trick which enables one to incorporate the Gribov horizon directly into the self-consistent Schwinger-Dyson equation in the gauge-fixed Yang-Mills theory, using the Gribov-Zwanziger framework with the horizon term. We obtain the following results, irrespective of the choice of the horizon term. (i) We find that there exists a family of solutions parameterized by one-parameter $w_R(0)$ which was assumed to be zero implicitly. The family includes both the scaling and decoupling solutions, and specification of the parameter discriminates between them. (ii) We observe that the inclusion of the horizon term cancels the ultraviolet divergence in the Schwinger-Dyson equation for the ghost propagator and the resulting (non-perturbative) self-consistent solution becomes ultraviolet finite. In other words, the horizon condition interpolates between the infrared behavior and the ultraviolet one. This leads to the incompatibility of the conventional multiplicative renormalization scheme with the Gribov