Kugo-Ojima color confinement criterion and Gribov-Zwanziger horizon condition

TL;DR

This paper connects the Kugo-Ojima confinement criterion with the Gribov-Zwanziger horizon condition, showing how the allowed Kugo-Ojima parameter values relate to confinement and lattice results.

Contribution

It reformulates the horizon condition in terms of the Kugo-Ojima parameter, clarifying the conditions for color confinement in gauge theories.

Findings

The Kugo-Ojima parameter value consistent with the horizon condition.

Ghost propagator behaves like a free particle at low momenta.

Gluon propagator remains non-zero at low momenta, matching lattice results.

Abstract

We rewrite the Zwanziger horizon condition in terms of the Kugo-Ojima parameter for color confinement. This enables one to explain which value of the Kugo-Ojima parameter is allowed if the horizon condition is imposed. Although all the calculations are performed in the limit of vanishing Gribov parameter for simplicity, the obtained value is consistent with the result of numerical simulations. Consequently, the ghost propagator behaves like free and the gluon propagator is non-vanishing at low momenta, in harmony with recent lattice results and decoupling solution of the Schwinger-Dyson equation. The Kugo-Ojima criterion is realized only when the restriction is removed.