A test of the Kugo-Ojima confinement criterion by lattice Landau gauge QCD simulations

TL;DR

This paper tests the Kugo-Ojima confinement criterion using lattice Landau gauge QCD simulations, finding partial agreement in the strong coupling region and insights into the horizon function behavior at weak coupling.

Contribution

First lattice QCD simulation testing the Kugo-Ojima criterion, connecting results with Zwanziger's theory and analyzing the horizon function.

Findings

Parameter u approaches -0.7 in strong coupling

Horizon function expectation value is negative or near zero at weak coupling

Provides empirical evidence related to confinement criteria in lattice QCD

Abstract

The first test of the Kugo-Ojima colour confinement criterion by the lattice Landau gauge QCD simulation is performed. The parameter u which is expected to be -1\delta^a_b in the continuum theory was found to be -0.7\delta^a_b in the strong coupling region. The data is analyzed in connection with the theory of Zwanziger. In the weak coupling region, the expectation value of the horizon function is negative or consistent to 0.