Color Confinement in Lattice Landau Gauge

TL;DR

This paper investigates color confinement in lattice Landau gauge QCD by measuring propagators and parameters, finding a maximum in the running coupling and a Kugo-Ojima parameter below the expected value, using lattice simulations and PMS analysis.

Contribution

It provides new lattice simulation data on infrared properties of Landau gauge QCD and analyzes them with PMS in the $ ilde{MOM}$ scheme, offering insights into confinement mechanisms.

Findings

The running coupling $ ext{α}_s(q)$ peaks around 1 and decreases near zero momentum.

The Kugo-Ojima parameter was approximately 0.8, below the expected 1.

Infrared behavior of propagators supports confinement scenarios.

Abstract

The problem of color confinement in lattice Landau gauge QCD is briefly reviewed in the light of Kugo-Ojima criterion and Gribov-Zwanziger theory. The infrared properties of the Landau gauge QCD is studied by the measurement of the gluon propagator, ghost propagator, Kugo-Ojima parameter and the running coupling via $\beta=6.4,32^4,48^4$ lattice simulation. The data are analyzed in the principle of minimum sensitivity(PMS) in the $\widetilde{MOM}$ scheme. We observe the running coupling $\alpha_s(q)$ has a maximum about 1 and decreases near q=0. The Kugo-Ojima parameter, which is expected to be 1 was about 0.8.