Indirect determination of the Kugo-Ojima function from lattice data

TL;DR

This paper uses lattice data and a dynamical equation to indirectly determine the Kugo-Ojima function u(q) in Landau gauge, revealing deviations from the confinement criterion in the infrared and analyzing its renormalization dependence.

Contribution

It introduces a method to determine u(q) indirectly from gluon and ghost data, confirming previous lattice results and exploring its infrared behavior and renormalization effects.

Findings

u(q) matches previous lattice simulations

Deviates from confinement scenario in infrared

u(0) depends on renormalization point

Abstract

We study the structure and non-perturbative properties of a special Green's function, u(q), whose infrared behavior has traditionally served as the standard criterion for the realization of the Kugo-Ojima confinement mechanism. It turns out that, in the Landau gauge, u(q) can be determined from a dynamical equation, whose main ingredients are the gluon propagator and the ghost dressing function, integrated over all physical momenta. Using as input for these two (infrared finite) quantities recent lattice data, we obtain an indirect determination of u(q). The results of this mixed procedure are in excellent agreement with those found previously on the lattice, through a direct simulation of this function. Most importantly, in the deep infrared the function deviates considerably from the value associated with the realization of the aforementioned confinement scenario. In addition, the dependence of u(q), and especially of its value at the origin, on the renormalization point is clearly established. Some of the possible implications of these results are briefly discussed.