On the dynamics of the Kugo-Ojima function

TL;DR

This paper investigates the Kugo-Ojima function's behavior in QCD, using a modern pinch technique framework and lattice data, revealing deviations from the traditional confinement criterion in the infrared region.

Contribution

It introduces a modern formulation of the pinch technique with Batalin-Vilkovisky quantization, linking the Kugo-Ojima function to auxiliary functions and analyzing its behavior across all momenta.

Findings

G(q^2) coincides with the Kugo-Ojima function u(q^2)

In the infrared, u(q^2) deviates from the confinement criterion value

The behavior of u(q^2) depends on the renormalization point

Abstract

In this talk, after reviewing the dynamical gluon mass generation mechanism within the pinch technique framework and its phenomenological predictions, we will introduce the modern formulation of the pinch technique which makes extensive use of the Batalin-Vilkovisky quantization formalism. In this framework a certain auxiliary function \Lambda_{\mu\nu}(q) - and its associated form factors G(q^2) and L(q^2) -play a prominent role. After showing that in the (background) Landau gauge \Lambda_{\mu\nu}(q) fully constrains the QCD ghost sector, we show that G(q^2) coincides with the Kugo-Ojima function u(q^2), whose infrared behavior has traditionally served as the standard criterion for the realization of the Kugo-Ojima confinement mechanism. The determination of the behavior of G(q^2) (and therefore of the Kugo-Ojima function) for all momenta through a combination of the available lattice data on the gluon and ghost propagators as well as the dynamical equation G(q^2) satisfies, will be then discussed. In particular we will show that (i) in the deep infrared the function deviates considerably from the value associated with the realization of the Kugo-Ojima confinement scenario, and (ii) establish the dependence on the renormalization point of u(q^2), and especially of its value at q^2=0.