A dynamical study of the Kugo-Ojima function

As has been recently realized, a certain two-point function $\Lambda$ -- and its associated form factors G and L -- play a prominent role in the PT-BFM formulation of the Schwinger-Dyson equations used to study gauge-invariantly the gluon and ghost propagators. After showing that in the (background) Landau gauge $\Lambda$ fully constrains the QCD ghost sector, we show that G coincides with the Kugo-Ojima function u, 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 for all momenta through a combination of the available lattice data on the gluon and ghost propagators, as well as the dynamical equation G satisfies, will be then discussed. In particular we will show that in the deep infrared the function deviates considerably from the value associated with the realization of the Kugo-Ojima confinement scenario; the dependence on the renormalization point of u, and especially of its value at q=0, will be also briefly discussed.