  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.
