  In order to construct a gauge invariant two-point function in a Yang-Mills
theory, we propose the use of the all-order gauge invariant transverse
configurations A^h. Such configurations can be obtained through the
minimization of the functional A^2_{min} along the gauge orbit within the BRST
invariant formulation of the Gribov-Zwanziger framework recently put forward in
[1,2] for the class of the linear covariant gauges. This correlator turns out
to provide a characterization of non-perturbative aspects of the theory in a
BRST invariant and gauge parameter independent way. In particular, it turns out
that the poles of <A^h A^h> are the same as those of the transverse part of the
gluon propagator, which are also formally shown to be independent of the gauge
parameter entering the gauge condition through the Nielsen identities. The
latter follow from the new exact BRST invariant formulation introduced before.
Moreover, the correlator <A^h A^h> enables us to attach a BRST invariant
meaning to the possible positivity violation of the corresponding temporal
Schwinger correlator, giving thus for the first time a consistent, gauge
parameter independent, setup to adopt the positivity violation of <A^h A^h> as
a signature for gluon confinement. Finally, in the context of gauge theories
supplemented with a fundamental Higgs field, we use <A^h A^h> to probe the pole
structure of the massive gauge boson in a gauge invariant fashion.
