We discuss the different methods to obtain reliable informations about the
deep infra-red behaviour of the gluon and ghost Green functions in QCD. We
argue that a clever combination of analytical inputs and numerical ones is
necessary. We illustrate this statement about the distinction between two
classes of solutions of the ghost propagator Dyson-Schwinger equation (GPDSE).
We conclude that the solution II ("decoupling") with a finite renormalised
ghost dressing function at zero momentum is strongly favored by lattice QCD, We
derive a method to solve numerically the GPDSE using lattice inputs concerning
the gluon propagator. We derive an analytical small momentum expansion of the
Ghost dressing function. We prove from the large cut-off behaviour of the ghost
propagator renormalisation constant, Z3, that the bare ghost
dressing function is infinite at the infinite cut-off limit.Comment: 12 pages 6 figure