Artefacts and power corrections: Revisiting the MOM Z psi (p**2) and Z(V)

The NLO term in the OPE of the quark propagator vector part Z and the vertex function g1 of the vector current in the Landau gauge should be dominated by the same h A 2 i condensate as in the gluon propagator. On the other hand, the perturbative part has been calculated to a very high precision thanks to Chetyrkin and collaborators. We test this on the lattice, with both Wilson-clover and GW (Ginsparg-Wilson) overlap fermion actions at � = 6.0,6.4,6.6,6.8. Elucidation of discretisation artefacts appears to be absolutely crucial. First hypercubic artefacts are eliminated by a powerful method. Other, very large, non perturbative, O(4) symmetric artefacts, impede in general the analysis. However, in two special cases with overlap action - 1) for Z ; 2) for g1, but only at large p 2 - we are able to identify the h A 2 i condensate; it agrees with the one resulting from gluonic Green functions. We conclude that the OPE analysis of quark and gluon Green function has reached a quite consistent status, and that the power corrections have been correctly identified.