Artifacts and ⟨A2⟩ power corrections: Reexamining Zψ(p2) and ZV in the momentum-subtraction scheme

Abstract

The next-to-leading-order (NLO) term in the operator product expansion (OPE) of the quark propagator vector part Zψ and the vertex function g1 of the vector current in the Landau gauge should be dominated by the same ⟨A2⟩ 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 clover and overlap fermion actions at β=6.0, 6.4, 6.6, 6.8. Elucidation of discretization artifacts appears to be absolutely crucial. First hypercubic artifacts are eliminated by a powerful method, which gives results notably different from the standard democratic method. Then, the presence of unexpected, very large, nonperturbative, O(4) symmetric discretization artifacts, increasing towards small momenta, is demonstrated by considering ZMOMV, which should be constant in the absence of such artifacts. They impede in general the analysis of OPE. However, in two special cases with overlap action—(1) for Zψ; (2) for g1, but only at large p2—we are able to identify the ⟨A2⟩ 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. A practical consequence of the whole analysis is that the renormalization constant Zψ (=Z−12 of the momentum-subtraction (MOM) scheme) may differ sizably from the one given by democratic selection methods. More generally, the values of the renormalization constants may be seriously affected by the differences in the treatment of the various types of artifacts, and by the subtraction of power corrections.