2015/03/31 by Ph. Boucaud, J. -P. Leroy, Boucaud, Ph. +9
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #hep-lat
paper · pdf · doi:10.48550/arxiv.1503.09083
One reference added; some minor material errors corrected; no substantial change with respect to the first version
arxiv created 2015/04/02 · arxiv updated 2015/04/03
It is recalled why, as already stated in a previous paper, there seems to be an inconsistency in identifying the non perturbative ZA,MOM as the renormalisation of the axial current, or equivalently, in setting as normalisation condition that the renormalised vertex=1 at p2 = mu2 at some renormalisation scale mu, where p is the momentum in the legs. Indeed, unlike the vector case, the Ward-Takahashi (WT) identity for the axial current is shown to imply both the renormalisation scale independence of ZA and a mu2 dependence of ZA,MOM. This mu2 dependence is simply related to certain invariants in the pseudoscalar vertex and can persist in the chiral limit due to the spontaneous breaking of chiral symmetry (pion pole). It is seen clearly in the mu2 dependence of some lattice calculations of ZA,MOM/ZV,MOM near the chiral limit.