Four-dimensional helicity scheme and dimensional reconstruction

The four-dimensional helicity regularization scheme is often used in one-loop QCD computations. It was recently argued in by [W. B. Kilgore, Phys. Rev. D 83, 114005 (2011)] that this scheme is inconsistent beyond the one-loop order in perturbation theory. In this paper, we clarify the reason for this inconsistency by studying the perturbative expansion of the vector current correlator in one-flavor QED through three-loop order. We develop a simple, practical way to fix the four-dimensional helicity scheme using the idea of dimensional reconstruction and demonstrate its application in several illustrative examples.