The four-dimensional helicity scheme and dimensional reconstruction

TL;DR

This paper investigates the limitations of the four-dimensional helicity scheme in higher-order QCD calculations, identifies the source of its inconsistency, and proposes a practical fix using dimensional reconstruction demonstrated through QED examples.

Contribution

It clarifies the inconsistency of the four-dimensional helicity scheme beyond one loop and introduces a simple method to correct it via dimensional reconstruction.

Findings

Identifies the source of inconsistency in the scheme beyond one loop

Develops a practical correction method using dimensional reconstruction

Demonstrates the method with QED examples

Abstract

The four-dimensional helicity regularization scheme is often used in one-loop QCD computations. It was recently argued in Ref. [1] 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.