Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD

TL;DR

This paper demonstrates that higher covariant derivative Pauli-Villars regularization fails to produce a consistent beta function in QCD, due to unphysical corrections, thus questioning its viability as a gauge-invariant regularization method.

Contribution

It provides a detailed calculation showing the failure of a proposed gauge-invariant regularization scheme in QCD, resolving a long-standing open problem.

Findings

The regularization yields an incorrect beta function coefficient of -23/6 instead of -11/3.

Unphysical logarithmic corrections are generated by Pauli-Villars determinants.

Modifying the scheme to avoid unphysical corrections breaks gauge invariance.

Abstract

We compute the beta function at one loop for Yang-Mills theory using as regulator the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Faddeev and Slavnov. This regularization prescription has the appealing feature that it is manifestly gauge invariant and essentially four-dimensional. It happens however that the one-loop coefficient in the beta function that it yields is not $-11/3,$ as it should be, but $-23/6.$ The difference is due to unphysical logarithmic radiative corrections generated by the Pauli-Villars determinants on which the regularization method is based. This no-go result discards the prescription as a viable gauge invariant regularization, thus solving a long-standing open question in the literature. We also observe that the prescription can be modified so as to not generate unphysical logarithmic corrections, but at the expense of losing manifest gauge invariance.