HIGHER COVARIANT DERIVATIVE PAULI-VILLARS REGULARIZATION DOES NOT LEAD TO A CONSISTENT QCD

We compute the beta function at one loop for Yang-Mills theory using a s regulator the combination of higher covariant derivatives and Pauli- Villars determinants proposed by Faddeev and Slavnov. This regularizat ion prescription has the appealing feature that it is manifestly gauge invariant and essentially four-dimensional. It happens however that t he 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 lo garithmic radiative corrections generated by the Pauli-Villars determi nants on which the regularization method is based. This no-go result d iscards the prescription as a viable gauge invariant regularization, t hus solving a long-standing open question in the literature. We also o bserve that the prescription can be modified so as to not generate unp hysical logarithmic corrections, but at the expense of losing manifest gauge invariance,