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 precsription can be modified so as to not generate unphysical logarithmic corrections, but at the expense of losing manifest gauge invariance. (orig.).
Martin, C P;
[1]
Ruiz Ruiz, F
[2]
- Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica
- Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Amsterdam (Netherlands). Sectie H
Citation Formats
Martin, C P, and Ruiz Ruiz, F.
Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD.
Netherlands: N. p.,
1994.
Web.
Martin, C P, & Ruiz Ruiz, F.
Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD.
Netherlands.
Martin, C P, and Ruiz Ruiz, F.
1994.
"Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD."
Netherlands.
@misc{etde_180952,
title = {Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD}
author = {Martin, C P, and Ruiz Ruiz, F}
abstractNote = {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 precsription can be modified so as to not generate unphysical logarithmic corrections, but at the expense of losing manifest gauge invariance. (orig.).}
place = {Netherlands}
year = {1994}
month = {Dec}
}
title = {Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD}
author = {Martin, C P, and Ruiz Ruiz, F}
abstractNote = {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 precsription can be modified so as to not generate unphysical logarithmic corrections, but at the expense of losing manifest gauge invariance. (orig.).}
place = {Netherlands}
year = {1994}
month = {Dec}
}