Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-10-28
Nucl.Phys. B436 (1995) 545-581
Physics
High Energy Physics
High Energy Physics - Theory
43 pages, Latex file (uses the macro axodraw.sty, instructions of how to get it and use it included), FTUAM 94/9, NIKHEF-H 94/
Scientific paper
10.1016/0550-3213(94)00527-L
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.
Martin C. P.
Ruiz Fernando Ruiz
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