Unitarity violation in non-abelian Pauli-Villars regularization

Abstract

We regularize QCD using the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Slavnov. It is known that for pure Yang-Mills theory the Pauli-Villars determinants generate unphysical logarithmic radiative corrections at one loop that modify the beta function. Here we prove that when the gauge fields are coupled to fermions so that one has QCD, these unphysical corrections translate into a violation of unitarity. We provide an understanding of this by seeing that Slavnov's choice for the Pauli-Villars determinants introduces extra propagating degrees of freedom that are responsible for the unitarity breaking. This shows that Slavnov's regularization violates unitarity, hence that it should be rejected.

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References in corpus (3)

• Chern-Simons Theory as the Large Mass Limit of Topologically Massive Yang-Mills Theory
• Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD
• Higher covariant derivative regulators and non-multiplicative renormalization

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• Consistency of the Hybrid Regularization with Higher Covariant Derivative and Infinitely Many Pauli-Villars