  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.
