Ambiguities in Pauli–Villars regularization

We investigate regularization of scalar one-loop integrals in the Pauli–Villars subtraction scheme. The results depend on the number of subtractions, in particular the finite terms that survive after the divergences have been absorbed by renormalization. Therefore the process of Pauli–Villars regularization is ambiguous. We discuss how these ambiguities may be resolved by applying an asymptotically large number of subtractions, which results in a regularization that is automatically valid in any number of dimensions