Ambiguities in Pauli-Villars regularization

TL;DR

This paper examines the ambiguities in Pauli-Villars regularization of scalar one-loop integrals and proposes a method involving an infinite number of subtractions to achieve a consistent, dimension-independent regularization scheme.

Contribution

It introduces a novel approach of using asymptotically large subtractions to resolve ambiguities in Pauli-Villars regularization across dimensions.

Findings

Regularization ambiguities depend on subtraction count.

Infinite subtractions lead to dimension-independent regularization.

Method ensures consistent regularization in any number of dimensions.

Abstract

We investigate regularization of scalar one-loop integrals in the Pauli- Villars subtraction scheme. The results depend on the number of sub- tractions, in particular the finite terms that survive after the diver- gences have been absorbed by renormalization. Therefore the process of Pauli-Villars regularization is ambiguous. We discuss how these am- biguities 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.