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

TL;DR

This paper presents a regularization scheme for Yang-Mills theory combining higher covariant derivatives with infinitely many Pauli-Villars fields, effectively avoiding unphysical divergences and deriving renormalization group functions.

Contribution

It introduces a novel regularization method that maintains manifest invariance and cancels divergences without unphysical logarithmic divergences, applicable to divergent theories including supersymmetric gauge theories.

Findings

No unphysical logarithmic divergences appear.

Renormalization group functions are successfully derived.

Quadratic divergences are canceled through the proposed scheme.

Abstract

We study the regularization and renormalization of the Yang-Mills theory in the framework of the manifestly invariant formalism, which consists of a higher covariant derivative with an infinitely many Pauli-Villars fields. Unphysical logarithmic divergence, which is the problematic point on the Slavnov's method, does not appear in our scheme, and the well-known vale of the renormalization group functions are derived. The cancellation mechanism of the quadratic divergence is also demonstrated by calculating the vacuum polarization tensor of the order of $\Lambda^0$ and $\Lambda^{-4}$. These results are the evidence that our method is valid for intrinsically divergent theories and is expected to be available for the theory which contains the quantity depending on the space-time dimensions, like supersymmetric gauge theories.