A Note on the Quadratic Divergence in Hybrid Regularization

TL;DR

This paper investigates the quadratic divergence in Yang-Mills theory under hybrid regularization, demonstrating the necessity of higher derivative terms for ghost fields to cancel divergences.

Contribution

It provides an explicit calculation showing the importance of higher derivative ghost terms in the hybrid regularization scheme.

Findings

Higher derivative terms for ghost fields are essential for divergence cancellation.

Explicit diagram calculations confirm the necessity of these terms.

Hybrid regularization effectively manages quadratic divergences in Yang-Mills theory.

Abstract

We consider the quadratic divergence of the Yang-Mills theory when we use the hybrid regularization method consisting of the higher covariant derivative terms and the Pauli-Villars fields. By the explicit calculation of the diagrams, we show that the higher derivative terms for the ghost fields are necessary for the complete cancellation of the quadratic divergence.