Renormalizability of the dimension two gluon operator $A^{2}$ in a class of nonlinear covariant gauges

TL;DR

This paper demonstrates that a specific class of nonlinear covariant gauges in Yang-Mills theories allows for the multiplicative renormalization of the dimension two gluon operator, ensuring theoretical consistency at all orders.

Contribution

It introduces a class of nonlinear covariant gauges with proven all-order multiplicative renormalizability and shows the gluon operator $A^2$ can be consistently included.

Findings

The gauges satisfy a linearly broken ghost Ward identity.

The $A^2$ operator can be introduced multiplicatively renormalized.

The renormalizability holds to all orders.

Abstract

In this work we discuss a class of nonlinear covariant gauges for Yang-Mills theories which enjoy the property of being multiplicatively renormalizable to all orders. This property follows from the validity of a linearly broken identity, known as the ghost Ward identity. Furthermore, thanks to this identity, it turns out that the local composite dimension two gluon operator $A_{\mu}^{a}A_{\mu}^{a}$ can be introduced in a mulptiplicatively renormalizable way.