A Partially Fixed Background Field Gauge

TL;DR

This paper introduces a partially fixed background field gauge that simplifies calculations and enables proof of a hard-region matching formula in spontaneously broken gauge theories with heavy vectors.

Contribution

It proposes a new gauge fixing method that facilitates effective field theory matching in theories with spontaneously broken gauge symmetries.

Findings

Partial fixing of the background field gauge simplifies calculations.

The new gauge allows proof of a hard-region matching formula.

It addresses issues with gauge fixing in broken symmetry theories.

Abstract

We examine the incorporation of gauge symmetries in the modern effective field theory (EFT) matching paradigm with a particular focus on spontaneously broken symmetries. The presence of gauge symmetries entails the introduction of gauge-fixing terms in matching calculations, which may prevent (partial) cancellation between loops from the underlying theory and those of the EFT, thereby preventing the establishment of a hard-region matching formula. While this is not an issue when using the background field (BF) gauge for unbroken gauge theories, we find ourselves unable to demonstrate the cancellation with the ordinary BF gauge in spontaneously broken gauge theories when the massive vectors are heavy and decouple from the theory. As a convenient alternative, we construct a partially fixed BF gauge that, in addition to being simpler than the ordinary BF gauge, allows us to prove a hard-region matching formula.