The factorisation of glue and mass terms in SU(N) gauge theories

TL;DR

This paper analyzes the structure of glue in gauge-invariant expansions of mass terms in SU(N) Yang-Mills theories, deriving explicit expressions and exploring ambiguities in the expansion.

Contribution

It provides a detailed derivation of the gauge-invariant expansion of the A^2 mass term and introduces explicit higher-order terms, revealing non-uniqueness in the expansion.

Findings

Explicit expression for next-to-next-to-leading order term

Demonstration of non-uniqueness in the expansion

Extension of the expansion to higher orders

Abstract

In this paper we investigate the structure of the glue in Zwanziger's gauge invariant expansion for the A^2-type mass term in Yang-Mills theory. We show how to derive this expansion, in terms of the inverse covariant Laplacian, and extend it to higher orders. In particular, we give an explicit expression, for the first time, for the next to next to leading order term. We further show that the expansion is not unique and give examples of the resulting ambiguity.