The Nielsen identities in screened theories

TL;DR

This paper derives one-loop expressions for the gluon Nielsen identity within the screened massive expansion of Yang-Mills theory, discussing gauge-parameter-independence and providing evidence for phase invariance.

Contribution

It provides explicit one-loop formulas for the Nielsen identity in a screened expansion framework and explores gauge invariance properties in perturbative and resummation schemes.

Findings

Evidence supports invariance of the phase under gauge parameter changes.

No formal proof of invariance in resummation schemes, but numerical evidence suggests it.

Explicit one-loop expressions for gluon Nielsen identity are derived.

Abstract

One-loop explicit expressions are derived for the gluon Nielsen identity in the formalism of the screened massive expansion for Yang-Mills theory. The gauge-parameter-independence of the poles and residues is discussed in a strict perturbative context and, more generally, in extended resummation schemes. No exact formal proof was reached by the approximate resummation schemes, but some evidence is gathered in favor of an exact invariance of the phase, consistently with previous numerical studies.