Forests, Groves and Higgs Bosons: Gauge Invariance Classes in Spontaneously Broken Gauge Theories

TL;DR

This paper classifies gauge invariance classes of tree-level Feynman diagrams in spontaneously broken gauge theories, revealing new classes in nonlinear scalar sectors and clarifying their relation to Ward identities.

Contribution

It provides a formal proof for gauge and flavor flip formalism and identifies new gauge invariance classes in theories with nonlinear scalar sectors.

Findings

New gauge invariance classes in nonlinear scalar sectors

Decomposition of amplitudes satisfying Ward identities

Equivalence of classes in unitarity gauge and linear scalar sectors

Abstract

We determine the gauge invariance classes of tree level Feynman diagrams in spontaneously broken gauge theories, providing a proof for the formalism of gauge and flavor flips. We find new gauge invariance classes in theories with a nonlinearly realized scalar sector. In unitarity gauge, the same gauge invariance classes correspond to a decomposition of the scattering amplitude into pieces that satisfy the relevant Ward Identities individually. In theories with a linear realized scalar sector in R_\xi gauge, no additional nontrivial gauge invariance classes exist compared to the unbroken case.