Forests, groves and Higgs bosons - Gauge invariance classes in spontaneously broken gauge theories

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 linearly realized scalar sector in R-xi gauge, no additional non-trivial gauge invariance classes exist compared to the unbroken case.