Vacuum misalignment and pattern of scalar masses in the SU(5)/SO(5) composite Higgs model

TL;DR

This paper classifies operators in SU(5)/SO(5) composite Higgs models, analyzes scalar mass patterns and Higgs potential, and explores LHC phenomenology, revealing universal scalar mass patterns and promising collider signatures.

Contribution

It provides a comprehensive classification of operators affecting the Higgs potential and scalar masses in SU(5)/SO(5) models, with implications for collider phenomenology.

Findings

Custodial triplet misalignment is CP forbidden.

Universal scalar mass patterns depend on custodial symmetry.

Scalar states below 1 TeV can produce distinctive LHC signals.

Abstract

Composite Higgs models based on SU(5)/SO(5) are characterised by the presence of custodial triplets, like the Georgi-Machacek model. We classify all the operators giving rise to the top mass and Higgs potential in presence of fermion partial compositeness, with top partners in two-index representations of SU(5). A detailed study of each operator allows us to find correlations in the couplings of Higgs and non-Higgs pseudo-Nambu-Goldstone bosons, which depend only on one, two or three independent parameters. We also analyse the Higgs potential, finding that a misalignment along the custodial invariant triplet direction is forbidden by CP conservation. Avoiding custodial breaking allows us to select a handful of feasible models, which feature universal patterns in the scalar masses related to their transformation properties under the custodial symmetry. Finally, we briefly study the LHC phenomenology of the scalars, which are always below 1 TeV even for multi-TeV condensation scales, and find promising same-sign lepton final states enriched by hard photons.