A Minimally Symmetric Higgs Boson

TL;DR

This paper proposes a minimal symmetry framework for the Higgs boson, using four shift symmetries on its components, leading to a universal effective Lagrangian applicable to all PNGB Higgs models.

Contribution

It introduces a minimal symmetry setup with four shift symmetries for the Higgs doublet, deriving a universal effective Lagrangian independent of the UV symmetry group.

Findings

High-energy vector boson scatterings could reveal the minimally symmetric Higgs.

The effective Lagrangian is universal across different PNGB Higgs models.

Abstract

Models addressing the naturalness of a light Higgs boson typically employ symmetries, either bosonic or fermionic, to stabilize the Higgs mass. We consider a setup with the minimal amount of symmetries: four shift symmetries acting on the four components of the Higgs doublet, subject to the constraints of linearly realized SU(2)xU(1) electroweak symmetry. Up to terms that explicitly violate the shift symmetries, the effective lagrangian can be derived, irrespective of the spontaneously broken group G in the ultraviolet, and is universal in all models where the Higgs arises as a pseudo-Nambu-Goldstone boson (PNGB). Very high energy scatterings of vector bosons could provide smoking gun signals of a minimally symmetric Higgs boson.