Minimally symmetric Higgs boson

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)L×U(1)Y 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 among all models where the Higgs arises as a pseudo-Nambu-Goldstone boson. Very high energy scatterings of vector bosons could provide smoking gun signals of a minimally symmetric Higgs boson.