Gravitational interaction of Higgs boson and weak boson scattering

With the LHC discovery of a 125 GeV Higgs-like boson, we study the gravitational interaction of the Higgs boson via the unique dimension-four operator involving the Higgs doublet and scalar curvature, ξH^HR, with nonminimal coupling ξ. This Higgs portal term can be transformed away in the Einstein frame and induces gauge-invariant effective interactions in the Higgs sector. We study the weak boson scattering in the Einstein frame and explicitly demonstrate the longitudinal-Goldstone boson equivalence theorem in the presence of ξ coupling. With these, we derive a perturbative unitarity bound on the Higgs gravitational coupling ξ in the Einstein frame, which is stronger than that inferred from the LHC Higgs measurements. We further study ξ-dependent weak boson scattering cross sections at the TeV scale and propose a new LHC probe of Higgs-gravity coupling ξ via weak boson scattering experiments.