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Gravitational Interaction of Higgs Boson and Weak Boson Scattering

With the LHC discovery of a 125 GeV Higgs-like boson, we study gravitational interaction of the Higgs boson via the unique dimension-4 operator involving Higgs doublet and scalar curvature, $\,ξH^†H R\,$, with nonminimal coupling $\,ξ\,$. This Higgs portal term can be transformed away in Einstein frame and induces gauge-invariant effective interactions in the Higgs sector. We study the weak boson scattering in Einstein frame, and explicitly demonstrate the longitudinal-Goldstone boson equivalence theorem in the presence of $\,ξ\,$ coupling. With these, we derive unitarity bound on the Higgs gravitational coupling $\,ξ\,$ in Einstein frame, which is stronger than that inferred from the current LHC Higgs measurements. We further study $ξ$-dependent weak boson scattering cross sections at TeV scale, and propose a new LHC probe of the Higgs-gravity coupling $\,ξ\,$ via weak boson scattering experiments.