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With the LHC discovery of a 125 GeV Higgs-like boson, we study gravitationalinteraction of the Higgs boson via the unique dimension-4 operator involvingHiggs doublet and scalar curvature, $\,\xi H^\dag H R\,$, with nonminimalcoupling $\,\xi\,$. This Higgs portal term can be transformed away in Einsteinframe and induces gauge-invariant effective interactions in the Higgs sector.We study the weak boson scattering in Einstein frame, and explicitlydemonstrate the longitudinal-Goldstone boson equivalence theorem in thepresence of $\,\xi\,$ coupling. With these, we derive unitarity bound on theHiggs gravitational coupling $\,\xi\,$ in Einstein frame, which is strongerthan that inferred from the current LHC Higgs measurements. We further study$\xi$-dependent weak boson scattering cross sections at TeV scale, and proposea new LHC probe of the Higgs-gravity coupling $\,\xi\,$ via weak bosonscattering experiments.

Gravitational Interaction of Higgs Boson and Weak Boson Scattering