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, $\,\xi H^\dag H R\,$, with nonminimal coupling $\,\xi\,$. 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 $\,\xi\,$ coupling. With these, we derive unitarity bound on the Higgs gravitational coupling $\,\xi\,$ in Einstein frame, which is stronger than that inferred from the current LHC Higgs measurements. We further study $\xi$-dependent weak boson scattering cross sections at TeV scale, and propose a new LHC probe of the Higgs-gravity coupling $\,\xi\,$ via weak boson scattering experiments.