Radion effects on unitarity in gauge-boson scattering

The scalar field associated with fluctuations in the positions of the two branes, the "radion," plays an important role in determining the cosmology and collider phenomenology of the Randall-Sundrum solution to the hierarchy problem. It is now well known that the radion mass is on the order of a weak scale, and that its couplings to standard model fields are order O(TeV-1) to the trace of the energy momentum tensor. We calculate longitudinal vector boson scattering amplitudes to explore the constraints on the radion mass and its coupling from perturbative unitarity. The scattering cross section can indeed become nonperturbative at energies prior to reaching the TeV brane cutoff scale, but only when some curvature-Higgs mixing on the TeV brane is present. We show that the coefficient of the curvature-Higgs mixing operator must be less than about 3 for the 4D effective theory to respect perturbative unitarity up to the TeV brane cutoff scale. Mass bounds on the Higgs boson and the radion are also discussed.