Tree-Level Unitarity in the Presence of Warped Geometries

Perturbative unitarity for W+LW-L → W+LW-L scattering is discussed within the Randall-Sundrum theory with two 3-branes. It is shown that the exchange of massive 4D Kaluza-Klein gravitons leads to amplitudes growing linearly with the CM energy squared. If the curvature, m0, of the metric is too small, the gravitational contributions lead to a violation of unitarity. However, m0 must be small enough relative to the 5D Planck mass, MPl 5, to avoid quantum gravitational effects. As a result, we find that there is only a small range of m0/MPl for which the model is consistent. The width of the window is determined by the size of the 4D cutoff of the theory. The extension of the Randall-Sundrum scenario to include curvature-Higgs mixing is also considered and limits on the mixing parameter are determined. (author)