KK Gravitons and Unitarity Violation in the Randall-Sundrum Model

We show that perturbative unitarity for $W_LW_L$ scattering places significant constraints on the Randall-Sundrum theory with two 3-branes, with matter confined to the TeV brane. The exchange of massive 4D Kaluza-Klein gravitons leads to amplitudes growing linearly with the CM energy squared. Summing over KK gravitons up to a scale $\lbar$ and testing unitarity at $\sqrt s=\lbar$, one finds that unitarity is violated for $\lbar$ below the 'naive dimensional analysis' scale, $\Lambda_{NDA}$. We evaluate $\lbar$ as a function of the curvature ratio $m_0/M_{Planck}$ for the pure gravity theory. We then demonstrate that unitarity need not be violated at $\lbar$ in the presence of a heavy Higgs boson. In fact, much larger Higgs masses are consistent with unitarity than if no KK gravitons are present. Observation of the mass and width (or cross section) of one or more KK gravitons at the LHC will directly determine $m_0/M_{Planck}$ and the scale $\hat \Lambda$ specifying the couplings of matter to the KK gravitons. With this information in hand and a measurement of the Higgs boson mass, one can determine the precise scale $\lbar$ below which unitarity will remain valid.