The scalar sector of the Randall-Sundrum model
We derive the effective potential for the Standard Model Higgs-boson sector interacting with Kaluza-Klein excitations of the graviton ($h_\mu^{\nu n}$) and the radion ($\phi$) and show that {\it only} the Standard Model vacuum solution of $\partial V(h)/\partial h =0$ (h is the Higgs field) is allowed. We then consider the consequences of the curvature-scalar mixing xi R \Hhat^\dagger \Hhat$ (where $\Hhat$ is a Higgs doublet field on the visible brane), which causes the physical mass eigenstates h and $\phi$ to be mixtures of the original Higgs and radion fields. First, we discuss the theoretical constraints on the allowed parameter space. Next, we give precise procedures for computing the h and $\phi$ couplings given the {\it physical} eigenstate masses, mh and $\mphi$, xi and the new physics scales of the model. We show that LEP/LEP2 data implies that not both the h and $\phi$ can be light. In the allowed region of parameter space, we examine numerically the couplings and branching ratios of the h and $\phi$ for several cases with $\mh=120\gev$ and $\mphi\leq 300\gev$. The resulting prospects for detection of the h and $\phi$ at the LHC, a future LC and a $\gam\gam$ collider are reviewed. For moderate $|\xi|$, both the anomalous $h\to gg$ coupling and (when $\mh>2\mphi$) the non-standard decay channel $h \to \phi\phi$ can substantially impact h discovery. Presence of the latter is a direct signature for non-zero xi. We find that $BR(h \to \phi\phi)$ as large as $30 \div 40 %$ is possible when $|\xi|$ is large. Conversely, if $\mphi>2\mh$ then $BR(\phi\to hh)$ is generally large. The feasibility of experimentally measuring the anomalous gg and $\gam\gam$ couplings of the h and $\phi$ is examined.