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.