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 ($\varphi$) and show that {\it only} the Standard Model vacuum solution of $\mathrm{\partial }V(h)\mathrm{/}\mathrm{\partial }h=0$ (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 $\varphi$ 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 $\varphi$ couplings given the {\it physical} eigenstate masses, mh and $\text{mphi}$, xi and the new physics scales of the model. We show that LEP/LEP2 data implies that not both the h and $\varphi$ can be light. In the allowed region of parameter space, we examine numerically the couplings and branching ratios of the h and $\varphi$ for several cases with $\text{mh}=120\text{gev}$ and $\text{mphi}\le 300\text{gev}$. The resulting prospects for detection of the h and $\varphi$ at the LHC, a future LC and a $\text{gam}\text{gam}$ collider are reviewed. For moderate $\mathrm{\mid }\xi \mathrm{\mid }$, both the anomalous $h\to gg$ coupling and (when $\text{mh}>2\text{mphi}$) the non-standard decay channel $h\to \varphi \varphi$ can substantially impact h discovery. Presence of the latter is a direct signature for non-zero xi. We find that $BR(h\to \varphi \varphi )$ as large as $30÷40$ is possible when $\mathrm{\mid }\xi \mathrm{\mid }$ is large. Conversely, if $\text{mphi}>2\text{mh}$ then $BR(\varphi \to hh)$ is generally large. The feasibility of experimentally measuring the anomalous gg and $\text{gam}\text{gam}$ couplings of the h and $\varphi$ is examined.