The scalar sector of the Randall-Sundrum model

We consider 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)(nun)) and the radion (phi) and show that only the Standard Model vacuum solution of partial derivativeV(h)/partial derivativeh = 0 (h is the Higgs field), is allowed. We then turn to our main focus: the consequences of the curvature-scalar mixing xiR (H) over cap (dagger)(H) over cap (where (H) over cap 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 physical eigenstate masses, m(h) and m(phi), xi and the new physics scales of the model. Relations among these new-physics scales are discussed and a set of values not far above the smallest values required by precision electroweak constraints and RunI data is chosen. A simple result for the sum of the ZZh and ZZphi squared couplings relative to the ZZh(SM) squared coupling is derived. We demonstrate that this sum rule in combination with LEP/LEP2 data implies that not both the h and phi can be light. We present explicit results for the still allowed region in the (m(h), m(phi)) plane that remains after imposing the appropriate LEP/LEP2 upper limits coming from the Higgs-strahlung channel. In the remaining allowed region of parameter space, we examine numerically the couplings and branching ratios of the h and phi for several cases with m(h) = 120 GeV and m(phi) less than or equal to 300 GeV The resulting prospects for detection of the h and phi at the LHC, a future LC and a gammagamma collider are reviewed. For moderate \xi\, both the anomalous h --> gg coupling and (when m(h) > 2m(phi)) the non-standard decay channel h --> phiphi can substantially impact h discovery. Presence of the latter is a direct signature for non-zero xi. We find that BR(h --> phiphi) as large as 30-40% is possible when \xi\ is large. Conversely, if m(phi) > 2m(h) then BR(phi --> hh) is generally large. Sensitivity to the model-dependent magnitude of the cubic radion potential term is discussed. We find that detection of a light phi might require the LC. Detection of a heavy phi might need to take into account the phi --> hh channel. The feasibility of experimentally measuring the anomalous gg and gammagamma couplings of the h and phi is examined. (C) 2003 Elsevier B.V. All rights reserved.