Precision electroweak data and the mixed radion-Higgs sector of warped extra dimensions

We derive the Lagrangian and Feynman rules up to bilinear scalar fields for the mixed Higgs-radion eigenstates interacting with Standard Model particles confined to a 3-brane in Randall-Sundrum warped geometry. We use the results to compute precision electroweak observables and compare theory predictions with experiment. We characterize the interesting regions of parameter space that simultaneously enable a very heavy Higgs mass and a very heavy radion mass, both masses being well above the putative Higgs boson mass limit in the Standard Model derived from the constraints of precision electroweak observables. For parameters consistent with the precision constraints the Higgs boson physical eigenstate is typically detectable, but its properties may be difficult to study at the large hadron collider. In contrast, masses and couplings are allowed for the physical radion eigenstate that make it unobservable at the LHC. A linear collider will significantly improve our ability to study the Higgs eigenstate, and will typically allow detection of the radion eigenstate if it is within the machine's kinematical reach