Electroweak constraints on warped models with custodial symmetry

It has been recently argued that realistic models with warped extra dimensions can have Kaluza-Klein particles accessible at the CERN Large Hadron Collider if a custodial symmetry, $SU(2{)}_{V}\ifmmode\times\else\texttimes\fi{}{P}_{LR}$, is used to protect the $T$ parameter and the coupling of the left-handed bottom quark to the $Z$ gauge boson. In this article we emphasize that such a symmetry implies that the loop corrections to both the $T$ parameter and the $Z{b}_{L}{\overline{b}}_{L}$ coupling are calculable. In general, these corrections are correlated, can be sizable, and should be considered to determine the allowed parameter space region in models with warped extra dimensions and custodial symmetry, including Randall-Sundrum models with a fundamental Higgs, models of gauge-Higgs unification, and Higgsless models. As an example, we derive the constraints that arise on a representative model of gauge-Higgs unification from a global fit to the precision electroweak observables. A scan over the parameter space typically leads to a lower bound on the Kaluza-Klein excitations of the gauge bosons of about 2\char21{}3 TeV, depending on the configuration. In the fermionic sector one can have Kaluza-Klein excitations with masses of a few hundred GeV. We present the constraints on these light fermions from recent Tevatron searches, and explore interesting discovery channels at the LHC.