A custodial symmetry for Zb(b)over-bar

We show that a subgroup of the custodial symmetry O(3) that protects Delta rho from radiative corrections can also protect the Zbq (b) over bar coupling. This allows one to build models of electroweak symmetry breaking, such as higgsless, little Higgs or 5D composite Higgs models, that are safe from corrections to Z -> b (b) over bar. We show that when this symmetry protects Zb (b) over bar it cannot simultaneously protect Zt (t) over bar and Wt (b) over bar. Therefore one can expect to measure sizable deviations from the SM predictions of these couplings at future collider experiments. We also show under what circumstances Zb(R)(b) over bar (R) can receive corrections in the right direction to explain the anomaly in the LEP/SLD forward-backward asymmetry A(FB)(b). (c) 2006 Elsevier B.V. All rights reserved.