A custodial symmetry for Zbb¯

We show that a subgroup of the custodial symmetry O(3) that protects Δρ from radiative corrections can also protect the Zbb¯ 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→bb¯. We show that when this symmetry protects Zbb¯ it cannot simultaneously protect Ztt¯ and Wtb¯. 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 ZbRb¯R can receive corrections in the right direction to explain the anomaly in the LEP/SLD forward-backward asymmetry AFBb.