A custodial symmetry for Zbb

TL;DR

The paper shows that a subgroup of the custodial symmetry can protect the Zbb coupling, allowing Higgsless, Little Higgs, and 5D composite Higgs scenarios to evade Z→bb corrections. Through an operator-analysis and explicit 5D AdS5 calculations, it demonstrates that Zb_L b_L can be protected while Zt t and Wt b can receive sizable corrections, and it explains how a positive shift in Zb_R b_R could address the A_FB^b anomaly. The results rely on specific fermion embeddings (notably b_L in (2,2)_{2/3}) and reveal that the protection is momentum-dependent, with potential 10–20% shifts under realistic parameters. The framework provides a testable path to natural EW symmetry breaking, with distinct, measurable signatures in future colliders for Ztt, Wtb, and possibly ZbR bR couplings.

Abstract

We show that a subgroup of the custodial symmetry O(3) that protects delta rho 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 Zb_R b_R can receive corrections in the right direction to explain the anomaly in the LEP/SLD forward-backward asymmetry A^b_{FB}.