T-Parity Violation by Anomalies

TL;DR

The paper shows that T-parity, used in Little Higgs models to suppress EW corrections and provide a dark-matter candidate, is generally broken by anomalies captured by the Wess-Zumino-Witten term. By analyzing a minimal SU(3)×SU(3)/SU(3) Little Higgs with a single Higgs, it derives the universal Higgs–gauge–WZW interactions and demonstrates how anomaly cancellation (via spectator leptons or mirror sectors) eliminates unphysical Chern-Simons terms while preserving T-parity–violating topological operators. It provides an explicit expression for the anomaly-free WZW interaction and computes a concrete decay width, Γ(tilde{B}→ZZ), illustrating that the axial tilde{B} cannot be stable and cannot serve as dark matter in this setup. The results extend to other popular models like $SU(5)/SO(5)$, $SU(6)/Sp(6)$, and moose-like constructions, highlighting the central role of anomaly structure in shaping collider signatures and informing UV completions of Little Higgs theories.

Abstract

Little Higgs theories often rely on an internal parity ("T-parity'') to suppress non-standard electroweak effects or to provide a dark matter candidate. We show that such a symmetry is generally broken by anomalies, as described by the Wess-Zumino-Witten term. We study a simple SU(3) x SU(3)/SU(3) Little Higgs scheme where we obtain a minimal form for the topological interactions of a single Higgs field. The results apply to more general models, including [SU(3) x SU(3)/SU(3)]^4, SU(5)/SO(5), and SU(6)/Sp(6).