Not T-parity but C-parity

TL;DR

This paper introduces a new $Z_2$ symmetry called collective parity ($ ext{C}$-parity) in the Littlest Higgs model, showing its consistency with $T$-parity and exploring implications for UV completion and $T$-parity violation.

Contribution

It identifies a new collective parity symmetry in the Littlest Higgs model and links it to the origin of collective symmetry in composite Higgs theories, providing a new perspective on UV completion.

Findings

$T$-parity is compatible with the newly identified $ ext{C}$-parity.

A novel path to UV complete the model is proposed.

Natural $T$-parity violating processes are demonstrated.

Abstract

We revisit the Littlest Higgs model with $T$-parity, and discover a $Z_2$ symmetry on collective symmetry. It is dubbed collective parity ($\EuScript{C}$-parity). We demonstrate that $T$-parity is consistent with $\EuScript{C}$-parity. We further investigate the origin of the collective symmetry in the context of composite Higgs and find a new path to the UV complete theory of the model. In addition, we demonstrate that $T$-parity violating processes naturally take place.