UV friendly T-parity in the SU(6)/Sp(6) little Higgs model

TL;DR

This paper explores a new implementation of T-parity in the SU(6)/Sp(6) little Higgs model, aiming to address electroweak constraints and facilitate UV completion, resulting in an inert two Higgs doublets model with potential dark matter implications.

Contribution

It introduces a novel T-parity implementation in the SU(6)/Sp(6) model, leading to a different low energy theory with an inert two Higgs doublets structure.

Findings

The model satisfies electroweak precision constraints.

The Higgs sector resembles an inert two Higgs doublets model.

Potential dark matter candidates are identified.

Abstract

Electroweak precision tests put stringent constraints on the parameter space of little Higgs models. Tree-level exchange of TeV scale particles in a generic little Higgs model produce higher dimensional operators that make contributions to electroweak observables that are typically too large. To avoid this problem a discrete symmetry dubbed T-parity can be introduced to forbid the dangerous couplings. However, it was realized that in simple group models such as the littlest Higgs model, the implementation of T-parity in a UV completion could present some challenges. The situation is analogous to the one in QCD where the pion can easily be defined as being odd under a new $Z_2$ symmetry in the chiral Lagrangian, but this $Z_2$ is not a symmetry of the quark Lagrangian. In this paper we examine the possibility of implementing a T-parity in the low energy $SU(6)/Sp(6)$ model that might be easier to realize in the UV. In our model, the T-parity acts on the low energy non-linear sigma model field in way which is different to what was originally proposed for the Littlest Higgs, and lead to a different low energy theory. In particular, the Higgs sector of this model is a inert two Higgs doublets model with an approximate custodial symmetry. We examine the contributions of the various sectors of the model to electroweak precision data, and to the dark matter abundance.