---
author:
- 'Shi-Ping He,'
- 'Ying-nan Mao,'
- Chen Zhang
- 'and Shou-hua Zhu'
bibliography:
- 'slhvss\_v3.bib'
title: 'On the $ZH\eta$ vertex in the simplest Little Higgs Model'
---

Introduction
============

The discovery of the $125\GeV$ Higgs-like boson [@Aad:2012tfa; @Chatrchyan:2012xdj] marks a prominent triumph of the Standard Model (SM). Nevertheless, it is widely believed that this is not the end of the story. The SM in its current form leaves too many unanswered questions, from theoretical ones like the issue of Higgs mass naturalness [@Giudice:2008bi; @Giudice:2013nak], to observational ones like the nature of the dark matter present in the universe [@Bertone:2004pz; @Lisanti:2016jxe]. Almost all models going beyond the SM (BSM) entail an enlargement of the scalar sector, and consequently forms of interaction which are absent in the SM could be possible. Searching for such kind of new interactions therefore may lead to decisive evidence of the existence of BSM and provide a clue to the nature of the BSM physics.

For example, Lorentz symmetry does not forbid the interaction of one gauge boson (denoted as $Z$) with two scalar bosons (denoted as $H$ and $\eta$) at the dimension-4 level, in the form like $$Z^\mu(H\partial_\mu\eta-\eta\partial_\mu H)
\label{eq:aszheta}$$ If $H$ denotes 