$ZH\eta$-vertex: EFT Analysis and the Behavior in the SLH Model

TL;DR

This paper re-analyzes the $ZH ext{eta}$-vertex using EFT in the SLH model, revealing that the coupling coefficient appears only at third order in the ratio of electroweak to high scale, contrasting previous results.

Contribution

It demonstrates that the $ZH ext{eta}$ coupling coefficient is suppressed at lower orders in the SLH model, correcting earlier assumptions about its magnitude.

Findings

The $c_{ZH ext{eta}}$ coefficient appears only at $ ext{O}(\xi^3)$ order.

The behavior differs from previous long-standing results.

The analysis uses EFT and careful removal of off-diagonal transitions.

Abstract

We re-analyze the $ZH\eta$-vertex with the form $Z_{\mu}(\eta\partial^{\mu}H-H\partial^{\mu}\eta)$, where $H$ is the 125 GeV Higgs boson and $\eta$ is an exotic pseudo-axion, based on the effective field theory (EFT) analysis and choose the simplest little Higgs (SLH) model as an example. For a pure gauge singlet pseudoscalar $\eta$, after carefully removing all off-diagonal two-point transitions, we show that its coefficient $c_{ZH\eta}$ cannot appear before $\mathcal{O}(\xi^3)$ level, where $\xi$ is the ratio between the electro-weak scale $v$ and a high scale $f$. The same behavior arises in the simplest little Higgs (SLH) model, which is quite different from the result that has already existed for a long time.