$ZHη$-vertex: EFT Analysis and the Behavior in the SLH Model

Abstract

We re-analyze the $ZHη$-vertex with the form $Z_μ(η\partial^μH-H\partial^μη)$, where $H$ is the 125 GeV Higgs boson and $η$ 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 $η$, after carefully removing all off-diagonal two-point transitions, we show that its coefficient $c_{ZHη}$ cannot appear before $\mathcal{O}(ξ^3)$ level, where $ξ$ 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.