On the $ZH\eta$ vertex in the simplest Little Higgs Model

TL;DR

This paper revisits the derivation of the $ZH\eta$ vertex in the simplest Little Higgs model, clarifying the effects of non-canonical normalization and two-point transitions, resulting in a different vertex than previously reported.

Contribution

It provides a general procedure for diagonalizing vector-scalar systems in gauge theories and applies it to the SLH model, revealing a revised $ZH\eta$ vertex.

Findings

The $ZH\eta$ vertex differs from previous literature.

A systematic diagonalization method for vector-scalar systems is presented.

An effective field theory perspective clarifies the vertex derivation.

Abstract

The issue of deriving $ZH\eta$ vertex in the simplest Little Higgs (SLH) model is revisited. Special attention is paid to the treatment of non-canonically-normalized scalar kinetic matrix and vector-scalar two-point transitions. We elucidate a general procedure to diagonalize a general vector-scalar system in gauge theories and apply it to the case of SLH. The resultant $ZH\eta$ vertex is found to be different from those which have already existed in the literature for a long time. We also present an understanding of this issue from an effective field theory viewpoint.