On the $ZHη$ vertex in the simplest Little Higgs Model

Abstract

The issue of deriving $ZHη$ 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 $ZHη$ 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.

Accepted version by PRD; 11 pages with two columns; Presentation of Sec. II refined; EFT analysis added in Sec. IIIC; References updated