The issue of deriving ZHη vertex in the simplest little Higgs (SLH) model is revisited. Special attention is paid to the treatment of noncanonically-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.

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Though the 125 GeV Higgs boson is consistent with the standard model (SM) prediction until now, the triple Higgs coupling can deviate from the SM value in the physics beyond the SM (BSM). In this paper, the radiative correction to the triple Higgs coupling is calculated in the minimal extension of the SM by adding a real gauge singlet scalar. In this model there are two scalars h and H and both of them are mixed states of the doublet and singlet. Provided that the mixing angle is set to be zero, namely the SM limit, h is the pure left-over of the doublet and its behavior is the same as that of the SM at the tree level. However the loop corrections can alter h-related couplings. In this SM limit case, the effect of the singlet H may show up in the h-related couplings, especially the triple h coupling. Our numerical results show that the deviation is sizable. For λ ΦS = 1 (see text for the parameter definition), the deviation δ (1) hhh can be 40%. For λ ΦS = 1.5, the δ (1) hhh can reach 140%. The sizable radiative correction is mainly caused by three reasons: the magnitude of the coupling λ ΦS , light mass of the additional scalar and the threshold enhancement. The radiative corrections for the hV V, hf f couplings are from the counter-terms, which are the universal correction in this model and always at O(1%). The hZZ coupling can be a complementarity to the triple h coupling because of the high precision measurement. In the optimal case, the triple h coupling is very sensitive to the BSM physics, and this model can be tested at future high luminosity hadron colliders and electron-positron colliders.