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 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.

Spontaneous CP -violation in the simplest little Higgs model and its future collider tests: The scalar sector

“…The matrix elements of F were also calculated to Oððv=fÞ 3 Þ in Ref. [34]. The gauge-fixing term must provide a two-point transition like…”

“…In the calculation of c iR;q , the improved formalism affects their imaginary parts since the η component in G cannot be ignored due to the improved SLH formalism [34]. For the third generation, m t =m T ∼ Oðv=fÞ, and thus c iL;q can reach Oð1Þ.…”

“…In that research, the product of the three vertices was used as a quantity to measure the magnitude of CP violation [32,33]. However, in the SLH model, we recently showed that the Zh 1 h 2 vertex is suppressed by a factor ðv=fÞ 3 [34], which means that it is difficult to test. Thus, to test CP violation in the SLH model we can turn to extra heavy gauge bosons for help.…”

“…Based on the improved formalism of the SLH model [34], we obtained the Zh 1 h 2 vertex in Eq. (37).c as Zh 1 h 2 is suppressed by a factor ðv=fÞ 3 ≲ Oð10 −5 Þ, and thus the associated production channels cannot be used to measure this vertex.…”

“…V we present our conclusions and further discussions. In the Appendix we also present the improved SLH formalism [34], which is very helpful for model building.…”