Perturbative unitarity of Higgs derivative interactions

TL;DR

This paper investigates the perturbative unitarity bounds of dimension six derivative interactions involving Higgs doublets, analyzing their effects on vector boson scattering and the implications for various Higgs models.

Contribution

It derives unitarity bounds for derivative Higgs interactions and explores their model dependence in one and two Higgs doublet models.

Findings

Derivative interactions have limited impact on Standard Model discrimination.

Unitarity bounds vary significantly across different Higgs models.

High-energy vector boson scattering is sensitive to derivative interactions.

Abstract

We study the perturbative unitarity bound given by dimension six derivative interactions consisting of Higgs doublets. These operators emerge from kinetic terms of composite Higgs models or integrating out heavy particles that interact with Higgs doublets. They lead to new phenomena beyond the Standard Model. One of characteristic contributions by derivative interactions appear in vector boson scattering processes. Longitudinal modes of massive vector bosons can be regarded as Nambu Goldstone bosons eaten by each vector field with the equivalence theorem. Since their effects become larger and larger as the collision energy of vector bosons increases, vector boson scattering processes become important in a high energy region around the TeV scale. On the other hand, in such a high energy region, we have to take the unitarity of amplitudes into account. We have obtained the unitarity condition in terms of the parameter included in the effective Lagrangian for one Higgs doublet models. Applying it to some of models, we have found that contributions of derivative interactions are not so large enough to clearly discriminate them from the Standard Model ones. We also study it in two Higgs doublet models. Because they are too complex to obtain the bound in the general effective Lagrangian, we have calculated it in explicit models. These analyses tell us highly model dependence of the perturbative unitarity bounds.