Perturbative unitarity of Higgs derivative interactions

Abstract

We study the perturbative unitarity bound given by dimension six derivative interactions consisting of Higgs doublets. These interactions 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 from 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. Since their effects become larger and larger as the collision energy of vector bosons increases, vector boson scattering processes become important in the high energy region around the TeV scale. On the other hand, in such a high energy region, we have to take into account the unitarity of amplitudes. 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 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 the unitarity bound in two Higgs doublet models. Because they are too complex to obtain it in the general effective Lagrangian, we have calculated it in explicit models. These analyses tell that the perturbative unitarity bounds are highly model dependent. © The Author(s) 2013.