Abstract
We study the scalar sector of the most general multi Higgs doublet model satisfying explicitly an exact symmetry. We prove that such a model will exhibit decoupling if and only if the vacuum also satisfies the same symmetry. This general property is also shown independently and explicitly for three Higgs doublet models, by considering in detail all symmetry-constrained models and their possible vacua. We also discuss some specific characteristics of different decoupling patterns.
Highlights
There is great interest in models with extra scalars, for they can correct many of the shortcomings of the Standard Model (SM), such as the need for extra sources of CP violation to drive baryogenesis, the need for dark matter, or even, for example through a hierarchy of vacuum expectation values, explain the smallness of neutrino masses
An independent source of interest lies in the fact that the ATLAS and CMS collaborations [1,2] have found a fundamental scalar, prompting the obvious question: how many fundamental scalars are there in nature? Will it happen as in the fermion sector, where there are multiple families? As a result, many articles focus on N Higgs doublet models (NHDM)—for reviews, see, for example, [3,4,5] and references therein
The extra scalar fields have large masses and what is left at low energy is a state whose properties approach naturally those of the SM Higgs boson
Summary
There is great interest in models with extra scalars, for they can correct many of the shortcomings of the Standard Model (SM), such as the need for extra sources of CP violation to drive baryogenesis, the need for dark matter, or even, for example through a hierarchy of vacuum expectation values (vev), explain the smallness of neutrino masses. The couplings of the h125 to gauge bosons and the heaviest charged fermions are known to coincide with couplings expected in the SM, with errors of order 20% or better [6,7,8,9] This feature is easy to explain in models which have a so-called decoupling limit [10]. It has become commonplace to add specific symmetries to the NHDM It has been appreciated for a while that many such symmetry-constrained models cannot accommodate a decoupling limit; see, for example, [10,15,16,17].
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