Multi-Higgs doublet models: physical parametrization, sum rules and unitarity bounds

Abstract

If the scalar sector of the Standard Model is non-minimal, one might expect multiple generations of the hypercharge-1/2 scalar doublet analogous to the generational structure of the fermions. In this work, we examine the structure of a Higgs sector consisting of N Higgs doublets (where N ≥ 2). It is particularly convenient to work in the so-called charged Higgs basis, in which the neutral Higgs vacuum expectation value resides entirely in the first Higgs doublet, and the charged components of remaining N − 1 Higgs doublets are mass-eigenstate fields. We elucidate the interactions of the gauge bosons with the physical Higgs scalars and the Goldstone bosons and show that they are determined by an N × 2N matrix. This matrix depends on (N − 1)(2N − 1) real parameters that are associated with the mixing of the neutral Higgs fields in the charged Higgs basis. Among these parameters, N − 1 are unphysical (and can be removed by rephasing the physical charged Higgs fields), and the remaining 2(N − 1) 2 parameters are physical. We also demonstrate a particularly simple form for the cubic interaction and some of the quartic interactions of the Goldstone bosons with the physical Higgs scalars. These results are applied in the derivation of Higgs coupling sum rules and tree-level unitarity bounds that restrict the size of the quartic scalar couplings. In particular, new applications to three Higgs doublet models with an order-4 CP symmetry and with a Z 3 symmetry, respectively, are presented.

Extended Higgs sector of 2HDM with real singlet facing LHC data

“…As one can see from the couplings of h 1 to fermions given in Eq. (19), h 1 could be fermiophobic if R 12 ∝ cos α 2 sin α 1 vanish. This scenario might happens if we take α 1 ≈ 0 and/or α 2 ≈ π/2 which is possible since both α 1 and α 2 are free parameters in this model.…”

Electroweak breaking and Higgs boson profile in the simplest linear seesaw model

“…The Feynman rule for the quartic term would be 4λ, but remembering the factor of 1/ √ 2 for states with identical particles [54] we would get the amplitude…”

“…As in the case of any multi-doublet Higgs model, NHDM [54], the couplings of the CP even Higgs bosons to the vector bosons obey a sum rule,…”

Three-Higgs-doublet model under A4 symmetry implies alignment

“…A specially important sub-class of these are the supersymmetric models which necessitate two SU(2) L doublets with rather specific couplings. Models with n-Higgs doublets with n > 2 have also been under study [6][7][8].…”