Multi-Higgs doublet models: the Higgs-fermion couplings and their sum rules

Abstract

This is the second of a series of papers that explores the physical parameterization, sum rules and unitarity bounds arising from a non-minimal scalar sector of the Standard Model (SM) that consists of N Higgs doublets. In this paper, we focus on the structure and implication of the Yukawa interactions that couple the N scalar doublets to the SM fermions. We employ the charged Higgs basis, which is defined as the basis of scalar fields such that the neutral scalar field vacuum expectation value resides entirely in one of the N scalar doublet fields, and the charged components of the remaining N-1 scalar doublet fields are the physical (mass-eigenstate) charged Higgs fields. Based on the structure of the Yukawa Lagrangian of the model (and as a consequence of tree-level unitarity), one may deduce numerous sum rules, several of which have not appeared previously in the literature. These sum rules can be used to uncover intimate relations between the structure of the Higgs-fermion couplings and the scalar/gauge couplings. In particular, we show that the approximate alignment limit, in which the W+W- and ZZ couplings to the observed Higgs boson are approximately SM-like, imposes significant constraints on the Higgs-fermion couplings.

arXiv comment24 pages, 2 figures, 4 tables, uses jheppub.sty. Two typographical errors corrected, one clarification added and one reference updated in v3

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• Extended Higgs sector of 2HDM with real singlet facing LHC data
• Slight excess at 130 GeV in search for a charged Higgs boson decaying to a charm quark and a bottom quark at the Large Hadron Collider
• Off diagonal charged scalar couplings with the Z boson: the Zee model as an example
• Tree-level Unitarity in SU(2)${}_L\times$U(1)${}_Y\times$U(1)${}_{Y^{\prime }}$ Models
• Creating Oscillons and Oscillating Kinks in Two Scalar Field Theories
• Fermion masses and mixings in a $U(1{)}_X$ model based on the $\Sigma (18)$ discrete symmetry
• Minimal A4 Type-II Seesaw Realization of Testable Neutrino Mass Sum Rules
• ILC Phenomenology of the $Z_3$ symmetric Type-Z Three Higgs Doublet Model
• The Deconstruction of Flavor in the Privately Democratic Higgs Sector
• Flavour Invariants of the N Higgs Doublet Model
• Scalar and gauge sectors in the 3-Higgs Doublet Model under the S3-symmetry