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.
Highlights
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
This difficulty is a challenge, which one can address with extra symmetries, such as the Z2 symmetry introduced in the two Higgs doublet model (2HDM) following general theorems proposed by Glashow and Weinberg [5] and independently by Paschos [6]
The Standard Model employs a Higgs sector consisting of a hypercharge-one, doublet of scalar fields, the generational structure of the fermionic sector invites us to consider the possibility that the Higgs sector of the Standard Model is non-minimal, consisting of N Higgs doublets
Summary
We discuss the full Lagrangian of the most general N Higgs doublet model. Its physical significance is the matrix that takes the neutral scalars fields from the charged Higgs basis into their mass eigenstate basis. The minimization the scalar potential in the charged Higgs basis and the identification of the charged Higgs boson squared-masses are neatly summarized by the following equation obtained in ref. Performing the diagonalization of the neutral scalar squared-mass directly in the charged Higgs basis yields [7], 2v2Zi1,1j = −2(D±2 )ij +. In contrast with our previous publication [7], where both the scalar potential and the kinetic Lagrangian Feynman rules were in general distinct from the SM, here we find that the fermion-gauge couplings of the NHDM are identical to those of the SM These results are presented, where mun (mdn) is the n-th up-quark (down-quark) mass. No new sum rules arise exclusively from the fermion-gauge couplings
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