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

TL;DR

This paper investigates the Yukawa interactions in multi-Higgs doublet models, deriving sum rules and unitarity bounds that relate Higgs-fermion couplings to scalar and gauge interactions, especially under the alignment limit.

Contribution

It introduces new sum rules for Higgs-fermion couplings in N-Higgs doublet models using the charged Higgs basis, enhancing understanding of their structure and constraints.

Findings

Derived new sum rules for Yukawa couplings.

Identified constraints on Higgs-fermion interactions in the alignment limit.

Linked Higgs-fermion couplings to scalar and gauge sector properties.

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.