Abstract
We demonstrate how residual flavour symmetries, infrared signatures of symmetry breaking in complete models of flavour, can naturally forbid (or limit in a flavour specific way) flavour-changing neutral currents (FCNC) in multi-Higgs-doublet models (MHDM) without using mass hierarchies. We first review how this model-independent mechanism can control the fermionic mixing patterns of the Standard Model, and then implement the symmetries in the Yukawa sector of MHDM, which allows us to intimately connect the predictivity of a given flavour model with its ability to sequester FCNC. Finally, after discussing various subtleties of the approach, we sketch an A4 toy model that realises an explicit example of these simplified constructions.
Highlights
Multi-Higgs-doublet models (MHDM) [1,2,3] are well motivated generalisations of the Standard Model (SM) with additional SU(2) doublet scalars
We demonstrate how residual flavour symmetries, infrared signatures of symmetry breaking in complete models of flavour, can naturally forbid flavour-changing neutral currents (FCNC) in multi-Higgs-doublet models (MHDM) without using mass hierarchies
This is easiest to see in the Higgs basis, in which only one doublet has a non-vanishing vacuum expectation value (VEV) and all mass matrices are proportional to a single Yukawa
Summary
Multi-Higgs-doublet models (MHDM) [1,2,3] are well motivated generalisations of the Standard Model (SM) with additional SU(2) doublet scalars. The resulting proliferation of Yukawa couplings and neutral states associated with the extra scalars can potentially lead to large unobserved flavour-changing neutral currents (FCNC) at tree level This is easiest to see in the Higgs basis, in which only one doublet has a non-vanishing vacuum expectation value (VEV) and all mass matrices are proportional to a single Yukawa. Mass Matrix Ansätze, where Yukawa matrices are assumed to have specific textures in flavour space, which when transforming to the basis of physical mass-eigenstates yields desirable SM mass and mixing phenomenology and sufficiently suppressed tree-level FCNC Attempts in this direction include [11, 12]. In this note we instead apply residual family symmetries (RFS), Abelian symmetries of the SM fermion mass sector, to the extended Yukawa sector of MHDM to show that they can forbid (or limit in a flavour-specific way) tree-level FCNC while simultaneously controlling the CKM and/or PMNS mixing matrices of the SM.
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