Abstract
We construct models with a spontaneously broken $SU(3)_F$ flavour symmetry where three generations of Higgs multiplets transform in a flavour-triplet representation. The models are embedded in a supersymmetric Pati-Salam GUT framework, which includes left-right symmetry. We study the possible flavon representations and show that a model with flavons in the decuplet representation is able to reproduce the hierarchy structure of the quark and lepton mass and mixing matrices. This result requires no additional structure or fine-tunings except for an extra $Z_4$ discrete symmetry in the superpotential.
Highlights
The standard model (SM) contains a single complex doublet of scalar fields with one physical Higgs particle, which stands out as an extra field, unrelated to the fermionic matter or gauge fields
We consider the simplest possibility that a single SU(3)F symmetry universally applies to all Higgs and matter multiplets, and assume that it is spontaneously broken by VEVs of additional scalar fields which we collectively denote as flavons
We have studied supersymmetric models with a Pati–Salam gauge group and a SU(3)F flavour symmetry where the Higgs bi-doublet occurs in three generations and transforms as a flavour triplet
Summary
The standard model (SM) contains a single complex doublet of scalar fields with one physical Higgs particle, which stands out as an extra field, unrelated to the fermionic matter or gauge fields. We study the particular case that there are three Higgs generations [3,4,5] which can be associated with a flavour symmetry [6,7,8], relating the Higgs and matter sectors. Such a structure is present, for instance, in supersymmetric grand-unification models where Higgs and matter fields combine in a common gauge-group representation [9,10]. Models with only triplet flavons are feasible, but a model with a dominant decuplet contribution appears more natural and is able to qualitatively accommodate the observed mass- and mixinghierarchy patterns in both the quark and the lepton sectors
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