Masses and Mixings in a Grand Unified Toy Model

Abstract

The generation of the fermion mass hierarchy in the standard model of particle physics is a long-standing puzzle. The recent discoveries from neutrino physics suggests that the mixing in the lepton sector is large compared to the quark mixings. To understand this asymmetry between the quark and lepton mixings is an important aim for particle physics. In this regard, two promising approaches from the theoretical side are grand unified theories and family symmetries. In this note we try to understand certain general features of grand unified theories with Abelian family symmetries by taking the simplest SU(5) grand unified theory as a prototype. We construct an SU(5) toy model with $U(1{)}_F\otimes Z_2^{\prime }\otimes Z_2^{\prime \prime }\otimes Z_2^{\prime \prime \prime }$ family symmetry that, in a natural way, duplicates the observed mass hierarchy and mixing matrices to lowest approximation. The system for generating the mass hierarchy is through a Froggatt-Nielsen type mechanism. One idea that we use in the model is that the quark and charged lepton sectors are hierarchical with small mixing angles while the light neutrino sector is democratic with larger mixing angles. We also discuss some of the difficulties in incorporating finer details into the model without making further assumptions or adding a large scalar sector.

21 pages, 2 figures, RevTeX, v2: references updated and typos corrected, v3: updated top quark mass, comments on MiniBooNE result, and typos corrected

References in corpus (7)

• A model for fermion masses and lepton mixing in SO(10) x A4
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• Supersymmetric A_4 X Z_3 and A_4 Realizations of Neutrino Tribimaximal Mixing Without and With Corrections
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Cited by in corpus (2)

• Neutrino masses and tribimaximal mixing in the minimal renormalizable supersymmetric SU(5) grand unified model with A4 flavor symmetry
• Lepton-Jets and Low-Mass Sterile Neutrinos at Hadron Colliders