Towards a complete $A_4\times SU(5)$ SUSY GUT

Abstract

We propose a renormalisable model based on $A_4$ family symmetry with an $SU(5)$ grand unified theory (GUT) which leads to the minimal supersymmetric standard model (MSSM) with a two right-handed neutrino seesaw mechanism. Discrete ${\mathbb{Z}}_9\times {\mathbb{Z}}_6$ symmetry provides the fermion mass hierarchy in both the quark and lepton sectors, while ${\mathbb{Z}}_4^R$ symmetry is broken to ${\mathbb{Z}}_2^R$, identified as usual R-parity. Proton decay is highly suppressed by these symmetries. We discuss both the $A_4$ and $SU(5)$ symmetry breaking sectors, including doublet-triplet splitting, Higgs mixing and the origin of the $\mu$ term. The model provides an excellent fit (better than one sigma) to all quark and lepton (including neutrino) masses and mixing with spontaneous CP violation. With the $A_4$ vacuum alignments, $(0,1,1)$ and $(1,3,1)$, the model predicts the entire PMNS mixing matrix with no free parameters, up to a relative phase, selected to be $2\pi /3$ from a choice of the nine complex roots of unity, providing a direct link between neutrino oscillations and leptogenesis.

30 pages, 17 figures, 7 tables; Minor changes, references added, version accepted in JHEP

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Cited by in corpus (12)

• Neutrinoless double beta decay and neutrino mass
• GUT Physics in the era of the LHC
• Accidental Peccei-Quinn Symmetry from Discrete Flavour Symmetry and Pati-Salam
• Flavour and CP predictions from orbifold compactification
• Littlest Seesaw model from S4 x U(1)
• $\mathbf{SO}(10)\times {\mathbf{S}}_4$ Grand Unified Theory of Flavour and Leptogenesis
• Solving the strong CP problem with non-conventional CP
• Leptogenesis in a $\Delta (27)\times SO(10)$ SUSY GUT
• Littlest mu-tau seesaw
• Sign of CP Violating Phase in Quarks and Leptons
• Flavon alignments from orbifolding: $SU(5)\times SU(3)$ model with ${\mathbb{T}}^6/\Delta (54)$
• $A_4$ flavor symmetric model in SUSY SU(5) GUT