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.
Highlights
The Yukawa sector of the modelThe model involves an A4 × SU(5) CP invariant superpotential at the grand unified theory (GUT) scale, where all symmetries, including CP, are spontaneously broken along supersymmetric flat directions, as discussed in sections 3 and 4
Minimal supersymmetric standard model (MSSM) supplemented by a minimal two righthanded neutrino seesaw mechanism
We propose a renormalisable model based on A4 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
Summary
The model involves an A4 × SU(5) CP invariant superpotential at the GUT scale, where all symmetries, including CP, are spontaneously broken along supersymmetric flat directions, as discussed in sections 3 and 4. We have the θi superfields which break Z6 and help to control Dirac neutrino masses, and nine A4 breaking triplet flavons generally denoted φ, with various vacuum alignments, responsible for large lepton mixing With these assignments, only the top quark gets a mass from a renormalisable Yukawa coupling H5T3T3 (which has ZR4 charge 2 as required for an allowed superpotential term). In order to enhance predictivity we need the messengers listed, which is the price we pay for having a renormalisable theory at the GUT scale We denote these superfields either as fermion messengers, Xi, or scalar messengers, Σi, depending on whether they carry similar quantum numbers to, respectively, the quarks and leptons (with odd ZR4 charge) or the symmetry breaking scalars (with even ZR4 charge). We emphasise that the successful predictions of the model in the lepton sector (namely predicting the PMNS matrix) is independent of the specific values of these mass parameters
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