Towards a complete A4 × 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 ℤ9 × ℤ6 symmetry provides the fermion mass hierarchy in both the quark and lepton sectors, while R4 symmetry is broken to R2 , identified as usual R-parity. Proton decay is highly sup-pressed by these symmetries. The strong CP problem is solved in a similar way to the Nelson-Barr mechanism. We discuss both the A 4 and SU(5) symmetry breaking sectors, including doublet-triplet splitting, Higgs mixing and the origin of the μ term. The model provides an excellent fit (better than one sigma) to all quark and lepton (including neu-trino) 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 pa-rameters, up to a relative phase, selected to be 2π/3 from a choice of the nine complex roots of unity, which is identified as the leptogenesis phase. The model predicts a normal neutrino mass hierarchy with leptonic angles θ ι13  ≈ 8.7, θ ι12  ≈ 34, θ ι23  ≈ 46 and an oscillation phase δ ι ≈ − 87.

A preprint version of the article is available at ArXiv.

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Björkeroth, F., de Anda, F.J., de Medeiros Varzielas, I. et al. Towards a complete A4 × SU(5) SUSY GUT. J. High Energ. Phys. 2015, 141 (2015). https://doi.org/10.1007/JHEP06(2015)141

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Keywords

  • Neutrino Physics
  • GUT
  • Discrete and Finite Symmetries