SUSY SU(5) with singlet plus adjoint matter and A4 family symmetry

We propose a supersymmetric (SUSY) SU(5) Grand Unified Theory (GUT) including a single right-handed neutrino singlet and an adjoint matter representation below the GUT scale and extend this model to include an A4 family symmetry and a gauged anomaly-free Abelian group. In our approach hierarchical neutrino masses result from a combined type I and type III seesaw mechanism, and the A4 symmetry leads to tri-bimaximal mixing which arises indirectly. The mixing between the single right-handed neutrino and the matter in the adjoint is forbidden by excluding an adjoint Higgs, leading to a diagonal heavy Majorana sector as required by constrained sequential dominance. The model also reproduces a realistic description of quark and charged lepton masses and quark mixings, including the Georgi–Jarlskog relations and the leptonic mixing sum rules s=rcosδ and a=−r2/4 with r=θC/3.