A Grand Δ(96)×SU(5)Δ(96)×SU(5) Flavour Model

Recent results from the Daya Bay and RENO reactor experiments have measured the smallest lepton mixing angle and found it to have a value of θ13≈9°θ13≈9°. This result presents a new challenge for the existing paradigms of discrete flavour symmetries which attempt to describe all quark and lepton masses and mixing angles. Here we propose a Supersymmetric Grand Unified Theory of Flavour based on Δ(96)×SU(5)Δ(96)×SU(5), together with a U(1)×Z3U(1)×Z3 symmetry, including a full discussion of Δ(96)Δ(96) in a convenient basis. The Grand Δ(96)×SU(5)Δ(96)×SU(5) Flavour Model relates the quark mixing angles and masses in the form of the Gatto–Sartori–Tonin relation and realises the Georgi–Jarlskog mass relations between the charged leptons and down-type quarks. We predict a Bi-trimaximal (not Tri-bimaximal) form of neutrino mixing matrix, which, after including charged lepton corrections with zero phase, leads to the following GUT scale predictions for the atmospheric, solar, and reactor mixing angles: θ23≈36.9°θ23≈36.9°, θ12≈32.7°θ12≈32.7° and θ13≈9.6°θ13≈9.6°, in good agreement with recent global fits, and a zero Dirac CP phase δ≈0δ≈0.