A Grand Delta(96) x SU(5) Flavour Model

Abstract

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 theta_13 approximately 9 degrees. 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 Delta(96) x SU(5), together with a U(1) x Z3 symmetry, including a full discussion of Delta(96) in a convenient basis. The Grand Delta(96) x 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: theta_23=36.9 degrees, theta_12=32.7 degrees and theta_13=9.6 degrees, in good agreement with recent global fits, and a zero Dirac CP phase delta~0.

Comments: 35 pages, version to appear in NPB