Right unitarity triangles and tri-bimaximal mixing from discrete symmetries and unification

We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle, alpha approximate to 90 degrees. The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU(5), a discrete family symmetry such as A(4) or S-4, a shaping symmetry including products of Z(2) and Z(4) groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of alpha approximate to 90 degrees by a combination of purely real or purely imaginary vacuum expectation values (vevs) of the flavons responsible for family symmetry breaking. This leads to quark mass matrices with 1-3 texture zeros that satisfy the "phase sum rule" and lepton mass matrices that satisfy the "lepton mixing sum rule" together with a new prediction that the leptonic CP violating oscillation phase is close to either 0 degrees, 90 degrees, 180 degrees, or 270 degrees depending on the model, with neutrino masses being purely real (no complex Majorana phases). This leads to the possibility of having right-angled unitarity triangles in both the quark and lepton sectors. (C) 2011 Elsevier B.V. All rights reserved.