We propose new classes of models which predict both tri-bimaximal lepton
mixing and a right-angled Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle,
alpha approximately 90 degrees. The ingredients of the models include a
supersymmetric (SUSY) unified gauge group such as SU(5), a discrete family
symmetry such as A4 or S4, a shaping symmetry including products of Z2 and Z4
groups as well as spontaneous CP violation. We show how the vacuum alignment in
such models allows a simple explanation of alpha approximately 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, 90, 180, 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.Comment: 29 pages, 4 figures, version to be published in NP
