Tri-bimaximal-Cabibbo Mixing

Recent measurements of the lepton mixing angle ${\theta }_{13}$ by the Daya Bay and RENO reactor experiments are consistent with the relationship ${\theta }_{13}\approx {\theta }_C\mathrm{/}\sqrt{2}$ where ${\theta }_C$ is the Cabibbo angle. We propose Tri-bimaximal-Cabibbo (TBC) mixing, in which $\sin \theta_{13}= \sin \theta_C/\sqrt{2}$,$\sin \theta_{23}= 1/\sqrt{2}$and$\sin \theta_{12}= 1/\sqrt{3}$. We show that TBC mixing may arise approximately from Tri-bimaximal, Bi-maximal or Golden Ratio neutrino mixing, together with Cabibbo-like charged lepton corrections arising from a Pati-Salam gauge group, leading to predictions for the CP-violating phase of $\delta \approx \pm 90^o, \pm 180^o, \pm 75^o$, respectively. Alternatively, we show that TBC neutrino mixing may realised accurately using the type I see-saw mechanism with partially constrained sequential right-handed neutrino dominance, assuming a family symmetry which is broken by a flavon common to quarks and neutrinos.