Tri-bimaximal-Cabibbo Mixing

Abstract

Recent measurements of the lepton mixing angle $θ_{13}$ by the Daya Bay and RENO reactor experiments are consistent with the relationship $θ_{13}\approx θ_C/\sqrt{2}$ where $ θ_C$ is the Cabibbo angle. We propose Tri-bimaximal-Cabibbo (TBC) mixing, in which $\sin θ_{13}= \sin θ_C/\sqrt{2}$, $\sin θ_{23}= 1/\sqrt{2}$ and $\sin θ_{12}= 1/\sqrt{3}$. 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 $δ\approx \pm 90^o, \pm 180^o, \pm 75^o$, 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.