Quark-lepton complementarity, neutrino and standard model data predict $({\theta }_{13}^{PMNS}=9_{-2}^{+1}{)}^{\circ }$

Abstract

The complementarity between the quark and lepton mixing matrices is shown to provide a robust prediction for the neutrino mixing angle ${\theta }_{13}^{PMNS}$. We obtain this prediction by first showing that the matrix $V_M$, product of the CKM and PMNS mixing matrices, may have a zero (1,3) entry which is favored by experimental data. Hence models with bimaximal or tribimaximal forms of the correlation matrix $V_M$ are quite possible. Any theoretical model with a vanishing (1,3) entry of $V_M$ that is in agreement with quark data, solar, and atmospheric mixing angle leads to ${\theta }_{13}^{PMNS}=(9{}_{-2}^{+1}{)}^{\circ }$. This value is consistent with the present 90% CL experimental upper limit.

Comments: 15 pages, 7 figures. Final version to appear in the journal