Quark-Lepton Complementarity Predictions for ${\theta }_{23}^{pmns}$ and CP Violation

Abstract

In the light of recent experimental results on ${\theta }_{13}^{pmns}$, we re-investigate the complementarity between the quark and lepton mixing matrices and obtain predictions for most unsettled neutrino mixing parameters like ${\theta }_{23}^{pmns}$ and CP violating phase invariants $J$, $S_1$ and $S_2$. This paper is motivated by our previous work where in a QLC model we predicted the value for ${\theta }_{13}^{pmns}=(9{}_{-2}^{+1}{)}^{\circ }$, which was found to be in strong agreement with the experimental results. In the QLC model the non-trivial correlation between CKM and PMNS mixing matrices is given by a correlation matrix ($V_c$). We do numerical simulation and estimate the texture of the $V_c$ and in our findings we get a small deviation from the Tri-Bi-Maximal (TBM) texture and a large from the Bi-Maximal one, which is consistent with the work already reported in literature. In the further investigation we obtain quite constrained limits for $si{n}^2{\theta }_{23}^{pmns}=0.4235_{-0.0043}^{+0.0032}$ that is narrower to the existing ones. We also obtain the constrained limits for the three CP violating phase invariants $J$, $S_1$ and $S_2$: as $J<0.0315$, $S_1<0.12$ and $S_2<0.08$, respectively.

Comments: 18 pages, 10 figures