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 $\theta_{13}^{pmns}=(9{^{+1}_{-2}})^\circ$, 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 $sin^2{\theta_{23}^{pmns}}= 0.4235_{-0.0043}^{+0.0032}$ 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.