Quark-lepton complementarity model based predictions for $\theta_{23}^{PMNS}$ with neutrino mass hierarchy

After the successful investigation and confirmation of non zero $\theta_{13}^{PMNS}$ by various experiments, we are standing at a square where we still encounter a number of issues, which are to be settled. In this paper, we have extended our recent work towards a precise prediction of the $\theta_{23}^{PMNS}$ mixing angle, taking into account the neutrino mass hierarchy. We parameterize the non-trivial correlation between quark (CKM) and lepton (PMNS) mixing matrices in quark-lepton complementarity (QLC) model as $V_{c}= U_{CKM}. \psi. U_{PMNS}$, where $\psi$ is a diagonal phase matrix. Monte Carlo simulations are used to estimate the texture of $V_{c}$ and compare the results with the standard Tri-Bi-Maximal (TBM) and Bi-Maximal(BM) structures of neutrino mixing matrix. We have predicted the value of $\theta_{23}^{PMNS}$ for normal and inverted neutrino mass hierarchies. The value of $\theta_{23}^{PMNS}$ obtained for two cases are about $1.3\sigma$ away from each other, implying the better precision can give us a strong hint for the type of neutrino mass hierarchy.