Investigating the sterile neutrino parameters with QLC in 3 + 1 scenario

Abstract: In the scenario with four generation quarks and leptons and using a 3 + 1 neutrino model having one sterile and the three standard active neutrinos with a $4 \times 4$ unitary transformation matrix, $U_{PMNS_{4}}$, we perform a model-based analysis using the latest global data and determine bounds on the sterile neutrino parameters i.e. the neutrino mixing angles. Motivated by our previous results, where, in a quark-lepton complementarity (QLC) model we predicted the values of $\theta_{13}^{PMNS}=(9_{-2}^{+1})^{\circ}$ and $\theta_{23}^{PMNS}=(40.60_{-0.3}^{+0.1})^{\circ}$. In the QLC model the non-trivial correlation between $CKM_4$ and $PMNS_4$ mixing matrix is given by the correlation matrix $V_{c_{4}}$. Monte Carlo simulations are performed to estimate the texture of $V_{c4}$ followed by the calculation of $PMNS_4$ using the equation, $U_{PMNS_{4}}= (U_{CKM_{4}} . \psi_{4})^{-1}.V_{c_{4}}$, where $\psi_{4}$ is a diagonal phase matrix. The sterile neutrino mixing angles, $\theta_{14}^{PMNS}$, $\theta_{24}^{PMNS}$ and $\theta_{34}^{PMNS}$ are assumed to be freely varying between $(0-\pi/4)$ and obtained results which are consistent with the data available from various experiments, like No$\nu$A, MINOS, SuperK, Ice Cube-DeepCore. In further investigation, we analytically obtain approximately similar ranges for various neutrino mixing parameters $\mid{ U_{\mu 4}}\mid ^2$ and $\mid{ U_{\tau 4}}\mid ^2$.