Quasi-degenerate Neutrino mass models and their significance: A model independent investigation

The prediction of possible ordering of neutrino masses relies mostly on the model selected. Alienating the $\mu-\tau$ interchange symmetry from discrete flavour symmetry based models, turns the neutrino mass matrix less predictive. But this inspires one to seek the answer from other phenomenological frameworks. We need a proper parametrization of the neutrino mass matrices concerning individual hierarchies. In the present work, we attempt to study the six different cases of Quasi-degenerate (QDN) neutrino models. The related mass matrices, $m_{LL}^{\nu}$ are parametrized with two free parameters ($\alpha,\eta$) and standard Wolfenstein parameter ($\lambda$). The input mass scale $m_0$ is selected around $\sim 0.08\,eV$. We begin with a $\mu-\tau$ symmetric neutrino mass matrix tailed by a correction from charged lepton sector. The parametrization accentuates the existence of four independent texture zero building block matrices which are common to all the QDN models under $\mu-\tau$ symmetric framework. These remain invariant irrespective of any choice of solar angle. In our parametrization, the neutrino sector controls the solar angle, whereas the reactor and atmospheric angles are dictated by the charged lepton sector. In the framework of oscillation experiments, cosmological observation and future experiments involving $\beta$-decay and $0\nu\beta\beta$ experiments, all QDN models are tested and a reason to rule out anyone out of the six models is unfounded. A strong preference for $\sin^2\theta_{12}=0.32$ is observed for QDNH-$Type A$ model.