Neutrino Mass Hierarchy, \(\theta _{23}\) and CP-Violation in a Variant of Magic Majorana Neutrino Mass Matrix

In this work, we consider an extension of the magic symmetry ansatz within the paradigm of the \(\text {TM}_2\) mixing scheme, wherein (2,2) element of the effective low energy neutrino mass matrix \(M_\nu \) is, also, equal to the “magic sum”. The new constraint reduces the number of free parameters making the mass matrix highly predictive with strong correlations and homoscedasticity amongst the physical observables, in particular, neutrino mass hierarchy, atmospheric mixing angle ( \(\theta _{23}\) ) and CP phase \(\delta \) . The cosmological bound on sum of neutrino masses refutes inverted hierarchy of neutrino masses at 95% CL implying \(\text {TM}_2\) with normal hierarchy as the only viable possibility in the model. Also, \(\theta _{23}\) is found to be non-maximal ( \(\theta _{23}\ne 45^o\) ) to accommodate CP-violation observable in neutrino oscillation experiments.