Trimaximal Mixing and Extended Magic Symmetry in a Model of Neutrino Mass Matrix

The trimaximal mixing scheme (TM$_2$) results in \textit{``magic"} neutrino mass matrix ($M_\nu$) which is known to accommodate neutrino oscillation data. In this paper, we propose a phenomenological ansatz for $M_\nu$ by extending the magic symmetry that leads to further reduction in the number of free parameters, thereby, increasing the predictability of the model. The neutrino mixing parameters, effective Majorana mass $m_{ee}$ and $CP$ invariants ($J_{CP}, I_1,I_2$) are found to exhibit strong correlations for TM$_2$ mixing paradigm. One of the generic feature of the model is the requirement of non-maximal $\theta_{23}$ for possible $CP$ violation measurable in neutrino oscillation experiments. The observables $m_{ee}$ and sum of neutrino masses ($\sum m_i$) have imperative implications for yet unknown neutrino mass hierarchy. For inverted hierarchy, the lower bound on $m_{ee}>0.02$ eV, predicted by the model, is found to be within the sensitivity reach of the $0\nu\beta\beta$ decay experiments. Also, cosmological bound of $0.12$ eV on $\sum m_i$, at 95\% CL, refutes inverted hierarchy implying TM$_2$ with normal hierarchy as the only viable possibility in the model. We have, also, illustrated a scenario wherein such a construction of the neutrino mass matrix can be realized using $\Delta(54)$ symmetry in the framework of Type-I+II seesaw mechanism.