$T_7$ Flavor Symmetry gym: The Key to Unlocking the Neutrino Mass Puzzle

Abstract: Recent research has indicated that the Standard Model (SM), while historically highly effective, is found to be insufficient due to its prediction of zero mass for neutrinos. With the exception of a few, the majority of the parameters related to neutrinos have been determined by neutrino oscillation experiments with excellent precision. Experiments on neutrino oscillation and neutrino mixing have shown that neutrinos are massive. To fill in gaps, discrete symmetries are becoming more common alongside continuous symmetries while describing the observed pattern of neutrino mixing. Here, we present a $T_7$ flavor symmetry to explain the masses of charged leptons and neutrinos. The light neutrino mass matrix is derived using seesaw mechanism of type I, which involves the Dirac neutrino mass matrix as well as the right-handed neutrino mass matrix. We estimate the Pontecorvo-Maki-Nakagawa-Sakata matrix ($U_{PMNS}$), three mixing angles, $\theta_{12}$, $\theta_{23}$ and $\theta_{13}$, which are strongly correlated with the recent experimental results. The extent of $CP$ violation in neutrino oscillations is obtained by calculating Jarskog invariant $(J_{CP})$ on the behalf of $U_{PMNS}$. We also find the masses of three neutrinos and Effective Majorana neutrino mass parameter $\langle m_{ee} \rangle$ which is $1.0960$ $meV$ and $10.9217$ $meV$ for normal and inverted hierarchy, respectively.