Effect of sterile neutrino on low energy processes in minimal extended seesaw with $\Delta(96)$ symmetry and $\text{TM}_{1}$ mixing

We study the effect of sterile neutrino on some low scale processes in the framework of minimal extended seesaw (MES). MES is the extension of the seesaw mechanism with the addition of sterile neutrino of intermediate mass. The MES model in this work is based on $\Delta(96)\times C_{2}\times C_{3}$ flavor symmetry. The structures of mass matrices in the framework lead to $TM_{1}$ mixing with $\mu \text{-}\tau$ symmetry. The model predicts maximal value of Dirac CP phase. We carry out our analysis to study the new physics contributions from the sterile neutrino to different charged lepton flavor violation (cLFV) processes involving muon and tau leptons as well as neutrinoless double beta decay (0$\nu\beta\beta$). The model predicts normal ordering (NO) of neutrino masses and we perform the numerical analysis considering normal ordering (NO) only. We find that sterile neutrino mass in GeV range can lead to cLFV processes that are within the reach of current and planned experiments. The GeV scale sterile neurtrino in our model is consistent with the current limits on the effective neutrino mass set by $0\nu\beta\beta$ experiments.