$A_{5}$ symmetry and deviation from Golden Ratio mixing with charged lepton flavor violation

A neutrino mass model that can satisfy the exact golden ratio mixing is constructed using $A_{5}$ discrete symmetry group. The deviation from the golden ratio mixing is studied by considering the contribution from the charged lepton sector in a linear seesaw framework. A definite pattern of charged lepton mass matrix predicted by the model controls the leptonic mixing angles. By taking the observed $\theta_{13}$ as the input value, we can obtain the values of all the mixing angles and Dirac CP-violating phase within the current experimental bounds. The model predicts that only the normal neutrino mass ordering is consistent with the current oscillation data. We also study the two body charged lepton flavor violation (cLFV) processes such as $\mu \rightarrow e +\gamma$, $\tau \rightarrow e +\gamma$ and $\tau \rightarrow \mu+ \gamma$ and neutrinoless double beta decay parameter $m_{\beta \beta}$. The present neutrino mass model can explain the current and future sensitivity of $\mu \rightarrow e +\gamma$, $\tau \rightarrow e+ \gamma$ processes and the present sensitivity of neutrinoless double beta decay parameter when the masses of quasi-Dirac neutrinos are in the TeV range. On the other hand, the model cannot reproduce the present sensitivity of $\tau \rightarrow \mu+ \gamma$ but can explain the future sensitivity and the present sensitivity of neutrinoless double beta decay parameter simultaneously when the masses of the quasi-Dirac neutrinos are in the TeV range.