On Lepton Flavor Violation and Dark Matter in Scotogenic model with Trimaximal Mixing

We examine the Scotogenic model employing the TM$_2$ mixing matrix, $U_{\text{TM}_2}$, for neutrinos and parameterize the Yukawa coupling matrix $y$ based on the diagonalization condition for the neutrino mass matrix, $m_{\nu}$. Our investigation centers on analyzing the relic density of cold dark matter ($\Omega h^2$) and possible lepton flavor violation (LFV) in the model. In particular, we study coannihilation dynamics and LFV, in the model, considering various coannihilation scenarios including non-zero mass splitting between lightest sterile neutrinos. While analyzing, we have taken into consideration respective experimental constraints on $\Omega h^2$ and LFV alongside neutrino oscillation data. Our study reveals that in both normal and inverted hierarchy of neutrino masses, splitting between masses of $N_1$ and $N_2$ can be up to $\approx 15\%$ for the model to be in consonance with the above constraints. In the second part, we have extended the analysis incorporating extended magic symmetry in $m_\nu$ enabling us to completely determine Yukawa coupling matrix ($y$). We observe a notable exclusion of the effective Majorana mass $|m_{ee}|$ parameter space by cosmological bound on sum of neutrino masses, particularly in the normal hierarchy while inverted hierarchy scenario is excluded due to constraints coming from extended magic symmetry. These findings shed light on the interplay among the Scotogenic model, TM$_2$ mixing, and extended magic symmetry, offering insights into the permitted parameter space and hierarchy exclusion.