Common origin of $θ_{13}$ and dark matter within the flavor symmetric scoto-seesaw framework

Abstract: To understand the observed pattern of neutrino masses and mixing as well as to account for the dark matter we propose a hybrid scoto-seesaw model based on the $A_4$ discrete flavor symmetry. In this setup, including at least two heavy right-handed neutrinos is essential to employ the discrete flavor symmetry that mimics once popular tribimaximal neutrino mixing at the leading order via type-I seesaw. The scotogenic contribution then acts as a critical deviation to reproduce the observed value of the reactor mixing angle $\theta_{13}$ (within the trimaximal mixing scheme) and to accommodate potential dark matter candidates, pointing towards a common origin of $\theta_{13}$ and dark matter. The model predicts the atmospheric angle to be in the upper octant, excludes some regions on the Dirac CP phase, and restricts the Majorana phases too. Further, normal and inverted mass hierarchies can be distinguished for specific values of the relative phases associated with the complex light neutrino mass matrix. Owing to the considered flavor symmetry, contributions coming from the scotogenic mechanism towards the lepton flavor violating decays such as $\mu \rightarrow e \gamma$, $\tau \rightarrow e \gamma$ vanish, and a lower limit on the second right-handed neutrino mass can be obtained. Prediction for the effective mass parameter appearing in the neutrinoless double beta decay falls within the sensitivity of future experiments such as LEGEND-1k and nEXO.