Predictions from scoto-seesaw with $A_4$ modular symmetry

Abstract: This paper's novelty lies in introducing a hybrid scoto-seesaw model rooted in $A_4$ discrete modular symmetry leading to several interesting phenomenological implications. The scoto-seesaw framework leads to generation of one mass square difference $( \Delta m^2_{\rm atm}$) using the type-I seesaw mechanism at the tree level. Additionally, the scotogenic contribution is vital in obtaining the other mass square difference ($\Delta m^2 {\rm sol}$) at the loop level, thus providing a clear interpretation of the two different mass square differences. The non-trivial transformation of Yukawa couplings under the $A_4$ modular symmetry helps to explore neutrino phenomenology with a specific flavor structure of the mass matrix. In addition to predictions for neutrino mass ordering, mixing angles and CP phases, this setup leads to precise predictions for $\sum m_i$ as well as $|m{ee}|$. In particular, the model predicts $\sum m_i \in (0.073,0.097)$ eV and $\left| m_{ee}\right| \in (3.15,6.66)\times 10^{-3} $ eV range; within reach of upcoming experiments. Furthermore, our model is also promising for addressing lepton flavor violations, i.e., $\ell_\alpha \to \ell_\beta \gamma$, $\ell_\alpha \to 3\ell_\beta$ and $\mu - e $ conversion rates while staying within the realm of current experimental limits.