Tri-Resonant Leptogenesis in a Non-Holomorphic Modular A$_4$ Scotogenic Model

We investigate low-scale baryogenesis \textit{via} tri-resonant leptogenesis within the scotogenic model with a scalar dark matter embedded in non-holomorphic modular $A_4$ symmetry framework. The model naturally accommodates three nearly degenerate right-handed (RH) neutrinos when they are assigned to the triplet representation of $A_4$. The near degeneracy originates from treating the symmetric contribution to the Majorana mass matrix, arising from the $\mathbf{3}\otimes\mathbf{3}$ decomposition of $A_4$, as a small perturbation to the dominant singlet contribution. Generalized CP (gCP) symmetry is imposed in the model, rendering the complex modulus $\tau$ as the sole source of CP violation. In particular, for the inverted hierarchy (IH), the predicted $3\sigma$ range of $\theta_{23}$ lies in the lower octant close to maximal value while CP phase $\delta_{\mathrm{CP}}$ and the Majorana phase $\alpha_{21}$ are predicted to lie close to $0^\circ$ or $360^\circ$. Also, in this case, predicted values of $m_{ee}$ and $\sum_i m_i$ can be tested and constrained by future neutrinoless double beta decay $(0\nu\beta\beta)$ experiments, as well as by cosmological observations, particularly DESI+BAO and Planck data. In fact DESI+BAO disallows IH in the model. We further show that successful baryogenesis can be achieved for both normal hierarchy (NH) and inverted hierarchy (IH) of light neutrino masses with RH neutrino masses as low as $537~\mathrm{GeV}$ rendering this scenario experimentally testable. For NH, RH neutrino mass degeneracy of $\mathcal{O}(10^{-7}\!-\!10^{-6})$ is required, while for IH a stronger degeneracy of $\mathcal{O}(10^{-8})$ is needed. Remarkably, in the NH case, successful baryogenesis can occur even in the deep washout regime with decay parameters of $\mathcal{O}(10^{5})$ owing to the tri-resonant enhancement of the CP asymmetry and the inclusion of flavor effects.