Resonant leptogenesis in inverse see-saw framework with modular $S_4$ symmetry

We introduce a lepton mass generation and flavor mixing model, realized through a (2,3) inverse seesaw structure based on modular $S_4$ symmetry. The model employs modular forms to construct the lepton Yukawa couplings, significantly simplifies the construction by reducing redundant parameters. A detailed numerical analysis demonstrates consistency with current neutrino oscillation data, yielding specific outputs for the mixing angles and CP-violating phases. The Dirac CP phase is localized near $\delta_{\rm CP} \sim 350^\circ$. It further predicts an effective Majorana mass $|m_{ee}| \sim \mathcal{O}(10^{-3}) \,\text{eV}$, within the scope of upcoming experiments on neutrinoless double beta decay such as nEXO and AMoRE-II. The model also remains consistent with current bounds on charged lepton flavor violating processes from MEG and BaBar. We further explore resonant leptogenesis enabled by quasi-degenerate heavy neutrino states, and show that the observed baryon asymmetry of the universe can be successfully generated in this scenario. The combined treatment of low-energy observables and high-scale baryogenesis demonstrates the predictivity and testability of the modular $S_4$-based ISS(2,3) framework.