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 ${\delta }_{\mathrm{C}\mathrm{P}}\sim {350}^{\circ }$. It further predicts an effective Majorana mass $\mathrm{\mid }{m}_{ee}\mathrm{\mid }\sim \mathcal{O}({10}^{-3})\text{eV}$, 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.