Connecting flavor and baryon asymmetry via leptogenesis in effective Froggatt-Nielsen theory

We investigate the hierarchical flavor structure of the Standard Model in a Froggatt-Nielsen (FN) framework, where the spontaneous breaking of a U(1)_{\rm FN} symmetry by a complex flavon field generates fermion masses and mixing patterns through higher-dimensional operators. Extending the setup with three right-handed neutrinos (RHNs), light neutrino masses arise via the Type-I seesaw mechanism. Allowing complex FN coefficients enables a consistent description of the CKM and PMNS matrices while inducing CP-violating signatures in meson decays. Building on our previous work, where the lightest RHN acts as a viable dark matter (DM) candidate produced through freeze-in or freeze-out mechanisms, we investigate the origin of the baryon asymmetry of the Universe. The heavier RHNs generate a lepton asymmetry through out-of-equilibrium decays, including both Standard Model channels and additional flavon-induced processes in which the flavon appears as an intermediate or final-state particle. We compute the corresponding one-loop CP asymmetries and incorporate these effects in the Boltzmann equations. We show that although freeze-in and freeze-out DM production occur in two qualitatively distinct regions of the FN symmetry-breaking scale v_\phi, successful thermal leptogenesis can be achieved in both regimes. In the large-v_\phi (freeze-in-compatible) region the results approach the standard leptogenesis limit, while in the freeze-out-compatible region the lower value of v_\phi implies lighter RHNs, requiring resonant enhancement. This tightly constrained framework, in which v_\phi simultaneously controls RHN masses and the interaction strengths of the flavon and DM sectors, provides a predictive and unified description of flavor hierarchies, neutrino masses, CP violation, dark matter, and baryogenesis within a single effective theory.