Neutrino Phenomenology and Leptogenesis from Non-Invertible Fusion Symmetry

We constructed a minimal type-I seesaw model with two right-handed neutrinos, in which the flavor structure is determined by a non-invertible \(\mathbb{Z}_2\)-gauged \(\mathbb{Z}_5\) fusion symmetry~($\mathbb{Z}^{IN}_5$). The framework, incorporating a second Higgs doublet and an auxiliary \(\mathbb{Z}_2\) parity, yields predictive neutrino mass textures without introducing flavon fields. A fit to neutrino data selects the inverted mass ordering with \(m_3=0\) and predicts a nearly maximal Dirac CP phase, together with a characteristic prediction for the effective Majorana mass governing neutrinoless double-beta decay($0νββ$). We further investigate thermal leptogenesis and show that the framework can reproduce the observed baryon asymmetry of the Universe. Our results establish a connection between predictive neutrino phenomenology and leptogenesis within a minimal framework based on non-invertible fusion symmetry.