A Minimal Realization of Radiative Dirac Neutrino Masses via a Non-Invertible Fusion Rule

Abstract

We propose a minimal one-loop radiative framework for Dirac neutrino mass matrix. As a consequence, the Yukawa hierarchies among the SM fermions are alleviated, and radiative type-I seesaw framework is realized. To regulate divergent loop contributions, we introduce an effective cutoff scale $\Lambda \sim 100 \, {\rm TeV}$. By introducing a scalar leptoquark and imposing appropriate assignments of ising fusion rule to the particle content, we successfully realize a minimal construction. Furthermore, the presence of the leptoquark leads to rich phenomenology, including semi-leptonic decays, neutral meson mixing, lepton flavor violations and lepton $g-2$, thereby rendering the model experimentally testable. After formulating each sector of our model, we perform a comprehensive numerical analysis, taking into account all relevant experimental constraints for both normal and inverted hierarchies of neutrino masses. Our analysis reveals characteristic tendencies within the viable parameter space.