Radiative mediation of CP violation via non-invertible selection rules

A

bstract

We propose a novel mechanism in which leptonic CP-violating phases are generated dynamically through the radiative breaking of non-invertible selection rules. In this framework, tree-level mass matrices, initially constrained to be real by a CP-like symmetry within a non-invertible structure, acquire flavor-dependent phases once loop corrections are incorporated. Furthermore, these corrections can also generate mass terms, thereby addressing the mass hierarchy problem. As an illustrative example, we employ the Inverse Seesaw (ISS) model to demonstrate how the Majorana mass of the light sterile neutrino N _L arises via this mechanism while simultaneously realizing CP violation. Then, we perform a numerical analysis to check the model-consistency in current experimental data. Although our analysis is carried out within the ISS framework, the mechanism has broader implications, potentially offering new perspectives on CP-related problems such as the strong CP problem, leptogenesis, and baryogenesis. This work thus establishes a foundation for exploring the dynamical breaking of non-invertible selection rules as a novel origin of CP violation in particle physics.