Exploring spontaneous CP violation in an axion model with seesaw mechanism

We investigate an expansion of the Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model aiming at realizing spontaneous CP violation. By introducing singlet heavy Majorana neutrinos and an additional new singlet scalar, we formulate the Yukawa Lagrangian and scalar potential for the extended model, highlighting their pivotal role in inducing CP violation. This study reveals that CP can spontaneously be broken at the 1-loop level, facilitated by the generation of the quartic couplings in the scalar potential which are imperative for inducing spontaneous CP violation. We discuss the implications of the model on the new axion. By presenting the leptonic Yukawa Lagrangian and the structure of the Dirac neutrino mass matrix within the minimal seesaw framework, we study the interply between the CP-violating phase arising from the extended DFSZ model and the phases of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix. A brief numerical analysis is conducted to illustrate the compatibility of the extended DFSZ model with observed neutrino oscillation parameters, providing insights into the origin of leptonic CP violation.