Leptonic CP Violation Phases, Quark-Lepton Similarity and Seesaw Mechanism

Abstract

We explore generic features of the leptonic CP violation in the framework of the seesaw type I mechanism with similarity of the Dirac lepton and quarks mass matrices $m_D$. For this, we elaborate on the standard parametrization conditions which allow to simultaneously obtain the Dirac and Majorana phases. If the only origin of CP violation is the left-handed (LH) transformation which diagonalizes $m_D$ (similar to quarks), the leptonic CP violation is suppressed and the Dirac phase is close to $\pi$ or to $0$ with $\sin \delta_{CP} \approx (\sin \theta_{13}^q /\sin \theta_{13}) \cos \theta_{23} \sin \delta_q \sim \lambda^2 \sin \delta_q$. Here $\lambda \sim \theta_C$, is the Cabibbo mixing angle, and $\theta_{13}^q$ and $\theta_{13}$ are the 1-3 mixing angles of quarks and leptons respectively. The Majorana phases $\beta_1$ and $\beta_2$ are suppressed as $\lambda^3\sin\delta_q$. For Majorana neutrinos implied by seesaw, the right-handed (RH) transformations are important. We explore the simplest extension inspired by Left-Right (L-R) symmetry with small CKM-type CP violation. In this case, seesaw enhancement of the CP violation occurs due to strong hierarchy of the eigenvalues of $m_D$ leading to $\delta_{CP} \sim 1$. The enhancement is absent under the phase factorization conditions which require certain relations between parameters of the Majorana mass matrix of RH neutrinos.