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 $π$ or to $0$ with $\sin δ_{CP} \approx (\sin θ_{13}^q /\sin θ_{13}) \cos θ_{23} \sin δ_q \sim λ^2 \sin δ_q$. Here $λ\sim θ_C$, is the Cabibbo mixing angle, and $θ_{13}^q$ and $θ_{13}$ are the 1-3 mixing angles of quarks and leptons respectively. The Majorana phases $β_1$ and $β_2$ are suppressed as $λ^3\sinδ_q$. 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 $δ_{CP} \sim 1$. The enhancement is absent under the phase factorization conditions which require certain relations between parameters of the Majorana mass matrix of RH neutrinos.