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.

arXiv comment30 pages. v3(typos fixed, matches version published in Nucl. Phys. B)

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