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 mD. 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 mD (similar to quarks), the leptonic CP violation is suppressed and the Dirac phase is close to π or to 0 with sinδCP≈(sinθ13q/sinθ13)cosθ23sinδq∼λ2sinδq. Here λ∼θC, is the Cabibbo mixing angle, and θ13q and θ13 are the 1–3 mixing angles of quarks and leptons respectively. The Majorana phases β1 and β2 are suppressed as λ3sinδq. 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 mD leading to δCP∼1. The enhancement is absent under the phase factorization conditions which require certain relations between parameters of the Majorana mass matrix of RH neutrinos.
Highlights
Establishing the leptonic CP violation is one of the major experimental frontiers in neutrino physics
V we explore a specific case of CP violation in the RH sector, which corresponds approximately to a L-R symmetry of the theory
The main assumption in this paper is that the Dirac mass matrix of neutrinos has similar structure to that of quarks: mD ∼ mu or ∼ md, as can be motivated by the Grand unification or common flavor symmetry with the same charge assignments
Summary
Establishing the leptonic CP violation is one of the major experimental frontiers in neutrino physics. The ansatz (1) can be naturally realized in the seesaw type I mechanism [21] which is the simplest and the most natural explanation of smallness of neutrino masses as well as large lepton mixing [22]. It is simplest because only RH neutrinos are added to the theory. An observation of (large) leptonic CP violation in oscillation experiments and/or neutrinoless double beta decay would be a signature that there is a new source of CP violation, beyond the leptonic analogue of KM-phase and coming from the RH sector, or that neutrino masses do not arise from a canonical seesaw.
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