Rephasing invariants of CP violation for heavy and light Majorana neutrinos

TL;DR

This paper develops rephasing invariants of CP violation in the seesaw mechanism, linking heavy and light Majorana neutrinos, and explores their implications for CP asymmetries and lepton-violating processes.

Contribution

It introduces explicit Majorana- and Dirac-type CP invariants for the seesaw model using a comprehensive parametrization, enhancing understanding of CP violation in neutrino physics.

Findings

Explicit formulas for CP invariants of $R$ and $U$ matrices.

Analysis of invariants' roles in neutrino decay asymmetries.

Potential implications for lepton-flavor- and lepton-number-violating processes.

Abstract

In the canonical seesaw mechanism, the strengths of charged-current interactions for light and heavy Majorana neutrinos are described respectively by the $3\times 3$ matrices $U$ and $R$ that are correlated with each other via the exact seesaw relation and the unitarity condition. We write out the Majorana-type invariants of CP violation of $R$ and $U$, which are insensitive to redefining the phases of three charged-lepton fields; and the Dirac-type invariants of CP violation of $R$ and $U$ that are insensitive to the rephasing of both the charged-lepton fields and the neutrino fields. Such invariants are explicitly calculated with the help of a full Euler-like block parametrization of the seesaw flavor structure containing nine active-sterile flavor mixing angles and six independent CP-violating phases, and their corresponding roles in the CP-violating asymmetries of three heavy Majorana neutrino decays and in the flavor oscillations of three light Majorana neutrinos are briefly discussed. We point out that similar rephasing invariants arising from the interplay between $R$ and $U$ may also manifest themselves in a variety of lepton-flavor-violating and lepton-number-violating processes.