# CP Properties of Leptons in Mirror Mechanism

## TL;DR

This paper explores how the mirror mechanism can explain lepton mass hierarchies and mixing matrices, emphasizing CP properties and the Dirac nature of neutrinos, leading to specific predictions about CP violation.

## Contribution

It demonstrates that the mirror mechanism reproduces lepton mixing properties and CP characteristics, assuming neutrinos are Dirac particles with an inverse spectrum.

## Key findings

- Reproduces CKM and PMNS matrix hierarchies
- Predicts small  neutrino mixing angle and CP violation
- Suggests no Majorana phases in the PMNS matrix

## Abstract

Formation of quark and lepton mass matrices through intermediate states of heavy mirror fermions is capable of reproducing main qualitative properties of weak mixing matrices (CKM and PMNS matrices). The reproduction includes the hierarchy of CKM matrix elements, a general form of the PMNS matrix, involving the smallness of the neutrino mixing angle \theta_{13}, and leads to very small neutrino masses. For leptons, these properties appear only for the Dirac nature of SM neutrino and its inverse spectrum. In such a lepton system, not only do spontaneous mirror symmetry violation and the observed mass hierarchy of charged leptons (e,\mu,\tau) govern the structure of the PMNS matrix but also permit assessment of its allowed complexity, that is, the CP properties of leptons. The PMNS matrix then contains no Majorana phases and its Dirac phase \delta_{CP} corresponds to |\sin\delta_{CP}|, which is significantly smaller than unity.

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Source: https://tomesphere.com/paper/1812.02403