Neutrino mass, mixing and discrete symmetries

Alexei Y Smirnov

doi:10.1088/1742-6596/447/1/012004

Abstract

Status of the discrete symmetry approach to explanation of the lepton masses and mixing is summarized in view of recent experimental results, in particular, establishing relatively large 1-3 mixing. The lepton mixing can originate from breaking of discrete flavor symmetry Gf to different residual symmetries Gℓ and Gv in the charged lepton and neutrino sectors. In this framework the symmetry group condition has been derived which allows to get relations between the lepton mixing elements immediately without explicit model building. The condition has been applied to different residual neutrino symmetries Gv. For generic (mass independent) Gv = Z2 the condition leads to two relations between the mixing parameters and fixes one column of the mixing matrix. In the case of Gv = Z2 × Z2 the condition fixes the mixing matrix completely. The non-generic (mass spectrum dependent) Gv lead to relations which include mixing angles, neutrino masses and Majorana phases. The symmetries Gℓ, Gv, Gf are identified which lead to the experimentally observed values of the mixing angles and allow to predict the CP phase.

Highlights

A possibility to use the discrete flavor symmetries for understanding fermion masses and mixing had been proposed long time ago [1]
Status of the discrete symmetry approach to explanation of the lepton masses and mixing is summarized in view of recent experimental results, in particular, establishing relatively large 1-3 mixing
The lepton mixing can originate from breaking of discrete flavor symmetry Gf to different residual symmetries Gl and Gν in the charged lepton and neutrino sectors

Summary

Introduction

A possibility to use the discrete flavor symmetries for understanding fermion masses and mixing had been proposed long time ago [1]. The TBM can be accidental and whole discrete flavor symmetry approach – phenomenologically irrelevant Further developments along this line were in two directions: (i) introduction of large corrections to TBM to reproduce results of measurements [11], (ii) modification of symmetries in such a way that they are consistent with nonzero 1-3 mixing [12]. With this the symmetry effects become rather hidden In this connection in the framework of residual symmetries (2) a formalism has been developed [13], [14], [15] which allows to obtain consequences of flavor symmetries for mass and mixing without model building.

Masses and mixing: status and implications

Conclusion