Deviation from tri-bimaximal mixing and large reactor mixing angle

Ahmed Rashed

doi:10.1016/j.nuclphysb.2013.05.022

Abstract

Recent observations for a non-zero θ13 have come from various experiments. We study a model of lepton mixing with a 2–3 flavor symmetry to accommodate the sizable θ13 measurement. In this work, we derive deviations from the tri-bimaximal (TBM) pattern arising from breaking the flavor symmetry in the neutrino sector, while the charged leptons contribution has been discussed in a previous work. Contributions from both sectors towards accommodating the non-zero θ13 measurement are presented.

Highlights

Neutrino oscillations can be parametrized in terms of three mixing angles θ12, θ13, θ23 and Dirac (δ) and Majorana (ζ1, ζ2) CP violating phases c12c13 s12c13 s13e−iδ (1)s12s23 − c12s13c23eiδ −c12s23 − s12s13c23eiδ c13c23 where cij ≡ cos θij, sij ≡ sin θij, and Pν ≡ {1, eiζ1, eiζ2} is a diagonal phase matrix, which is physically relevant if neutrinos are Majorana particles
We extended our model in Ref. [32] to treat the leptonic mixing in the flavor symmetric limit with the tri-bimaximal pattern
The charged lepton sector was considered in Ref. [32] in a basis where the charged lepton Yukawa matrix is nondiagonal with a 2−3 symmetric structure except for one breaking by the muon mass

Summary

Introduction

Neutrino oscillations can be parametrized in terms of three mixing angles θ12, θ13, θ23 and Dirac (δ) and Majorana (ζ1, ζ2) CP violating phases. The leptonic mixing matrix is obtained from the contributions of the diagonalization of the charged lepton and neutrino mass matrices. Many models have been introduced to study the leptonic mixing in the basis where the charged lepton mass matrix is diagonal. Our approach considers both contributions from the charged lepton and neutrino sector to obtain the leading order leptonic mixing as well as deviations from it. If one starts with a 2 − 3 symmetric mass matrix for the charged lepton sector and requires it to be diagonalized by unitary matrices of pure numbers one recovers the decoupled 2 − 3 symmetry; decoupling of the first generation from the second and third generations.

The TBM matrix from flavor symmetry

Symmetry Breaking

Numerical results

Conclusion