Lepton Mixing and Flavor Symmetries

Abstract

In the thesis we have studied how to use discrete groups as a horizontal (flavor) symmetry to account for the observed fermion flavor structures. In particular, one aims to interpret the large mass ratios between generations: mu ≪ mc ≪ mt; md ≪ ms ≪ mb; me ≪ mμ ≪ mτ , and the smallness of the offdiagonal elements of the quark weak mixing matrix, in addition to the tiny neutrino masses and their large mixings as recent data suggest. One of the proposed mixing pattern in literatures was the tri-bimaximal mixing (TBM) since the observed leptonic mixing angles were close to TBM values. We addressed the question ”Is the TBM mixing accidental?”. In other words we need to specify whether this mixing immediately follows from some (broken) symmetry or other principle, or it appears as a result of manystep construction, and fixing various parameters by introduction of additional symmetries and structures. In the case of TBM, the neutrino mass matrix has a special form and there are some relations between mass matrix elements. We can examine TBM by examining the symmetry arises in the mass matrix. Therefore if the data imply very specific mass matrix with small deviations from the TBM form, we can say that TBM is not accidental. We find the opposite: very strong deviations of mν from mTBM and strong violations of the TBM conditions (immediate manifestation of the symmetry) are allowed. This can be considered as an indication that TBM is accidental. We find that large variety of the mass 143 144 Chapter 5: Conclusions matrices with deviations from TBM explain experimental data. Due to strong deviations of mν from mTBM, some alternative approaches can be considered to explain the data. Namely, some other symmetry (which differs from the TBM symmetry) or other principle can be involved. For instance, matrices with texture zeros are allowed which indicates, e.g. U(1) underlying symmetry. Also matrices with different relations between the elements are possible, which testify for yet another class of symmetries. We show that the mass matrix may show no trace of symmetry having random values of elements. However, this corresponds to the quasi-degenerate spectrum which implies another way to explain the data. In some cases the matrix has certain flavor alignment: gradual change of values of matrix elements from mee to mττ . For certain ranges of masses and CP-phases the mass matrix has structure with strong hierarchy between matrix elements: dominant and sub-dominant ones. We find that corrections can change the dominant elements by factors O(1) and be much larger than the sub-dominant elements. This may support the idea of two-component structure of the mass matrix when the dominant block has certain (unbroken) flavor symmetry and appears at the lowest renormalizable level, whereas the sub-dominant structures can be result of symmetry breaking by, e.g., high order operators with flavon fields.