Ahmed Rashed (University of Mississippi)

The most common method of studying neutrino (lepton) mixing is the leading order mixing matrix method. We assume an approximated values for the mixing angles to construct the leading order term of the mixing matrix. This matrix describes the neutrino mixing in the limit of such a flavor symmetry. Thereafter, we present such a way to introduce deviations from the symmetric case in order to obtain the realistic mixing angles. From the theoretical point of view, there are three types of well motivated neutrino mixing patterns: tri-bimaximal mixing pattern (TB), bimaximal mixing pattern (BM), and democratic mixing pattern (DC), which may

arise from some discrete flavor symmetries, such as A4 and mu-tau symmetry, or some very special structures of neutrino mass matrices. Large number of flavor symmetries have been introduced in the literatures. After choosing a symmetry group, one needs to know the irreducible representations and their well-defined multiplication rules. By identifying particles with the representations and demanding that the total Lagrangian is a unique under the chosen symmetry group, the Yukawa couplings and hence the mixing matrices are constrained. However, even after choosing a symmetry group, there remains considerable freedom regarding the identification of the particle content with the irreducible representations of the group, the type and number of new particles introduced, and the way in which neutrino mass is generated.

We need strong constraints to pin down a single symmetry group or at least to minimize the possible number of flavor symmetries that can describe the neutrino mixing. The recent indications for non-zero value of the third mixing angle theta_13 has opened the door for new generations of experiments to look up CP violation into the neutrino mixing. The question then arises ” how can these models be distinguished from one another? could we investigate the sizable measurements of theta_13 and the future measurements of the CP violating phase to put strong constraints on the possible symmetries that can describe the neutrino mixing? This, in turn, should reduce the large number of possible symmetries that can describe the neutrino mixing.”