Abstract: |
I will discuss a scenario with three Majorana neutrinos in which a discrete, finite flavor group Gf is combined with a generalized CP transformation. I will show the conditions necessary in order to consistently define such a setup. If the residual symmetries are Ge, being a subgroup of Gf, in the charged lepton sector and Gnu=Z2 x CP in the neutrino sector, lepton mixing angles and CP phases(Dirac as well as Majorana), in general, only depend on one single parameter theta which can take values between 0 and pi. I will give several examples for the flavor group Gf=S4, the group of permutations of four distinct objects. I will also show how such a scenario can be implemented in a supersymmetric model for leptons with the flavor symmetry S4 x Z3. The parameter theta is directly related to the reactor mixing angle and it is naturally of the correct size. The atmospheric mixing angle and the Dirac phase are both maximal, while the two Majorana phases are trivial. The solar mixing angle is constrained by sin^2 theta_{12} >= 1/3. Since neutrino masses depend effectively only on two real parameters at leading order, they have to be normally ordered and the absolute neutrino mass scale and the sum of neutrino masses are predicted. The hierarchy among the charged lepton masses is correctly reproduced without tuning. The vacuum alignment and subleading corrections are studied in detail and the latter are in general small. |