Abstract
Abstract Assuming three generations of Majorana neutrinos, we study the different mixing patterns that arise from the non-trivial breaking of the flavor group A 5 and CP to the residual symmetries Z 3, Z 5 or Z 2 × Z 2 in the charged lepton and to Z 2 × CP in the neutrino sector. All patterns contain only one free parameter θ and thus mixing angles as well as the Dirac and the two Majorana phases are strongly correlated. We perform an analytical and a numerical study of all possible mixing patterns. It turns out that only four patterns can describe the experimentally measured values of the mixing angles for a particular choice of θ well. All of them predict trivial Majorana phases, while the Dirac phase δ is maximal for two patterns and trivial for the two remaining ones. If δ is maximal, also the atmospheric mixing angle is fixed to be maximal.
Highlights
The charged lepton and neutrino sectors, respectively
Assuming three generations of Majorana neutrinos, we study the different mixing patterns that arise from the non-trivial breaking of the flavor group A5 and CP to the residual symmetries Z3, Z5 or Z2 × Z2 in the charged lepton and to Z2 × CP in the neutrino sector
We have discussed a scenario for three Majorana neutrinos with the flavor group A5 and a CP symmetry
Summary
We briefly recapitulate the essential ingredients of the approach [14] and summarize the necessary information on the group A5. We list the candidates of generators of residual flavor symmetries in the charged lepton and neutrino sectors as well as the CP transformations. Since we focus on the case in which the generations of LH leptons are assigned to an irreducible three-dimensional representation 3 of the flavor group, the CP transformation X as well as the elements of the flavor symmetry are represented by (unitary, complex) three-by-three matrices in the following. We mention that it can happen that an accidental CP symmetry Y , common to the charged lepton and the neutrino sectors, exists that leads to trivial CP phases This can be checked by searching for a transformation Y that fulfills the following constraints. For details see [14]
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