Lepton mixing from the interplay of the alternating group A5 and CP

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 x Z2 in the charged lepton and to Z2 x CP in the neutrino sector. All patterns contain only one free parameter theta 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 theta well. All of them predict trivial Majorana phases, while the Dirac phase delta is maximal for two patterns and trivial for the two remaining ones. If delta is maximal, also the atmospheric mixing angle is fixed to be maximal.