Alternative schemes of predicting lepton mixing parameters from discrete flavor and CP symmetry

We suggest two alternative schemes to predict lepton mixing angles as well as CP violating phases from a discrete flavor symmetry group combined with CP symmetry. In the first scenario, the flavor and CP symmetry is broken to the residual groups of the structure Z(2) x CP in the neutrino and charged lepton sectors. The resulting lepton mixing matrix depends on two free parameters theta(nu) and theta(l). This type of breaking pattern is extended to the quark sector. In the second scenario, an Abelian subgroup of the flavor group is preserved by the charged lepton mass matrix and the neutrino mass matrix is invariant under a single remnant CP transformation, all lepton mixing parameters are determined in terms of three free parameters. theta(1,2,3). We derive the most general criterion to determine whether two distinct residual symmetries lead to the same mixing pattern if the redefinition of the free parameters. theta(nu,l) and. theta(1,2,3) is taken into account. We have studied the lepton mixing patterns arising from the flavor group S-4 and CP symmetry which are subsequently broken to all of the possible residual symmetries discussed in this work.