Quark and Leptonic Mixing Patterns from the Breakdown of a Common Discrete Flavor Symmetry

Assuming the Majorana nature of neutrinos, we recently performed a scan of leptonic mixing patterns derived from finite discrete groups of order less than 1536. Here we show that the 3 groups identified there as giving predictions close to experiment, also contain another class of abelian subgroups that predict an interesting leading order quark mixing pattern where only the Cabibbo angle is generated at leading order. We further broaden our study by assuming that neutrinos are Dirac particles and find 4 groups of order up to 200 that can predict acceptable quark and leptonic mixing angles. Since large flavor groups allow for a multitude of leading order mixing patterns, we define a measure that is suitable to compare the predictivity of a given flavor group taking this fact into account. We give the result of this measure for a wide range of discrete flavor groups and identify the group (Z_18 \times Z_6) \rtimes S_3 as being most predictive in the sense of this measure. We further discuss alternative measures and their implications.