Twisted split fermions

The observed flavor structure of the standard model arises naturally in "split fermion" models which localize fermions at different places in an extra dimension. It has, until now, been assumed that the bulk masses for such fermions can be chosen to be flavor diagonal simultaneously at every point in the extra dimension, with all the flavor violation coming from the Yukawa couplings to the Higgs field. We consider the more natural possibility in which the bulk masses cannot be simultaneously diagonalized, that is, that they are twisted in flavor space. We show that, in general, this does not disturb the natural generation of hierarchies in the flavor parameters. Moreover, it is conceivable that all the flavor mixing and CP-violation in the standard model may come only from twisting, with the five-dimensional Yukawa couplings taken to be universal.