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.

Figure 1

The two solid blue lines in the upper figure are the eigenvalues of the mass matrix $\tilde{M}(z)$ given in Eq. (20). The localization region defined in the previous section lies between the two vertical dotted lines. The exact solution to the norm of the wave functions is in the lower figure in solid lines while the adiabatic approximation is in thick dashed green curves. Note that the departure of the adiabatic solution from the exact one occurs where the two eigenvalues approach one another.