The puzzle of flavor hierarchy in the standard model may be explained by
separating the fermions in extra dimensions. The resulting four dimensional
observables are suppressed by exponentially small overlaps of separated fermion
wave-functions. In order to localize fermions in the extra dimensions, one or
more gauge singlet scalars are introduced. In such “split fermion” models,
several assumptions have commonly been made. One of these assumptions is that
the Higgs vacuum expectation value (VEV) is either uniform throughout the extra
space, or confined to a “brane”. The theoretical motivation for these choices
is not clear. In particular, the Higgs VEV cannot be uniform since it couples
to the localizing scalars. We study the assumptions that are needed in order
to generate such configurations, and provide an underlying mechanism for
generating them. Another assumption that has always been made in the split
fermion models is that the fermion fields couple diagonally to the localizing
scalars. In that case flavor mixing occur only due to the couplings of the fermions
to the standard model Higgs field. We relax this simplifying assumption and
allow order one non diagonal couplings to the localizer. We find that within
this scenario of “twisted split fermions”, the hierarchical flavor structure of
the Standard Model can be recovered in the effective four dimensional theory.
Moreover, in this case the standard model flavor structure can arise from the
fermion coupling to the localizing scalars even when the five dimensional Yukawa
couplings to the Higgs are universal.
