normalization factor. The zero mode wave functions are, \^[(0)]{}(z) = [N]{}\_0 ( z )\^[1/2- c\_ ]{}  . These wavefunctions assume the right-handed zero mode is the one allowed by the boundary conditions; the left-handed case is given by $c \rightarrow -c$. The zero mode is exponentially peaked toward the UV boundary for $c < -1/2$ and toward the IR for $c > -1/2$. To avoid confusion, we adopt a notation where $c$’s explicitly refer to right-chiral fields, so the left-chiral fermions should be understood to actually have $-c$ as their mass parameter.

Assuming $\mathcal{O}(1)$ 5D Yukawa couplings, the hierarchy in the effective 4D Yukawa couplings can be motivated by the exponential suppression of the wave functions at the IR boundary for order one differences in $c$. In particular, one cannot allow strong suppression of the top quark wave functions on the IR boundary, because to reproduce the observed top mass one would have to adjust the 5d Yukawa coupling to be too strong to have a perturbative description. There is further motivation from precision electroweak data [@Agashe:2003zs; @Davoudiasl:2002ua], which prefers the light fermion mass parameters to be close to $-1/2$ (including the left-handed top, as it comes along with the 