10 A. Lepton spectrum in the ZMA L Y = g$_{5}$v$_{H}$ 2 √ 2 R ∫ R ′ R d z ( R z ) 4 z R ′ { ∑ s =1 , 2 [ ν ′$_{sL}$ ( ν$_{sR}$ + ˜ ν$_{sR}$ ) − ( ν$_{sL}$ + ˜ ν$_{sL}$ ) ν ′ sR ] (20) + s =3 ,α e ′$_{sL}$ ( e$_{sR}$ + ˜ e$_{sR}$ ) − e$_{sL}$ + ˜ e$_{sL}$ e ′$_{sR}$ } + h . c .. L Y = g$_{5}$h ˆ $^{a}$( x ) √ 2 R 1 √ 1 − ( R/R ′ ) 2 ∫ R ′ R d z ( R z ) 4 z R ′ ( ¯ ζ$_{k}$T ˆ a $_{C}$Γ $^{5}$ζ$_{k}$ + ¯ ζ$_{α}$T ˆ a $_{C}$Γ $^{5}$ζ$_{α}$ ) = − ig$_{5}$v$_{H}$ 2 R 1 1 − ( R/R ′ ) 2 R ′ R d z R z 4 z R ′ ¯ ζ$_{kL}$T 4 $_{C}$ζ$_{kR}$ + ¯ ζ$_{αL}$T 4 $_{C}$ζ$_{αR}$ + h . c . , (19) give a suppressed contribution. This so called zero mode approximation (ZMA) is convenient because of the transparent way the flavor structure leading to TBM mixing is realized. We will thus proceed in three steps, first we will compute the light lepton masses and mixing angles in the ZMA. Then, we will include the massive KK modes but still incorporating the localized Majorana masses and the Higgs effects in the mass matrix. Finally, we will take these into account considering the boundary conditions directly in the KK expansion. The Yukawa couplings, being originally gauge couplings, are flavor diagonal and do not mix different 5D multiplets where we have used in the last equality Γ 5 = − iγ $^{5}$, and assumed that the Higgs takes a v.e.v. 〈 h ˆ $^{a}$〉 = v$_{H}$δ ˆ a, $^{4}$. Neglecting R/R ′ ≪ 1 and inserting the expression for T 4 C in Appendix A 2, we get the Yukawa Lagrangian from the bulk In this section we only consider the leptonic zero modes. The localized Majorana masses and the Higgs couplings will be incorporated as mass terms to be diagonalized. The localized Dirac masses, on the other hand, have to be taken into account exactly. Since they mix different multiplets through the boundary conditions, the physical zero modes (the same will happen for massive modes) are split among all multiplets mixed by them. In particular, the LH lepton doublets live in all four multiplets. Note that as we do not include in the expansion the Majorana mass term, which is the only source of flavor violation, different generations do not mix. The properly normalized zero modes satisfying the corresponding