Top-bottom mass hierarchy, $s-\mu$ puzzle and gauge coupling unification with split multiplets

A supersymmetric 5D SU(5) grand unification is considered. The SU(5) is broken down to $G_{SM}=SU(3)\times SU(2)\times U(1)$ by the $Z_2\times Z_2'$ assignment of the bulk field(s). The matter fields are located at the fixed point(s). In the bulk, a Higgs multiplet $\bar 5_H$(containing the bottom doublet $H_1$) and the SU(5) gauge multiplet are located. At one fixed point, $H_2$(the top doublet) and the standard model matter multiplets are presented. Because of the difference of the locations of $H_1$ and $H_2$, one can obtain a hierarchy between top and bottom Yukawa couplings. We also present a possibility to understand the $s-\mu$ mass puzzle in this framework of the split multiplet.