Mass hierarchies from MSSM orientifold compactifications

We investigate phenomenologically viable four-and five-stack MSSM D-brane quivers which exhibit realistic fermion mass hierarchies. In our analysis, the mass hierarchies arise either from higher order terms containing the VEV's of SM singlets or from D-instanton effects, where the latter utilizes either family splitting or a factorizable Yukawa matrix. Extending the systematic bottom-up analysis of [1], we present the only four-stack quiver with a semi-realistic Yukawa texture. Investigation of five-stack MSSM models reveals many more quivers with analogous Yukawa textures, as well as a few examples which exhibit three different mass scales for the up-quarks, down-quarks, and electrons. Potential problems in this class of quivers are the presence of U(1) instantons, which might lead to undesired effects, such as R-parity violating couplings, and the presence of dimension 5 operators that could lead to rapid proton decay. We present a five-stack setup which overcomes all of these problems and exhibits three different mass scales for the up-quarks, down-quarks and electrons.