Mass Hierarchies from MSSM Orientifold Compactifications

TL;DR

This work investigates MSSM-like quivers from orientifold compactifications to reproduce fermion mass hierarchies via two mechanisms: higher-order couplings with SM singlet vevs and non-perturbative D-instanton effects, including factorizable Yukawa matrices. Extending prior bottom-up analyses to four- and five-stack configurations, the authors find a unique four-stack quiver with a semi-realistic texture but proton-decay challenges, and several five-stack quivers—including one that yields three mass scales for up-quarks, down-quarks, and electrons while avoiding dangerous operators. A parallel set of studies reveals setups with R-parity violation from $U(1)$ instantons, underscoring the delicate balance between achieving realistic hierarchies and maintaining phenomenological viability. The results identify a viable five-stack quiver (the second setup) that realizes realistic Yukawa textures, three mass scales, neutrino and Higgs scale considerations, and suppressed proton decay, offering a concrete direction for further string phenomenology.

Abstract

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 arXiv:0905.3379, 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.