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Flavor Symmetry Based MSSM (sMSSM): Theoretical Models and Phenomenological Analysis

We present a class of supersymmetric models in which symmetry considerations alone dictate the form of the soft SUSY breaking Lagrangian. We develop a class of minimal models, denoted as sMSSM -- for flavor symmetry-based minimal supersymmetric standard model, which respect a grand unified symmetry such as SO(10) and a non-Abelian flavor symmetry H which suppresses SUSY-induced flavor violation. Explicit examples are constructed with the flavor symmetry being gauged SU(2)_H and SO(3)_H with the three families transforming as 2 + 1 and 3 representations respectively. A simple solution is found in the case of SU(2)_H for suppressing the flavor violating D--terms based on an exchange symmetry. Explicit models based on SO(3)_H without the D--term problem are developed. In addition, models based on discrete non-Abelian flavor groups are presented which are automatically free from D--term issues. The permutation group S_3 with a 2 + 1 family assignment, as well as the tetrahedral group A_4 with a 3 assignment are studied. In all cases, a simple solution to the SUSY CP problem is found, based on spontaneous CP violation leading to a complex quark mixing matrix. We develop the phenomenology of the resulting sMSSM, which is controlled by seven soft SUSY breaking parameters for both the 2 + 1 assignment and the 3 assignment of fermion families. These models are special cases of the phenomenological MSSM (pMSSM), but with symmetry restrictions. We discuss the parameter space of sMSSM compatible with LHC searches, B physics constraints and dark matter relic abundance. Fine-tuning in these models is relatively mild, since all SUSY particles can have masses below about 3 TeV.