U(1)' solution to the mu-problem and the proton decay problem in supersymmetry without R-parity

Understand

The Minimal Supersymmetric Standard Model (MSSM) is plagued by two major fine-tuning problems: the mu-problem and the proton decay problem.

• We present a simultaneous solution to both problems within the framework of a U(1)'-extended MSSM (UMSSM), without requiring R-parity conservation.
• We identify several classes of phenomenologically viable models and provide specific examples of U(1)' charge assignments.
• Our models generically contain either lepton number violating or baryon number violating renormalizable interactions, whose coexistence is nevertheless automatically forbidden by the new U(1)' gauge symmetry.