Renormalization Group Invariants in the MSSM and Its Extensions

We derive one-loop renormalization group (RG) invariant observables and analyze their phenomenological implications in the MSSM and its μ problem solving extensions, U(1) model and NMSSM. We show that there exist several RG invariants in the gauge, Yukawa and soft-breaking sectors of each model. In general, RG invariants are highly useful for projecting experimental data to messenger scale, for revealing correlations among the model parameters, and for probing the mechanism that breaks supersymmetry. The Yukawa couplings and trilinear soft terms in U(1) model and NMSSM do not form RG invariants though there exist approximate invariants in low tan β domain. In the NMSSM, there are no invariants that contain the Higgs masssquareds. We provide a comparative analysis of RG invariants in all three models and analyze their model-building and phenomenological implications by a number of case studies.