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Decoupling heavy sparticles in hierarchical SUSY scenarios: Two-loop Renormalization Group equations

Two loop renormalization group equations for dimensionless as well as dimensionful parameters are obtained for the low energy theories that result from decoupling heavy scalar particles in Split SUSY and Effective SUSY scenarios, assuming that only a single Higgs field survives at low energy. For the Effective SUSY case two scenarios are considered: first, when the only light third generation scalars are the partners of the left-handed quark doublet and the right-handed top quark --which yields the minimal matter content compatible with naturalness-- and second, when all the scalars of the third generation are light. These beta functions implementing decoupling will be useful to avoid the problems of perturbation theory in the MSSM in a mass-independent scheme such as DR-bar when large hierarchies in the spectrum are present.