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Higgs Mass and Unnatural Supersymmetry

Assuming that supersymmetry exists well above the weak scale, we derive the full one-loop matching conditions between the SM and the supersymmetric theory, allowing for the possibility of an intermediate Split-SUSY scale. We also compute two-loop QCD corrections to the matching condition of the Higgs quartic coupling. These results are used to improve the calculation of the Higgs mass in models with high-scale supersymmetry or split supersymmetry, reducing the theoretical uncertainty. We explore the phenomenology of a mini-split scenario with gaugino masses determined by anomaly mediation. Depending on the value of the higgsino mass, the theory predicts a variety of novel possibilities for the dark-matter particle.