Stop on Top: SUSY Parameter Regions, Fine-Tuning Constraints

We analyze minimal supersymmetric models in order to determine in what parameter regions with what amount of fine-tuning they are capable of accomodating the LHC-allowed top-stop degeneracy window. The stops must be light enough to enable Higgs naturalness yet heavy enough to induce a 125 GeV Higgs boson mass. These two constraints imply a large mass splitting. By an elaborate scan of the parameter space, we show that stop-on-top scenario requires at least Delta_CMSSM ~ O(10^4) fine-tuning in the CMSSM. By relaxing the CMSSM parameter space with nonuniversal Higgs masses, we find that Delta_NUHM1 ~ O(10^4). The CMSSM with gravitino LSP works slightly better than the NUHM1 model. Compared to all these, the CMSSM with mu<0 and nonuniversal gauginos yield a much smaller fine-tuning Delta_{mu,g} ~ O(100). Our results show that gaugino sector can pave the road towards a more natural stop-on-top scenario.