Natural Supersymmetry and Implications for Higgs physics

We re-analyze the LHC bounds on light third generation squarks in Natural Supersymmetry, where the sparticles have masses inversely proportional to their leading-log contributions to the electroweak symmetry breaking scale. Higgsinos are the lightest supersymmetric particles; top and bottom squarks are the next-to-lightest sparticles that decay into both neutral and charged Higgsinos with well-defined branching ratios determined by Yukawa couplings and kinematics. The Higgsinos are nearly degenerate in mass, once the bino and wino masses are taken to their natural (heavy) values. We consider three scenarios for the stop and sbottom masses: (I) $\tilde{t}_R$ is light, (II) $\tilde{t}_L$ and $\tilde{b}_L$ are light, and (III) $\tilde{t}_R$, $\tilde{t}_L$, and $\tilde{b}_L$ are light. Dedicated stop searches are currently sensitive to Scenarios II and III, but not Scenario I. Sbottom-motivated searches ($2 b + \rm{MET}$) impact both squark flavors due to $\tilde{t} \ra b \charp_1$ as well as $\tilde{b} \ra b \neut_{1,2}$, constraining Scenarios I and III with somewhat weaker constraints on Scenario II. The totality of these searches yield relatively strong constraints on Natural Supersymmetry. Two regions that remain are: (1) the "compressed wedge", where $(m_{\tilde{q}} - |\mu|)/m_{\tilde{q}} \ll 1$, and (2) the "kinematic limit" region, where $m_{\tilde{q}} \gsim 600-750 GeV, at the kinematic limit of the LHC searches. We calculate the correlated predictions for Higgs physics, demonstrating that these regions lead to distinct predictions for the lightest Higgs couplings that are separable with $\simeq 10% measurements. We show that these conclusions remain largely unchanged once the MSSM is extended to the NMSSM in order to naturally obtain a large enough mass for the lightest Higgs boson consistent with LHC data.