The Reach of the High-Energy LHC for Gluinos and Top Squarks in SUSY Models with Light Higgsinos

We examine the top squark (stop) and gluino reach of the proposed 33 TeV energy upgrade of the Large Hadron Collider (LHC33) in the Minimal Supersymmetric Standard Model (MSSM) with light higgsinos and relatively heavy electroweak gauginos. In our analysis, we assume that stops decay to higgsinos via ${\tilde t}_1 \to t {\tilde{Z}}_1$, $\tilde{t}_1 \to t\tilde{Z}_2$ and $\tilde{t}$$_1 \to b\tilde{W}_1$ with branching fractions in the ratio 1:1:2 (expected if the decay occurs dominantly via the superpotential Yukawa coupling) while gluinos decay via $\tilde{g}\to t\tilde{t}_1$ or via three-body decays to third generation quarks plus higgsinos. These decay patterns are motivated by models of natural supersymmetry where higgsinos are expected to be close in mass to $m_Z$, but gluinos may be as heavy as $5 - 6$ TeV and stops may have masses up to $\sim 3 $ TeV. We devise cuts to optimize the signals from stop and gluino pair production at LHC33. We find that experiments at LHC33 should be able to discover stops with $> 5\sigma$ significance if $m_{\tilde{t}_1} < 2.3 \ (2.8) \ [3.2]$ TeV for an integrated luminosity of 0.3 (1)[3] ab$^{-1}$. The corresponding reach for gluinos extends to 5 (5.5) [6] TeV. These results imply that experiments at LHC33 should be able to discover at least one of the stop or gluino pair signals even with an integrated luminosity of 0.3 ab$^{-1}$ for natural SUSY models with no worse than 3% electroweak fine-tuning, and quite likely both gluinos and stops for an integrated luminosity of 3 ab$^{-1}$.