We investigate a strategy to search for light, nearly degenerate higgsinos within the natural MSSM at the LHC. We demonstrate that the higgsino mass range μ in 100−160 GeV, which is preferred by the naturalness, can be probed at 3σ significance through the monojet search at 14 TeV HL-LHC with 3000 fb⁻¹ luminosity. The proposed method can also probe certain region in the parameter space for the lightest neutralino with a high higgsino purity, that cannot be reached by planned direct detection experiments at XENON-1 T(2017).

We systematically calculate various flavor-changing neutral-current top-quark processes induced by supersymmetry at the Large Hadron Collider, which include five decay modes and six production channels. To reveal the characteristics of these processes, we first compare the dependence of the rates for these channels on the relevant supersymmetric parameters, then we scan the whole parameter space to find their maximal rates, including all the direct and indirect current experimental constraints on the scharm-stop flavor mixings. We find that, under all these constraints, only a few channels, through $cg\to t$ at parton level and $t\to ch$, may be observable at the Large Hadron Collider.

The flavor-changing top quark decays $\overrightarrow{t}\mathrm{cV}$ $(V=Z,\gamma ,g)$ induced by R-parity-violating couplings in the minimal supersymmetric standard model are evaluated. We find that the decays $\overrightarrow{t}\mathrm{cV}$ can be significantly enhanced relative to those in the R-parity-conserving supersymmetric model. Our results show that the top quark flavor-changing neutral current decay can be as large as $\mathrm{Br}\left(\overrightarrow{t}cg\right)\sim {10}^{-3},$ $\mathrm{Br}\left(\overrightarrow{t}cZ\right)\sim {10}^{-4},$ and $\mathrm{Br}\left(\overrightarrow{t}c\gamma \right)\sim {10}^{-5},$ which may be observable at the upgraded Fermilab Tevatron and/or the CERN LHC.