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Natural Supersymmetry, Muon $g-2$, and the Last Crevices for the Top Squark

We study the interplay of natural supersymmetry and a supersymmetric solution to the discrepancy observed in measurements of the muon magnetic moment. The strongest constraints on the parameter space currently come from chargino searches in the trilepton channel and slepton searches in the dilepton channel at the LHC, and vast regions are currently allowed, especially at large $\tanβ$. With light top squarks in the spectrum, as required from naturalness arguments, the situation changes dramatically; stop-assisted chargino and neutralino production via $\tilde{t} \rightarrow b \tildeχ_{1}^{\pm}$ and $\tilde{t} \rightarrow t \tildeχ_{1}^0$ are already probing the entire parameter space compatible with the muon magnetic moment at $\tanβ \sim \mathcal{O}(10)$, while upcoming stop searches will probe most of the parameter space at larger $\tanβ \sim 40$. Direct Higgsino searches as well as compressed slepton and stop searches are crucial to close out corners of parameter space. We consider one such example: in the presence of light sleptons and charginos as required to obtain appreciable contributions to the muon magnetic moment, compressed stops can dominantly undergo the following decay $\tilde{t} \, \rightarrow \, b \tilde{\ell} ν(\tildeν \ell) \, \rightarrow \, b \ell ν\tildeχ_{1}^0$, facilitated by off-shell charginos. We find that the enhanced branching to leptons leads to a $5 σ$ mass reach (with $3000$ fb$^{-1}$ of data at LHC14) of $m_{\tilde{t}} \, \sim \, 350$ GeV, with the mass difference between stops and the lightest neutralino being $\sim 80$ GeV. This will further close out a significant part of the parameter space compatible with naturalness and the muon magnetic moment.