Recent clarifications of naturalness in supersymmetry robustly require the presence of four light higgsinos with mass ~100-300 GeV while gluinos and (top)-squarks may lie in the multi-TeV range, possibly out of LHC reach. We project the high luminosity (300-3000 fb^{-1}) reach of LHC14 via gluino cascade decays and via same-sign diboson production. We compare these to the reach for neutralino pair production \tz_1\tz_2 followed by \tz_2\to\tz_1\ell^+\ell^- decay to soft dileptons which recoil against a hard jet. It appears that 3000 fb^{-1} is just about sufficient integrated luminosity to probe naturalness with up to 3\% fine-tuning at the 5-sigma level, thus either discovering natural supersymmetry or else ruling it out.
@article{arxiv.1604.07438,
title = {Multi-channel assault on natural supersymmetry at the high luminosity LHC},
author = {Howard Baer and Vernon Barger and Michael Savoy and Xerxes Tata},
journal= {arXiv preprint arXiv:1604.07438},
year = {2016}
}