Multichannel assault on natural supersymmetry at the high luminosity LHC

Recent clarifications of naturalness in supersymmetry robustly require the presence of four light Higgsinos with mass similar to 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 (Z) over tilde (1)(Z) over tilde (2) followed by (Z) over tilde (2) -> (Z) over tilde (1)l(+)l-decay to soft dileptons which recoil against a hard jet. It appears that 3000 fb(-1) is just about enough 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.