Minding the gap: Testing natural anomaly-mediated SUSY breaking at high luminosity LHC

While the minimal anomaly-mediated SUSY breaking model (mAMSB) seems ruled out by constraints on Higgs mass, naturalness and wino dark matter, a slightly generalized version dubbed natural AMSB (nAMSB) remains both viable and compelling. Like mAMSB, nAMSB features winos as the lightest gauginos, but unlike mAMSB, nAMSB allows a small $\ensuremath{\mu}$ parameter so that Higgsinos are the lightest of electroweakinos (EWinos). nAMSB spectra depend on the input value of gravitino mass ${m}_{3/2}$, where the lower range of ${m}_{3/2}$ is excluded by LHC gluino pair searches while a higher ${m}_{3/2}$ band is excluded by LHC limits on wino pair production followed by boosted hadronic wino decays. A remaining intermediate gap in ${m}_{3/2}$ values remains allowed by present LHC searches, but appears to be completely explorable by high luminosity upgrades of LHC (HL-LHC). We explore a variety of compelling discovery channels that may allow one to close the intermediate gap in ${m}_{3/2}$ values: (1) same-sign $\mathrm{diboson}+{\overline{)E}}_{T}$ (SSdB) production arising from wino pair production, leading to same-sign dileptons plus missing ${E}_{T}$, (2) trilepton production arising from wino pair production and (3) soft dilepton plus jet events from Higgsino pair production, (4) top-squark pair production. From our signal-to-background analysis along a nAMSB model line, we expect HL-LHC to either discover or rule out the nAMSB model with $3000\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity.