  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 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 ugrades 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 diboson +MET (SSdB)
production arising from wino pair production, leading to same-sign dileptons
plus MET, 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 fb^{-1}
of integrated luminosity.
