Detecting heavy neutral SUSY Higgs bosons decaying to sparticles at the high-luminosity LHC

In supersymmetry (SUSY) models with low electroweak naturalness (natSUSY), which have been suggested to be the most likely version of SUSY to emerge from the string landscape, higgsinos are expected at the few hundred GeV scale whilst electroweak gauginos inhabit the TeV scale. For TeV-scale heavy neutral SUSY Higgs bosons H and A, as currently required by LHC searches, then the dominant decay modes of H, A are into gaugino plus higgsino provided these decays are kinematically open. The light higgsinos decay to soft particles so are largely invisible whilst the gauginos decay to W, Z or h plus missing transverse energy (MET). Thus, we examine the viability of H,A-> W+MET, Z+MET and h+MET signatures at the high luminosity LHC (HL-LHC) in light of large Standard Model (SM) backgrounds from (mainly) t\bar{t}, VV and Vh production (where V=W, Z). We also examine whether these signal channels can be enhanced over backgrounds by requiring the presence of an additional soft lepton from the decays of the light higgsinos. We find significant regions in the vicinity of m_A~ 1-2 TeV of the m_A vs. \tan\beta plane which can be probed at the high luminosity LHC using these dominant signatures by HL-LHC at 5\sigma and at the 95% confidence level (CL).