Prospects for heavy neutral SUSY Higgs scalars in the hMSSM and natural SUSY at LHC upgrades

We examine production and decay of heavy neutral SUSY Higgs bosons pp-> H,\ A -> \tau\bar{\tau} within the hMSSM and compare against a perhaps more plausible natural supersymmetry scenario dubbed m_h^{125}({\rm nat}) which allows for a natural explanation for m_{weak}\simeq m_{W,Z,h}\sim 100 GeV while maintaining m_h\simeq 125 GeV. We evaluate signal against various Standard Model backgrounds from \gamma ,Z ->\tau\bar{\tau}, t\bar{t} and vector boson pair production VV. We combine the transverse mass method for back-to-back (BtB) taus along with the ditau mass peak m_{\tau\tau} method for acollinear taus as our signal channels. This technique ultimately gives a boost to the signal significance over the standard technique of using just the BtB signal channel. We evaluate both the 95% CL exclusion and 5\sigma discovery reach in the m_A vs. \tan\beta plane for present LHC with 139 fb^{-1}, Run 3 with 300 fb^{-1} and high luminosity LHC (HL-LHC) with 3000 fb^{-1} of integrated luminosity. For \tan\beta =10, the exclusion limits range up to m_A\sim 1, 1.1 and 1.4 TeV, respectively. These may be compared to the range of m_A values gleaned from a statistical analysis of the string landscape wherein m_A can range up to ~8 TeV.