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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 plausiblenatural supersymmetry scenario dubbed m_h^{125}({\rm nat}) which allows for anatural explanation for m_{weak}\simeq m_{W,Z,h}\sim 100 GeV while maintainingm_h\simeq 125 GeV. We evaluate signal against various Standard Modelbackgrounds from \gamma ,Z ->\tau\bar{\tau}, t\bar{t} and vector boson pairproduction 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 asour signal channels. This technique ultimately gives a boost to the signalsignificance 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_Avs. \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 astatistical analysis of the string landscape wherein m_A can range up to ~8TeV.

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