Exploring Heavy Higgs Bosons at a 100 TeV Hadron Collider within the Semi-Constrained NMSSM

In this study, we explore the detectability of heavy Higgs bosons in the $pp \to b\bar{b}H/A \to b\bar{b}t\bar{t}$ channel at a 100 TeV hadron collider within the semi-constrained Next-to-Minimal Supersymmetric Standard Model (NMSSM). We calculate their production cross sections and decay branching ratios, comparing these with simulation results from existing reference. We focus on the heavy, doublet-dominated CP-even Higgs $H$ and CP-odd Higgs $A$, with mass limits set below 10 TeV to ensure detectability. We find that at a collider with 3 ab$^{-1}$ of integrated luminosity, the potential for detecting heavy Higgs bosons varies significantly with their mass and $\tan\beta$. Heavy Higgs bosons below 2 TeV are within the testable range, while those heavier than 7 TeV fall below the exclusion and discovery thresholds, rendering them undetectable. For masses between 2 and 7 TeV, heavy Higgs bosons with $\tan\beta$ less than 20 can be detected, whereas those with $\tan\beta$ greater than 20 are beyond the current discovery or exclusion capabilities.