Probing the Scalar Sector: Discovery Reach for Heavy Higgs Pairs at a $\sqrt{s} = 6$ TeV Muon Collider in the 2HDM Alignment Limit
This study provides a comprehensive phenomenological investigation into the discovery potential of heavy Higgs boson pairs ($HH, HA, AA, H^+H^-$) at a $\sqrt{s}=6$~TeV Muon Collider. Utilizing the Two-Higgs-Doublet Model (2HDM) Type-I within the alignment limit ($\sin(β-α) \approx 1$), we evaluate two primary benchmarks with degenerate scalar masses of 1000~GeV (BP1) and 2000~GeV (BP2). Theoretical calculations performed reveal that Type-I branching fractions to third-generation fermions remain uniquely independent of $\tanβ$, providing a stable signal across the investigated parameter space. We demonstrate that the Muon Collider environment allows for the precise identification of high-multiplicity hadronic final states. A key finding of this research is that the signal processes yield distinctive topological signatures: an 8-jet state ($4j+4b$) for charged pairs and a highly complex 12-jet state ($8j+4b$) for neutral pairs ($HA/AA$). These signatures, combined with hard transverse momentum distributions and central pseudorapidity ($|η| \le 3$), allow for nearly absolute suppression of Standard Model backgrounds like $t\bar{t}$, $W^+W^-Z$, and $ZZZ$. At an integrated luminosity of 10~ab$^{-1}$, we report a staggering statistical significance of 104,000 for the $H^+H^-$ channel and 3343 for the $HA$ channel in the BP1 scenario. Furthermore, total selection efficiencies were found to increase from approximately 20\% at BP1 to 47\% at BP2, suggesting that the decay products of heavier scalars are kinematically easier to resolve. We conclude that a 6~TeV Muon Collider offers an unparalleled discovery reach for the extended scalar sector, providing a definitive facility for probing physics beyond the Standard Model.