Single production of a vector-like top as a probe of charged higgs bosons at a muon–proton collider

We investigate the discovery potential of a vector-like top partner ( T ) in the Type-II Two-Higgs-Doublet Model at a high-energy μ p μ p collider through the charged-Higgs cascade μ ⁺ p → ν _μ \,b̄ T → ν _μ \,b̄ H⁺ b μ + p → ν μ b ¯ T → ν μ b ¯ H + b with H⁺→ tb̄ H + → t b ¯ . The signal is characterized by four b jets, one charged lepton, and missing transverse energy. A detector-level analysis is performed for representative spectra with mH^± 600 m H ± ≃ 600 –650 GeV and mT 1.2 m T ≃ 1.2 –1.9 TeV. We find that a 5σ 5 σ discovery is achievable for mT 1.2 m T ≃ 1.2 TeV at integrated luminosities of 100 and 150~fb⁻¹ 150 fb - 1 even in the presence of $$20%$$ 20 % background systematics. For mT 1.5 m T ≃ 1.5 TeV, discovery remains possible for vanishing or moderate systematics, while heavier benchmarks require larger statistics and/or improved control of backgrounds.