| Summary: | Abstract The charged Higgs boson ( $$H^\pm $$ H ± ) with a mass below the top quark mass remains a viable possibility within the Type-I two-Higgs-doublet model under current constraints. While previous LHC searches have primarily focused on the $$H^\pm \rightarrow \tau ^\pm \nu $$ H ± → τ ± ν decay mode, the decay channel into an off-shell top quark and a bottom quark, $$H^\pm \rightarrow t^*b$$ H ± → t ∗ b , is leading or subleading for $$H^\pm $$ H ± masses between 130 and 170 GeV. This study investigates the discovery potential of future colliders for this off-shell decay mode through pair-produced charged Higgs bosons decaying via $$H^+H^-\rightarrow t^*b\tau \nu \rightarrow bbjj\tau \nu $$ H + H - → t ∗ b τ ν → b b j j τ ν . We perform signal-to-background analyses at the HL-LHC and a prospective 100 TeV proton–proton collider, employing cut-flow strategies and the Boosted Decision Tree method. However, due to the softness of the b jets, signal significances fall below detection thresholds at these facilities. Extending our study to a multi-TeV muon collider (MuC), we demonstrate that a 3 TeV MuC achieves high signal significance, surpassing the $$5\sigma $$ 5 σ threshold with an integrated luminosity of 1 ab $$^{-1}$$ - 1 and a 10% background uncertainty. Specifically, for $$M_{H^\pm } = 130$$ M H ± = 130 , 150, and 170 GeV, the significances are 13.7, 13.5, and 6.06, respectively. In contrast, a 10 TeV MuC requires 10 ab $$^{-1}$$ - 1 to achieve similar results. Our findings highlight the critical role of the MuC in probing the new signal channel $$H^\pm \rightarrow t^*b$$ H ± → t ∗ b , offering a promising avenue for future charged Higgs boson searches involving off-shell top quarks.
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