Unveiling the Unexplored Decay Mode of a Light Charged Higgs Boson to an Off-Shell Top Quark and a Bottom Quark

The charged Higgs boson (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^±→τν decay mode, the decay channel into an off-shell top quark and a bottom quark, H^± → t^*b, is leading or subleading for 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⁻→ t^*bτν→ bbjjτν. 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 5σ threshold with an integrated luminosity of 1 ab⁻¹, assuming a 10% background uncertainty. Specifically, for MH^± = 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 to achieve similar results. Our findings highlight the critical role of the MuC in probing the new signal channel H^±→ t^*b, offering a promising avenue for future charged Higgs boson searches involving off-shell top quarks.