Discovery prospects for the light charged Higgs boson decay to an off-shell top quark and a bottom quark at future high-energy colliders

The charged Higgs boson (\(H^\pm \)) 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 \(H^\pm \rightarrow \tau ^\pm \nu \) decay mode, the decay channel into an off-shell top quark and a bottom quark, \(H^\pm \rightarrow t^*b\), is leading or subleading for \(H^\pm \) 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 \(H^+H^-\rightarrow t^*b\tau \nu \rightarrow bbjj\tau \nu \). 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 \(5\sigma \) threshold with an integrated luminosity of 1 ab\(^{-1}\) and a 10% background uncertainty. Specifically, for \(M_{H^\pm } = 130\), 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 \(H^\pm \rightarrow t^*b\), offering a promising avenue for future charged Higgs boson searches involving off-shell top quarks.