One-loop expressions for $H^{\pm} \rightarrow W^{\pm} Z$ and their implications at muon--TeV colliders

One-loop contributions for decay process $H^{\pm} \rightarrow W^{\pm}Z$ within the Two-Higgs-Doublet Model are computed in the general $\mathcal{R}_ξ$ gauge, and its phenomenological applications at future muon--TeV colliders are studied in this paper. The analytic results are confirmed by several consistency tests, for example, the $ξ$-independence, the renormalization-scale stability and the ultraviolet finiteness of the one-loop amplitude. We first perform an updated parameter scan of the Type-X THDM in the phenomenological studies. The production of charged Higgs boson pairs at future muon--TeV colliders is investigated through the two processes $μ^+μ^- \rightarrow H^+H^- \rightarrow W^{\pm}W^{\mp}Zh$ and $μ^+μ^- \rightarrow γγ\rightarrow H^+H^- \rightarrow W^{\pm}W^{\mp}Zh$. Both signal events and their significances are evaluated with taking into account the corresponding Standard Model backgrounds. We find that the signal significances can exceed $5σ$ at several benchmark points in the viable parameter space of the Type-X THDM.