Probing one-loop-induced decay channel H ± → W ± γ in the two-higgs-doublet models at muon-TeV colliders

Abstract In this work, we study the one–loop–induced decay channel H ± → W ± γ in the general R ξ gauge within Two Higgs Doublet Models. We analytically verify the gauge invariance ( ξ -independence), ultraviolet finiteness, and renormalization-scale independence of the one-loop form factors, thereby confirming the consistency of our calculations. On the phenomenological side, we perform a parameter scan of the Type-I THDM and, based on the allowed parameter space, evaluate the branching ratios of this decay process. Furthermore, we investigate charged Higgs pair production at muon–TeV colliders through the representative processes μ + μ − → H + H − → W + W − hγ and μ + μ − → γγ → H + H − → W + W − hγ , as typical applications of our results. The events for the processes are computed within the allowed parameter regions of the Type-I THDM. The corresponding signal significances are evaluated, including the relevant Standard Model backgrounds. With the high integrated luminosity expected at muon–TeV colliders, our analysis indicates that the signal can be detected with a statistical significance exceeding 2 σ for several benchmark scenarios in the viable parameter space of the Type-I THDM.