Probing one-loop--induced decay channel $H^{\pm }\to W^{\pm }\gamma$ in the Two Higgs Doublet Models at muon-TeV colliders

Abstract

In this work, we study the one-loop--induced decay channel $H^{\pm }\to W^{\pm }\gamma$ in the general ${\mathcal{R}}_{\xi }$ gauge within Two Higgs Doublet Models. We analytically verify the gauge invariance ($\xi$-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 viable 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 ${\mu }^{+}{\mu }^{-}\to H^{+}{H}^{-}\to W^{+}{W}^{-}h\gamma$ and ${\mu }^{+}{\mu }^{-}\to \gamma \gamma \to H^{+}{H}^{-}\to W^{+}{W}^{-}h\gamma$, 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, at a center-of-mass energy of $\sqrt{s}=3$~TeV. With the high integrated luminosity expected at muon-TeV colliders, reaching up to $\mathcal{L}=3000{\text{fb}}^{-1}$, our analysis indicates that the signals can be detected with a statistical significance of $5\sigma$ for several benchmark scenarios in the viable parameter space of the Type-I THDM.

Comments: 35 pages, 7 Figures