A comprehensive study of the charged Higgs boson in the two Higgs doublet type-II seesaw model

Abstract

We investigate the phenomenology of the charged Higgs boson within the Two-Higgs-Doublet Type-II Seesaw Model (2HDMcT Type-III) at future ${\mu }^{+}{\mu }^{-}$ colliders. Focusing on $2\to 2$ processes such as ${\mu }^{+}{\mu }^{-}\to H_1^{+}{S}^{-}$ ($S^{-}=H_1^{-},H_2^{-}$) and ${\mu }^{+}{\mu }^{-}\to H_1^{+}{W}^{-}$, we incorporate both theoretical and experimental constraints to assess their production prospects. We find that $\sigma ({\mu }^{+}{\mu }^{-}\to H_1^{+}{H}_1^{-})$ can reach or exceed the corresponding $e^{+}{e}^{-}$ cross section, while $\sigma ({\mu }^{+}{\mu }^{-}\to H_1^{+}{H}_2^{-})$ is roughly eighteen times smaller but can be enhanced up to 0.62 fb upon relaxing electroweak precision observables constraints. Moreover, we observe that the cross section for ${\mu }^{+}{\mu }^{-}\to H_1^{+}{W}^{-}$ is significantly enhanced due to the large $\tan \beta$ amplification characteristic of the Type-III scenario. Furthermore, we conduct a signal-background analysis and determine the discovery ($5\sigma$) regions at a 3 TeV muon collider for the ${\mu }^{+}{\mu }^{-}\to H_1^{+}{H}_1^{-}$, ${\mu }^{+}{\mu }^{-}\to H_1^{+}{H}_2^{-}$, and ${\mu }^{+}{\mu }^{-}\to W^{\pm }{H}_1^{\mp }$ processes.

Comments: 22 pages, 11 figures, 17 tables