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

We investigate the phenomenology of the charged Higgs boson within the two-Higgs-doublet type-II seesaw model (2HDMcT type-III) at future μ + μ − colliders. Focusing on 2 → 2 processes such as μ + μ − → H 1 + S − ( S − = H 1 − , H 2 − ) and μ + μ − → H 1 + W − , we incorporate both theoretical and experimental constraints to assess their production prospects. We find that σ ( μ + μ − → H 1 + H 1 − ) can reach or exceed the corresponding e + e − cross section, while σ ( μ + μ − → H 1 + H 2 − ) is roughly 18 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 μ + μ − → H 1 + W − is significantly enhanced due to the large tan β amplification characteristic of the type-III scenario. Furthermore, we conduct a signal-background analysis and determine the discovery ( 5 σ ) regions at a 3 TeV muon collider for the μ + μ − → H 1 + H 1 − , μ + μ − → H 1 + H 2 − , and μ + μ − → W ± H 1 ∓