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We search for a five-plet singly charged Higgs $H_5^\pm$ in theGeorgi-Machacek model at the ep colliders. The charged Higgs bosons areproduced via the $ZW^{\pm}$ fusion process $p\, e^- \to j\, e^-\, H_5^\pm$, anddecay as $H_5^\pm \to Z\, W^{\pm} \to (l^+ l^-)\, (jj)$. With a detector-levelsimulation at the FCC-eh and LHeC, a multi-variate analysis is performed toyield limits on the production cross section times branching ratio $\sigma (p\,e^- \to j e^- H_5^\pm) \times {\rm BR}(H_5^\pm \to Z\, W^\pm)$ and on the modelparameter $\sin\theta_H$ for charged Higgs masses between 200 and 1000 GeV. Theeffects of electron beam polarization are also investigated.

Search for Singly Charged Higgs in Vector Boson Scattering at the ep Colliders