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

We search for a five-plet singly charged Higgs $H_5^{\pm }$ in the Georgi-Machacek model at the ep colliders. The charged Higgs bosons are produced via the $Z{W}^{\pm }$ fusion process $p{e}^{-}\to j{e}^{-}{H}_5^{\pm }$, and decay as $H_5^{\pm }\to Z{W}^{\pm }\to (l^{+}{l}^{-})(jj)$. With a detector-level simulation at the FCC-eh and LHeC, a multi-variate analysis is performed to yield 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 model parameter $\sin {\theta }_H$ for charged Higgs masses between 200 and 1000 GeV. The effects of electron beam polarization are also investigated.