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We explore the discovery prospect of the doubly-charged component of an$SU(2)_L$-triplet scalar at the future $e^- p$ collider FCC-eh, proposed tooperate with an electron beam energy of 60 GeV and a proton beam energy of 50TeV. We consider the associated production of the doubly-charged Higgs bosonalong with leptons and jet(s), and its subsequent prompt decay to same-signlepton pair. This occurs for ${\cal O}(1)$ Yukawa coupling of the scalartriplet with charged leptons, which is expected for reasonably small vacuumexpectation values of the neutral component of the triplet field that governsthe neutrino mass generation in the type-II seesaw. We present our analysis fortwo different final states, $3l+\ge1j$ and an inclusive $\ge2l+\ge1j$ channel.Considering its decay to electrons only, we find that the doubly-charged Higgswith mass around a TeV could be observed at $3\sigma$ confidence level with$\mathcal{O}(200)\, \rm{fb}^{-1}$ of integrated luminosity, while masses up to2 TeV could be probed within a few years of data accumulation. The signalproposed here becomes essentially background-free, if it is triggered in the$\mu\mu$ mode and a $5\sigma$ discovery is achievable in this channel for aTeV-scale doubly-charged Higgs with an integrated luminosity as low as$\mathcal{O} (50)\, \rm{fb}^{-1}$. We also highlight the sensitivity of FCC-ehto the Yukawa coupling responsible for production of the doubly-charged Higgsboson as a function of its mass in both the $ee$ and $\mu\mu$ channels.

Doubly-charged Higgs Boson at Future Electron-Proton Collider