Doubly Charged Higgs Production at Future $ep$ Colliders

The Higgs sector of the standard model can be extended by introducing an $SU(2)_L$ Higgs triplet $\Delta$ to generate the tiny neutrino masses in the framework of type-II seesaw mechanism. In this paper, we study the pair production of the introduced Higgs triplet at future $e^{-}p$ colliders. The corresponding production cross sections via vector boson fusion process at FCC-ep and ILC$\otimes$FCC are predicted, where the production of a pair of doubly charged Higgs is found to be dominant and then used to investigate the collider phenomenology of the Higgs triplet. Depending on the size of the Higgs triplet vacuum expectation value, the doubly charged Higgs may decay into a pair of same-sign charged leptons or a pair of same-sign $W$ bosons. In order to explore the discovery potential of the doubly charged Higgs at future $e^{-}p$ colliders, we discuss these two decay scenarios in detail and show respectively the detection sensitivity on the mass of the doubly charged Higgs.