Chasing Long-Lived Doubly Charged Scalars at Future Lepton Colliders

We come up with a novel search strategy for long-lived doubly charged scalars at future proposed lepton colliders. The doubly charged scalar studied in this work belongs to an $SU(2)_L$ complex scalar triplet that accounts for tiny neutrino masses via the Type-II Seesaw mechanism. For scalar masses $\lesssim 200$ GeV and appropriate values of the triplet vacuum expectation value, this state can be long-lived and decay predominantly into like-sign muon pairs (e.g. $\mu^+\mu^+$ or $\mu^-\mu^-$), producing distinctive displaced-vertex signals. We investigate the pair production of these scalars at the International Linear Collider (ILC) and a prospective muon collider, considering their planned center-of-mass energies. Incorporating theoretical and experimental constraints, we study the resulting signature of four leptons accompanied by missing transverse energy. Displaced vertices offer direct evidence of the scalar's long lifetime, while we further show that the invariant mass distribution of same-sign dilepton pairs serves as a powerful complementary probe for discovering doubly charged Higgs bosons at both the ILC and muon collider.