Low- and high-energy phenomenology of a doubly charged scalar

We explore the phenomenology of an $SU(2)$-singlet doubly charged scalar at the high and low energy frontier. Such a particle is predicted in different new physics models, like left-right symmetric models or the Zee-Babu model. Nonetheless, since its interactions with Standard Model (SM) leptons are gauge invariant, it can be consistently studied as a UV complete SM extension. Its signatures range from same-sign di-lepton pairs to flavour changing decays of charged leptons to muonium-antimuonium oscillations. In this article, we use a systematic effective-field-theory approach for studying the low-energy observables and comparing them consistently to collider bounds. For this purpose, experimental searches for doubly charged scalars at the Large Hadron Collider are reinterpreted, including large width effects, and projections for exclusion and discovery reaches in the high-luminosity phase are provided. The sensitivities of the future International Linear Collider and Compact Linear Collider for the doubly charged scalar are presented with focus on di-lepton final states and resonant production. Theoretically and phenomenologically motivated benchmark scenarios are considered showing the different impact of low- and high-energy observables. We find that future low- and high-energy experiments display strong complementarity in studying the parameter space of the model.