Doubly charged Higgs production within the Higgs triplet model at future electron-positron colliders

We investigate in detail the discovery potential of the doubly charged Higgs boson at the Compact Linear Collider in $e^-e^-$, $e^-\gamma$, $\gamma\gamma$, and $e^+e^-$ collision modes, within the Higgs triplet model at two extreme benchmark points as representatives of the Yukawa-like and gauge-like regions. In the Yukawa-like region, the most promising production mechanism is the single production via $e^-e^-$ and $e^-\gamma$ collisions. Given the subsequent decay of the doubly charged Higgs into a same-sign lepton pair, CLIC can achieve statistical significance well beyond the discovery threshold, within the parameter space permitted by experimental constraints. In the gauge-like region, with the $\ell^{\pm}\ell^{\pm} + \geq 3j$ final state, CLIC exhibits robust discovery potential for the doubly charged Higgs boson, up to a mass of approximately $1.2~\mathrm{TeV}$. We also investigate the search for doubly charged Higgs at the HL-LHC. Our results demonstrate that CLIC possesses greater advantages and offers superior discovery potential for the doubly charged Higgs boson, compared to the HL-LHC.