Single production of the doubly charged scalar in the littlest Higgs model

Single production of the doubly charged scalars ${\mathrm{\Phi }}^{\pm \pm }$ via $e\gamma$, $ep$ and $pp$ collisions is studied in the context of the little Higgs$(LH)$ model. Our numerical results show that the new particles ${\mathrm{\Phi }}^{\pm \pm }$ can be abundantly produced and their possible signatures should be detected in future high energy linear $e^{+}{e}^{-}$ collider$(ILC)$. The cross section for single production of ${\mathrm{\Phi }}^{\pm \pm }$ at the $LHC$ is much smaller than that at the $ILC$ or the $THERA$.