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

Single production of the doubly charged scalars $\Phi^{\pm\pm}$ 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 $\Phi^{\pm\pm}$ 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 $\Phi^{\pm\pm}$ at the $LHC$ is much smaller than that at the $ILC$ or the $THERA$.