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

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Single production of the doubly charged scalars $Φ^{\pm\pm}$ via $eγ$, $ep$ and $pp$ collisions is studied in the context of the little Higgs$(LH)$ model. Our numerical results show that the new particles $Φ^{\pm\pm}$ 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 $Φ^{\pm\pm}$ at the $LHC$ is much smaller than that at the $ILC$ or the $THERA$.
Latex, 17 pages, 7 figures; revised version, adding some references and correcting some typos

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