The production of the new gauge boson $B_{H}$ via $e^{-}\gamma$ collision in the littlest Higgs model

The new lightest gauge boson $B_H$ with mass of a few hundred GeV is predicted in the littlest Higgs model. $B_H$ should be accessible in the planed ILC and the observation of such particle can strongly support the littlest Higgs model. The realization of $\gamma\gamma$ and $e\gamma$ collision will open a wider window to probe $B_H$. In this paper, we study the new gauge boson $B_{H}$ production processes $e^{-}\gamma\to e^{-}\gamma B_{H}$ and $e^{-}\gamma\to e^{-}Z B_{H}$ at the ILC. Our results show that the production cross section of the process $e^{-}\gamma\to e^{-}Z B_{H}$ is less than one fb in the most parameter spaces while the production cross section of the process $e^{-}\gamma\to e^{-}\gamma B_{H}$ can reach the level of tens fb and even hundreds of fb in the sizable parameter spaces allowed by the electroweak precision data. With the high luminosity, the sufficient typical signals could be produced, specially via $e^{-}\gamma\to e^{-}\gamma B_{H}$. Because the final electron and photon beams can be easily identified and the signal can be easily distinguished from the background produced by $Z$ and $H$ decaying, $B_H$ should be detectable via $e\gamma$ collision at the ILC. Therefore, the processes $e^{-}\gamma\to e^{-}\gamma B_{H}$ and $e^{-}\gamma\to e^{-}Z B_{H}$ provide a useful way to detect $B_{H}$ and test the littlest Higgs model