The associated productions of the new gauge boson $B_{H}$ in the littlest Higgs model with a SM gauge boson via $e^+e^-$ collision

With the high energy and luminosity, the planned ILC has the considerable capability to probe the new heavy particles predicted by the new physics models. In this paper, we study the potential to discover the lightest new gauge boson $B_{H}$ of the littlest Higgs model via the processes $e^+e^- to gamma (Z)B_H$ at the ILC. The results show that the production rates of these two processes are large enough to detect $B_H$ in a wide range of the parameter space, specially for the process $e^+e^- to gamma B_H$. Furthermore, there exist some decay modes for $B_H$ which can provide the typical signal and clean background. Therefore, the new gauge boson $B_H$ should be observable via these production processes with the running of the ILC if it exists indeed.