The neutral gauge boson BH with the mass of hundreds GeV is the lightest particle predicted by the littlest Higgs (LH) model, and such particle should be the first signal of the LH model at the planed ILC if it exists indeed. In this paper, we study some processes of the BH production associated with the fermion pair at the ILC, i.e., γγ → ff̄BH. The studies show that the most promising processes to detect BH among γγ → ff̄BH are γγ → l′+l′−BH l′ = e, μ), and they can produce the sufficient signals in most parameter space preferred by the electroweak precision data at the ILC. On the other hand, the signal produced via the certain BH decay modes is typical and such signal can be easily identified from the SM background. Therefore, BH, the lightest gauge boson in the LH model, would be detectable at the photon collider realized at the ILC.

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 γγ and eγ collision will open a wider window to probe B H . In this paper, we study the new gauge boson B H production processes e − γ → e − γB H and e − γ → e − ZB H at the ILC. Our results show that the production cross section of the process e − γ → e − ZB H is less than one fb in the most parameter spaces while the production cross section of the process e − γ → e − γB 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 − γ → e − γB 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 eγ collision at the ILC. Therefore, the processes e − γ → e − γB H and e − γ → e − ZB H provide a useful way to detect B H and test the littlest Higgs model.

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 BH of the Littlest Higgs model via the processes e + e − → γ(Z)BH at the ILC. The results show that the production rates of these two processes are large enough to detect BH in a wide range of the parameter spaces, specially for the process e + e − → γBH. Furthermore, there exist some decay modes for BH which can provide the typical signal and clean backgrounds. Therefore, the new gauge boson BH should be observable via these production processes with the running of the ILC if it exist.