Single production of charged gauge bosons from little Higgs models in association with top quark at the LHC

In the context of the little Higgs models, we discuss single production of the new charged gauge bosons in association with top quark at the $CERN$ Large Hadron Collider$(LHC)$. We find that the new charged gauge bosons $W_{H}^{-}$ and $X^{-}$, which are predicted by the littlest Higgs model and the SU(3) simple model, respectively, can be abundantly produced at the $LHC$. However, since the main backgrounds coming from the processes $pp\to t\bar{t}+X$ and $pp\to tW^{-}+X$ are very large, the values of the ratios $N_{W}$ and $N_{X}$ are very small in most of the parameter space. It is only possible to detect the signal of the gauge boson $W_{H}^{-}$ via the process $pp\to gb+X\to tW_{H}^{-}+X$ at the $LHC$ in a small region of the parameter space.