The new charged gauge boson $W^{\mathrm{\prime }}$ and the subprocess $eq\to \nu q^{\mathrm{\prime }}$ at $e^{+}{e}^{-}$ and $ep$ colliders

In the framework of the little Higgs models and the three-site Higgsless model, we discuss the contributions of the new charged gauge boson $W^{\mathrm{\prime }}$ to the process $eq\to \nu q^{\mathrm{\prime }}$ and the possibility of detecting $W^{\mathrm{\prime }}$ via this process in future high energy linear $e^{+}{e}^{-}$ collider $(ILC)$ and $ep$ collider $(THERA)$ experiments. Our numerical results show that the process $eq\to\nu q’$israthersensitivetothecoupling$W’ff’$ and one can use this process to distinguish different new physics models in future $ILC$ and $THERA$ experiments.