The cross-section for the $\gamma e^{-} \rightarrow Ze^{-} \rightarrow l^{-} l^{+} e^{-} $ scattering at the LHeC

A measurement of Z production cross-section in $\gamma e^{-}$ collision at Large Hadron-electron Collider (LHeC) is presented to compare to that at International Linear Collider (ILC). The total cross-section depends strongly on the polarization of the initial and final $e^{-}$ beams, the electron beam energy $E_{e}$ with the energy of the proton beam taken to be $E_{p} = 7$ TeV. The result shows that the total cross-section in $\gamma e^{-} \rightarrow Z e^{-} \rightarrow l^{-}l^{+}e^{-}$ at LHeC is much larger than that at ILC.