\begin{document}$ \gamma e^{-} $\end{document} collisions at the Large Hadron-electron Collider (LHeC) is presented for comparison to that at the International Linear Collider (ILC). The total cross-section depends strongly on the polarization of the initial and final \begin{document}$ e^{-} $\end{document} beams and the electron beam energy \begin{document}$ E_{e} $\end{document}; the energy of the proton beam was set to \begin{document}$ E_{p} = 7 $\end{document} TeV. The results show that the total cross-section in \begin{document}$ \gamma e^{-} \rightarrow Z e^{-} \rightarrow l^{-}l^{+}e^{-} $\end{document} at the LHeC is much larger than that at the ILC."> The cross-section for the <inline-formula><tex-math id="M1">\begin{document}${{\boldsymbol\gamma e}^{\bf -} {\bf\rightarrow} {\boldsymbol Ze}^{\bf -} {\bf\rightarrow}{\boldsymbol l}^{\bf -} {\boldsymbol l}^{\bf +}{\boldsymbol e}^{\bf -} }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/d943773c-906e-4ba0-ad87-f57d445a59bf/CPC-2022-0105_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/d943773c-906e-4ba0-ad87-f57d445a59bf/CPC-2022-0105_M1.png"/></alternatives></inline-formula> scattering at the LHeC -
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