Bounds on the non-standard couplings at the LHeC and the FCC-he

We examine the potential of the ${e}^{-}p\to {e}^{-}{\gamma }^{⁎}p\to {e}^{-}{W}^{-}{q}^{\prime }X$ (${\gamma }^{⁎}$ is the Weizsacker-Williams photon) reaction to probe the non-standard ${W}^{+}{W}^{-}\gamma $ couplings at the Large Hadron electron Collider (LHeC) and the Future Circular Collider-hadron electron (FCC-he). Using the effective Lagrangian approach with various values of the center-of-mass energy and integrated luminosity, we find 95% confidence level bounds on the anomalous coupling $\Delta {\kappa }_{\gamma }$ and ${\lambda }_{\gamma }$ parameters. We assume center-of-mass energies of the electron-proton system $\sqrt{s}=1.30,1.98,7.07,10\text{TeV}$ and luminosities $L=10-1000{\text{fb}}^{-1}$. The best limits obtained from the process ${e}^{-}p\to {e}^{-}{\gamma }^{⁎}p\to {e}^{-}{W}^{-}{q}^{\prime }X$ on the anomalous $\Delta {\kappa }_{\gamma }$ and ${\lambda }_{\gamma }$ couplings are $\Delta {\kappa }_{\gamma }=|0.00069|$ and ${\lambda }_{\gamma }=\left[-0.0099,0.0054\right]$. These bounds show that the process under consideration is a very promising option to probe the non-standard $\Delta {\kappa }_{\gamma }$ and ${\lambda }_{\gamma }$ couplings at the LHeC and the FCC-he. Our results also provide complementary information on other results for $\Delta {\kappa }_{\gamma }$ and ${\lambda }_{\gamma }$ couplings.