Bounds on the non-standard W⁺W⁻γ couplings at the LHeC and the FCC-he

Abstract

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 $\mathrm{\Delta }{\kappa }_{\gamma }$ 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 $\mathcal{L}=10-1000{\text{ fb}}^{-1}$. The best limits obtained from the process $e^{-}p\to e^{-}{\gamma }^{⁎}p\to e^{-}{W}^{-}{q}^{\prime }X$ on the anomalous $\mathrm{\Delta }{\kappa }_{\gamma }$ and ${\lambda }_{\gamma }$ couplings are $\mathrm{\Delta }{\kappa }_{\gamma }=|0.00069|$ and ${\lambda }_{\gamma }=[-0.0099,0.0054]$. These bounds show that the process under consideration is a very promising option to probe the non-standard $\mathrm{\Delta }{\kappa }_{\gamma }$ and ${\lambda }_{\gamma }$ couplings at the LHeC and the FCC-he. Our results also provide complementary information on other results for $\mathrm{\Delta }{\kappa }_{\gamma }$ and ${\lambda }_{\gamma }$ couplings.