Analysis of the anomalous quartic $WWWW$ couplings at the LHeC and the FCC-he

Abstract: The quartic gauge boson couplings that identify the strengths of the gauge boson self-interactions are exactly determined by the non-Abelian gauge nature of the Standard Model. The examination of these couplings at $ep$ collisions with high center-of-mass energy and high integrated luminosity provides an important opportunity to test the validity of the Standard Model and the existence of new physics beyond the Standard Model. The quartic gauge boson couplings can contribute directly to multi-boson production at colliders. Therefore, we examine the potential of the process $ep \rightarrow \nu_{e}W^{+}W^{-} j$ at the Large Hadron Electron Collider and the Future Circular Collider-hadron electron to study non-standard $WWWW$ couplings in a model independent way by means of the effective Lagrangian approach. We present an investigation on measuring $W^{+}W^{-}$ production in pure leptonic and semileptonic decay channels. In addition, we calculate the sensitivity limits at $95\%$ Confidence Level on the anomalous $\frac{f_{M0}}{\Lambda^{4}}$, $\frac{f_{M1}}{\Lambda^{4}}$, $\frac{f_{M7}}{\Lambda^{4}}$, $\frac{f_{S0}}{\Lambda^{4}}$, $\frac{f_{S1}}{\Lambda^{4}}$, $\frac{f_{T0}}{\Lambda^{4}}$, $\frac{f_{T1}}{\Lambda^{4}}$ and $\frac{f_{T2}}{\Lambda^{4}}$ couplings obtained by dimension-8 operators through the process $ep \rightarrow \nu_{e}W^{+}W^{-} j$ for the Large Hadron Electron Collider and the Future Circular Hadron Electron Collider's different center-of-mass energies and integrated luminosities. Our results show that with the process $ep \rightarrow \nu_{e}W^{+}W^{-} j$ at the Large Hadron Electron Collider and the Future Circular Collider-hadron electron the sensitivity estimated on the anomalous $WWWW$ couplings can be importantly strengthened.