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

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