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.

确定规范玻色子自相互作用强度的四次规范玻色子耦合完全由标准模型的非阿贝尔规范性质决定。在具有高质心能量和高积分光度的ep碰撞中对这些耦合的检查为测试标准模型的有效性和超出标准模型的新物理的存在提供了重要机会。四次规范玻色子耦合可以直接促进对撞机的多玻色子产生。因此，我们研究了大型强子电子对撞机和未来圆形对撞机-强子电子过程\(ep \rightarrow \nu _{e}W^{+}W^{-} j\)的潜力，以研究非-标准万维网通过有效的拉格朗日方法以独立于模型的方式耦合。我们对测量纯轻子和半轻子衰变通道中的\(W^{+}W^{-}\)产生进行了调查。此外，我们计算了\(95\%\)对异常\(\frac{f_{M0}}{\Lambda ^{4}}\)、\(\frac{f_{M1 }}{\Lambda ^{4}}\) , \(\frac{f_{M7}}{\Lambda ^{4}}\) , \(\frac{f_{S0}}{\Lambda ^{4 }}\) , \(\frac{f_{S1}}{\Lambda ^{4}}\) , \(\frac{f_{T0}}{\Lambda ^{4}}\) , \(\ frac{f_{T1}}{\Lambda ^{4}}\)和\(\frac{f_{T2}}{\Lambda ^{4}}\)8维算子通过过程\(ep \rightarrow \nu _{e}W^{+}W^{-} j\)获得的耦合，用于大型强子电子对撞机和未来圆形强子电子对撞机的不同中心-质量能量和综合光度。我们的结果表明，通过大型强子电子对撞机和未来圆形对撞机-强子电子的过程\(ep \rightarrow \nu _{e}W^{+}W^{-} j\)，灵敏度估计在异常WWWW耦合可以得到重要加强。