Non-Abelian structure of the standard model (SM) predicts the self-interactions of gauge bosons triple gauge couplings (TGC) and quartic gauge couplings (QGC). On the other hand, it is also important to determine the deviations from SM via anomalous triple gauge couplings and anomalous quartic gauge couplings (aQGC) to test the nature of the SM and to see the effects of new physics arising from the beyond the standard model. In this study, we focus on the e − p → jZ γ ν e → j(l + l −)γ ν e process to examine the WWZ γ aQGC at the Future Circular Collider-hadron electron with center-of-mass energy TeV using a model-independent way in the effective theory approach. A Cut-based method is applied to analyse the signal and relevant SM background. Using the total cross-sections, we constrained the anomalous f T,i=0,1,2,5,6,7/Λ4 couplings arising from dimension-8 operators at 95% confidence level for the dilepton decay of the Z-boson. The results are composed of integrated luminosities of and 3 ab −1 under the systematic uncertainties of 0%, 5% and 10%. In the calculations, we use the form factor to eliminate the effects of the violation of unitarity. With this, we obtained the limits for the energy scale of the form factor Λ = 1 TeV. In addition to all this, we use the advantages of ep collisions for analysing the process with much cleaner environment and lower background effects compared with the pp collisions. The obtained sensitivities on f T, i=0, 1, 2, 5, 6, 7/Λ4 are comparable with the experimental results and related phenomenological studies in the literature.
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