Bounds on anomalous quartic $WWZ\gamma$ couplings in $e^-p$ collisions at the FCC-he

Non-Abelian structure of the Standard Model 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 Standard Model (SM) via anomalous triple gauge couplings (aTGC) and anomalous quartic gauge couplings (aQGC) to test the nature of the Standard Model (SM) and to see the effects of new physics arising from the beyond standard model (BSM). In this study, we focus on the $e^-p \to j Z\gamma \nu_e \to j (l^{+} l^{-})\gamma \nu_e$ process to examine the $WWZ\gamma$ anomalous quartic gauge couplings (aQGC) at the Future Circular Collider-hadron electron (FCC-he) with center-of-mass energy $\sqrt{s}=5.29$ TeV using with a model-independent way in the effective theory approach. A Cut-based method are applied to analyse the signal and relevant SM background. Using with the total cross-sections, we constrained on the anomalous $ f_ {T,i=0,1,2,5,6,7}/\Lambda^4$ couplings arising from dimension-8 operators at $95\%$ Confidence Level (C.L.) for the dilepton decay of the $Z$-boson. The results are composed with integrated luminosities of ${\cal L}=1,2$ and $3$ $\rm ab^{-1}$ under the systematic uncertainties of $\%0$, $\%5$ and $\%10$. In the calculations, we use the form factor to eleminate the effects of the violation of unitarity. With this, we obtained the limits for the energy scale of the form factor $\Lambda=1$ TeV. In addition to all this, we use the adventages of $ep$ collisions for analysing the process with much cleaner environment and lower background effects comparing with the $pp$ collisions. The obtained sensitivities on $ f_ {T,i=0,1,2,5,6,7}/\Lambda^4$ are comparable with the experimental results and related phenomenological studies in the literature.Comment: 19 pages, 5 figure