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It is essential to directly investigate the self-couplings of gauge bosons inthe Standard Model (SM) due to its non-Abelian nature, as these couplings playa significant role in comprehending the gauge structure of the model. Thediscrepancies between the Standard Model's expectations and the measured valueof gauge boson self-couplings would serve as strong evidence towards theexistence of new physics phenomena that extend beyond the Standard Model. Suchdeviations could provide valuable insights into the nature of new physics andpotentially lead to a deeper understanding of fundamental particles and theirinteractions. In this study, we examine the sensitivities of anomalouscouplings associated with dimension-8 operators that affect the $\gamma \gamma\gamma \gamma$ and $Z \gamma \gamma \gamma$ quartic vertices. The study focuseson the process $e^- \gamma \to e^-\gamma\gamma$ with the incoming photon underWeizs\"acker-Williams approximation at the stage-3 scenerio of Compact LinearCollider (CLIC) that is refer to a CoM energy of 3 TeV. Due to the CLICoptions, we take into account the both unpolarized and $\mp80\%$ polarizedelectron beam with the related integrated luminosities of ${\cal L}=5, 4, 1$$\rm ab^{-1}$ under the systematic uncertainties of $\delta_{sys}=0, 3, 5$.Obtained sensitivities on the anomalous quartic gauge couplings (aQGCs) for theprocess $e^- \gamma \to e^-\gamma\gamma$ at $\sqrt{s}= 3$ TeV and variouspolarizations, are improved by a factor of 2-200 times better for the couplings$f_{T,j}/\Lambda^4$ compared with the experimental results.

Sensitivities on the anomalous quartic $\gamma\gamma\gamma\gamma$ and $\gamma \gamma\gamma Z$ couplings at the CLIC