Study of the projected sensitivity on the anomalous quartic gauge couplings via $Z\gamma\gamma$ production at the CLIC

Gauge boson self-couplings are completely defined by the non-Abelian gauge symmetry of the Standard Model (SM). For this reason, a direct search for these couplings is extremely significant in understanding the gauge structure of the SM. The possible deviation from the SM predictions of gauge boson self-couplings would be a sign of the presence of new physics beyond the SM. In this work, we study the sensitivities on the anomalous couplings defined by dimension-8 operators related to the $ZZ\gamma\gamma$ and $Z\gamma\gamma\gamma$ quartic vertices through the process $e^+e^- \to Z\gamma\gamma$ with Z-boson decaying to charged leptons at the Compact Linear Collider (CLIC). We analyze the center-of-mass energy of 3 TeV, integrated luminosities of ${\cal L}=1, 4, 5$ $\rm ab^{-1}$, systematic uncertainties of $\delta_{sys}=0\%, 3\%, 5\%$, unpolarized and polarized electron beams and considering the Initial State Radiation and Beamstrahlung effects for extraction of expected sensitivity on the anomalous $f_ {T,j}/\Lambda^4$ couplings at $95\%$ confidence level, which are especially sensitive to the $Z\gamma\gamma$ channel. It is clear from the results that we expect better limits on the couplings if the systematic error is improved. The best limits obtained on the anomalous quartic couplings for the process $e^+e^- \to Z\gamma\gamma$ with $\sqrt{s}= 3$ TeV, ${\cal L}=5$ $\rm ab^{-1}$, and $\delta_{sys}=0\%$ can be approximately improved up to about 1.1 times better than the limits obtained with $\delta_{sys}=5\%$. Our sensitivities on the anomalous quartic couplings can set more stringent sensitivity by two orders of magnitude concerning the best sensitivity derived from the current experimental limits. Finally, with initial electron beam polarization, the sensitivity of the anomalous quartic couplings improves by almost a factor of 1.2.