Probe of the anomalous neutral triple gauge couplings in photon-induced collision at future muon colliders

The anomalous $ZZ\gamma$ and $Z\gamma\gamma$ neutral triple gauge couplings occurred by dimension-eight operators are investigated through the process $\mu^+\mu^-\,\rightarrow\,\mu^+\gamma^*\mu^-\,\rightarrow\,\mu^+ Z(\nu\bar{\nu})\mu^-$ at muon collider with $\sqrt{s}=3$, $6$, $10$ $14$ TeV. charged lepton pseudo-rapidity, transverse momentum missing energy distributions taken in consideration for final state of analysis. sensitivities obtained $95\%$ Confidence Level integrated luminosity ${\cal L}_{\text{int}}=1$, $4$, $20$ ab$^{-1}$, respectively, according to center-of-mass energies taking into account effects systematic uncertainties $0\%$, $3\%$ $5\%$. best limits $C_{BB}/{\Lambda^4}$, $C_{BW}/{\Lambda^4}$, $C_{\widetilde{B}W}/{\Lambda^4}$ $C_{WW}/{\Lambda^4}$ without uncertainty 14 TeV 20 ab$^{-1}$ found be [-0.01026; 0.00636] TeV$^{-4}$, [-0.02482; 0.03053] [-0.01830; 0.02510] [-0.06981; 0.07387] respectively.