Probing the anomalous triple $ZZ\gamma$ and $Z\gamma \gamma$ couplings at the FCC-$\mu p$ and SPPC-$\mu p$

In this study, 24.5 TeV CoM energy FCC-$\mu p$ and 20.2 TeV CoM energy SPPC-$\mu p$ muon-proton colliders have been utilized to explore the anomalous $ZZ\gamma$ and $Z\gamma \gamma$ couplings corresponding to dim-8 operators through the process of ${\mu }^{-}\gamma \to Z{l}^{-}\to l^{-}\widetilde{{\nu }_l}{\nu }_l$. A cut-based method has been applied to enhance the signal background ratio in the analysis. Coupling sensitivities, at a 95% Confidence Level (C.L.), under the systematic uncertainties of 0% and 5%, were obtained with luminosities of ${\mathcal{L}}_{int}=5$ and 42.8 fb${}^{-1}$ for FCC-$\mu p$ and SPPC-$\mu p$ colliders, respectively. The sensitivities for anomalous $C_{BB}\mathrm{/}{\mathrm{\Lambda }}^4$, $C_{\tilde{B}W}\mathrm{/}{\mathrm{\Lambda }}^4$, $C_{BW}\mathrm{/}{\mathrm{\Lambda }}^4$ and $C_{WW}\mathrm{/}{\mathrm{\Lambda }}^4$ couplings without systematic uncertainty for FCC-$\mu p$ and SPPC-$\mu p$ were found as follows, respectively: [0.068; 0.070] TeV-4, [-0.187; 0.184] TeV-4, [-0.236; 0.238] TeV-4, [-0.619; 0.621] TeV-4, and [-0.066; 0.051] TeV-4, [-0.158; 0.151] TeV-4, [-0.207; 0.192] TeV-4, [-0.514; 0.522] TeV-4.