$ZZ\gamma$ and $Z\gamma\gamma$ anomalous couplings in $\gamma p$ collision at the LHC

We study the sensitivity of anomalous $ZZ\gamma$ and $Z\gamma\gamma$ vertex couplings $h_3^{\gamma,Z}$ and $h_4^{\gamma,Z}$, which would be powerful sign of new physics, via the subprocess $\gamma q\to Z q$ of the main reaction $pp\to p\gamma p\to Z q X$ at the LHC. We calculated limits on these couplings at 95% confidence level for various values of integrated luminosity. It is shown that the $pp\to p\gamma p\to Z q X$ reaction provides one order of magnitude improvement in the couplings $h_4^{\gamma,Z}$ compared to the current experimental limits obtained in events dominated by $Z\gamma$ production from the LHC and Tevatron.