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We study the sensitivity of anomalous $ZZ\gamma$ and $Z\gamma\gamma$ vertexcouplings $h_3^{\gamma,Z}$ and $h_4^{\gamma,Z}$, which would be powerful signof 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 couplingsat 95% confidence level for various values of integrated luminosity. It isshown that the $pp\to p\gamma p\to Z q X$ reaction provides one order ofmagnitude improvement in the couplings $h_4^{\gamma,Z}$ compared to the currentexperimental limits obtained in events dominated by $Z\gamma$ production fromthe LHC and Tevatron.

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