Probing the anomalous $\gamma\gamma\gamma Z$ coupling at the LHC with proton tagging

The sensitivities to the anomalous quartic gauge boson coupling $\gamma\gamma\gamma Z$ are estimated via $\gamma Z$ production with intact protons in the forward region at the LHC. Proton tagging proves to be a powerful tool to suppress the background, which allows consideration of the hadronic decays of the $Z$ boson in addition to the leptonic ones. We discuss the discovery potential for an integrated luminosity of $300\,\mathrm{fb}^{-1}$ and $3000\,\mathrm{fb}^{-1}$. The sensitivity we obtain at $300\,\mathrm{fb}^{-1}$ goes beyond the one expected from LHC bounds on the $Z\rightarrow \gamma\gamma\gamma$ decay by about three orders of magnitude. The $\gamma Z$ channel provides important discriminatory information with respect to the exclusive $\gamma\gamma$ channel, as many particles beyond the Standard Model (such as a radion or Kaluza Klein gravitons) predict a signal in the latter but not the former.