Abstract
The forward proton detectors recently installed and operating at the LHC open the possibility to observe photon collisions with high precision, providing a novel window on physics beyond the Standard Model. We review recent simulations and theoretical developments about the measurement of anomalous $\gamma\gamma\gamma\gamma$ and $Z\gamma\gamma\gamma$ interactions. The searches for these anomalous gauge interactions are expected to set bounds on a wide range of particles including generic electroweak particles, neutral particles with dimension-5 coupling to gauge bosons, polarizable dark particles, and are typically complementary from new physics searches in other channels.
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