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Under certain running conditions, the CERN Large Hadron Collider (LHC) can beconsidered as a photon-photon collider. Indeed, in proton-proton, proton-ion,ion-ion collisions, when incoming particles pass very close to each other invery peripheral collisions, the incoming protons or ions remain almost intactand continue their path along the beam axis. Then, only the electromagnetic(EM) fields of these ultra-relativistic charged particles (protons or ions)interact to leave a signature in the central detectors of the LHC experiments.The interest is that the photon-photon interactions happen at unprecedentedenergies (a few TeV per nucleon pairs) where the quantum electrodynamics (QED)theory can be tested in extreme conditions and unforeseen laws of nature couldbe discovered. In this report, we propose a focus on a particular reaction,called light-by-light scattering in which two incoming photons interact,producing another pair of photons. We describe how experimental results havebeen obtained at the LHC. In addition, we discuss prospects for on-shellphoton-photon interactions in dedicated laser beam facilities. Potentialsignatures of new physics might manifest as resonant deviations in therefractive index, induced by anomalous light-by-light scattering effects.Importantly, we explain how this process can be used to probe the physicsbeyond the standard model such as theories that include large extra dimensions.Finally, some perspectives and ideas are given for future data taking orexperiments.

Photon-photon physics at the LHC and laser beam experiments, present and future