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In this paper we present a detailed analysis of the contribution of the Light-- by -- Light (LbL), Durham and double diffractive processes for the diphotonproduction in ultraperipheral $PbPb$ collisions at the Large Hadron Collider(LHC), High -- Energy LHC (HE -- LHC) and Future Circular Collider (FCC). Theacceptance of the central and forward LHC detectors is taken into account andpredictions for the invariant mass, rapidity, transverse momentum andacoplanarity distributions are presented. Our results indicate that thecontribution of the Durham and double diffractive processes can be stronglysuppressed by the exclusivity cuts, which will allow to perform a preciseanalysis of the LbL scattering, as well the search of beyond Standard Modelphysics in this final state.

Exclusive and diffractive $\gamma \gamma$ production in $PbPb$ collisions at the LHC, HE -- LHC and FCC