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