We present results of the updated SuperChic 3 Monte Carlo event generator for central exclusive production. This extends the previous treatment of proton-proton collisions to include heavy ion (pA and AA) beams, for both photon and QCD-initiated production, the first time such a unified treatment of exclusive processes has been presented in a single generator. To achieve this we have developed a theory of the gap survival factor in heavy ion collisions, which allows us to derive some straightforward results about the $A$ scaling of the corresponding cross sections. We compare against the recent ATLAS and CMS measurements of light-by-light scattering at the LHC, in lead-lead collisions. We find that the background from QCD-initiated production is expected to be very small, in contrast to some earlier estimates. We also present results from new photon-initiated processes that can now be generated, namely the production of axion-like particles, monopole pairs and monopolium, top quark pair production, and the inclusion of $W$ loops in light-by-light scattering.
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