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We discuss the two-gluon exchange contribution (formally three-loops) toelastic photon-photon scattering in the high-energy approximation. The elastic$\gamma\gamma \to \gamma \gamma$ amplitude is given in the impact-factorrepresentation for all helicity configurations and finite quark masses. Wediscuss the importance of including the charm quark, which contribution, due tointerference, can enhance the cross section considerably. We investigate thecontribution to the $\gamma \gamma \to \gamma \gamma$ amplitude from the softregion, by studying its dependence on nonperturbative gluon mass. Helicity-flipcontributions are shown to be much smaller than helicity-conserving ones. Weidentify region(s) of phase space where the two-gluon exchange contributionbecomes important ingredient compared to box and nonperturbative VDM-Reggemechanisms considered in the literature. Consequences for the $A A \to A A\gamma \gamma$ reaction are discussed. Several differential distributions areshown. A feasibility study to observe the effect of two-gluon exchange ispresented. We perform a similar analysis for the $p p \to p p \gamma \gamma$reaction. Only by imposing severe cuts on $M_{\gamma \gamma}$ and a narrowwindow on photon transverse momenta the two gluon contribution becomescomparable to the box contribution but the corresponding cross section israther small.

physics letters b

Two-gluon exchange contribution to elastic $\gamma \gamma \to \gamma  \gamma$ scattering and production of two-photons in ultraperipheral  ultrarelativistic heavy ion and proton-proton collisions