$γγ\to γγ$ scattering in ultrarelativistic UPC

Abstract: We discuss diphoton semi(exclusive) production in ultraperipheral lead-lead collisions at energy of $\sqrt{s_{NN}}$ = 5.5 TeV (LHC) and in proton-proton collisions at $\sqrt{s_{pp}}$ = 7 TeV (LHC) and $\sqrt{s_{pp}}$ = 100 TeV (FCC). The nuclear calculations are based on equivalent photon approximation in the impact parameter space. The cross sections for elementary $\gamma\gamma \to \gamma\gamma$ subprocess are calculated including three different mechanisms: box diagrams with leptons and quarks in the loops, a VDM-Regge contribution with virtual intermediate hadronic excitations of the photons and the two-gluon exchange contribution. We get relatively high cross sections in heavy ion collisions. This opens a possibility to study the light-by-light (quasi)elastic scattering at the LHC. We find that the cross section for elastic $\gamma\gamma$ scattering could be measured in the lead-lead collisions for the diphoton invariant mass up to $W_{\gamma\gamma} \approx$ 15 - 20 GeV. Our Standard Model predictions are compared to a recent ATLAS experimental result. We present differential distributions for PbPb$\to$PbPb$\gamma\gamma$ and pp$\to$pp$\gamma\gamma$ reaction.