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Light-by-light scattering in UPC at the LHC

We discuss diphoton semi(exclusive) production in ultraperipheral $PbPb$ collisions at energy of $\sqrt{s_{NN}}=$ 5.5 TeV (LHC). The nuclear calculations are based on equivalent photon approximation in the impact parameter space. The cross sections for elementary $γγ\to γγ$ subprocess are calculated including two different mechanisms: box diagrams with leptons and quarks in the loops and a VDM-Regge contribution with virtual intermediate hadronic excitations of the photons. We got relatively high cross sections in $PbPb$ collisions ($306$ nb). This opens a possibility to study the $γγ\to γγ$ (quasi)elastic scattering at the LHC. We find that the cross section for elastic $γγ$ scattering could be measured in the lead-lead collisions for the diphoton invariant mass $W_{γγ} \approx 15-20$ GeV.