Light-by-light scattering in ultraperipheral heavy-ion collisions at the LHC

We present cross sections for diphoton production in (semi)exclusive $PbPb$ collisions, relevant for the LHC. The calculation is based on equivalent photon approximation in the impact parameter space. The cross sections for elementary elastic scattering $\gamma \gamma \to \gamma \gamma$ subprocess are calculated including two mechanisms: box diagrams with leptons and quarks in the loops and a mechanism based on vector-meson dominance (VDM-Regge) model with virtual intermediate vector-like excitations of the photons. We get measureable cross sections in $PbPb$ collisions. We present many interesting differential distributions which could be measured by the ALICE, CMS or ATLAS Collaborations at the LHC. We study whether a separation of box and VDM-Regge contributions is possible. We find that the cross section for elastic $\gamma \gamma$ scattering could be measured in the heavy-ion collisions for subprocess energies smaller than $W_{\gamma\gamma} \approx 15-20$~GeV.