Light-by-light scattering in ultraperipheral Pb-Pb collisions at energies available at the CERN Large Hadron Collider

We calculate cross sections for diphoton production in (semi)exclusive $\mathrm{PbPb}$ collisions, relevant for the CERN Large Hadron Collider (LHC). The calculation is based on the equivalent photon approximation in the impact parameter space. The cross sections for the elementary $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ subprocess are calculated including two different mechanisms. We take into account box diagrams with leptons and quarks in the loops. In addition, we consider a vector-meson dominance (VDM-Regge) contribution with virtual intermediate hadronic (vector-like) excitations of the photons. We get measurable cross sections in $\mathrm{PbPb}$ collisions. This opens a possibility to study the $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ (quasi)elastic scattering at the LHC. 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 or identification of different components (boxes, VDM-Regge) is possible. We find that the cross section for elastic $\ensuremath{\gamma}\ensuremath{\gamma}$ scattering could be measured in the heavy-ion collisions for subprocess energies smaller than ${W}_{\ensuremath{\gamma}\ensuremath{\gamma}}\ensuremath{\approx}15\text{--}20$ GeV.

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