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 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 gamma gamma -> gamma 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 PbPb collisions. This opens a possibility to study the gamma gamma -> gamma 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 gamma gamma scattering could be measured in the heavy-ion collisions for subprocess energies smaller than W gamma gamma approximate to 15-20 GeV.