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 $\gamma \gamma \to \gamma \gamma$ 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 $\mathrm{PbPb}$ collisions. This opens a possibility to study the $\gamma \gamma \to \gamma \gamma$ (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 $W_{\gamma \gamma }\approx 15\text{–}20$ GeV.

Figure 1

Light-by-light scattering mechanisms with the lepton and quark loops (left panel) and as an example one topology of diagram for intermediate the $W$-boson loop (right panel).

Figure 2

Other elementary $\gamma \gamma \to \gamma \gamma$ processes. The left panel represents the two-gluon exchange and the right panel is for the VDM-Regge mechanism.

Figure 3

Integrated $\gamma \gamma \to \gamma \gamma$ cross section as a function of the subsystem energy. The dashed lines show the contribution of boxes and the solid line represents the result of the VDM-Regge mechanism.

Figure 4

Elementary cross section $d\sigma /d{p}_{t,\gamma }$ as a function of the subprocess energy $W$ ($\gamma \gamma$ invariant mass in the nuclear process) and transverse momentum of one of the outgoing photons for the box (left panel) and VDM-Regge (right panel) mechanisms.

Figure 5

Elementary cross section $d\sigma /dz$ as a function of the subprocess energy $W$ ($\gamma \gamma$ invariant mass in the nuclear process) and $z=cos\theta$ for the box (left panel) and VDM-Regge (right panel) mechanisms.

Figure 6

$AA\to AA\gamma \gamma$ in ultrarelativistic UPC of heavy ions.

Figure 7

Predictions for the $\mathrm{PbPb}\to \mathrm{PbPb}\gamma \gamma$ reaction in UPC of heavy ions. Differential nuclear cross section as a function of impact parameter, $\gamma \gamma$ invariant mass, and rapidity of photon pairs at $\sqrt{s_{NN}}=5.5$ TeV and with extra cut on $W_{\gamma \gamma }>5.5$ GeV. The distributions with realistic charge density are depicted by the red (lower) lines and the distributions which are calculated using the monopole form factor are shown by the blue (upper) lines. The dashed lines show the results for the case when only box contributions (fermion loops) are included. The solid lines show the results for the VDM-Regge mechanism.

Figure 8

Distribution of the expected number of counts in 1 GeV bins for cuts specified in the figure legend. This figure should be compared with a similar figure in [11].

Figure 9

Results for the $\mathrm{PbPb}\to \mathrm{PbPb}\gamma \gamma$ reaction in UPC of heavy ions. Differential nuclear cross section as a function of photon transverse momentum $p_{t,\gamma }$ and cosine of the angle between outgoing photons $z=cos{\theta }^{*}$ at $\sqrt{s_{NN}}=5.5$ TeV with a minimal cut on $M_{\gamma \gamma }>1$ GeV for the VDM-Regge mechanism only. The solid lines show the results for the case when only box contributions (fermionic loops) are included. The dashed lines show the results for the VDM-Regge approach only.

Figure 10

Two-dimensional distribution in energies of the two photons in the laboratory frame for box (left panel) and VDM-Regge (right panel) contributions.

Figure 11

Contour representation of two-dimensional ($\mathrm{d}\sigma /\mathrm{d}{y}_{{\gamma }_1}\mathrm{d}{y}_{{\gamma }_2}$ in nb) distribution in rapidities of the two photons in the laboratory frame for box (left panel) and VDM-Regge (right panel) contributions with shown experimental rapidity coverage of the main ATLAS or CMS detectors. Only one-half of the ($y_{{\gamma }_1},y_{{\gamma }_2}$) space is shown for the VDM-Regge contribution. The second half can be obtained from the symmetry around the $y_{{\gamma }_1}=y_{{\gamma }_2}$ line.

Figure 12

Projection on rapidity of one of the photons. The cuts here are the same as in Fig. 11. For the VDM contribution, the dashed and dotted lines are projections on the $y_{{\gamma }_1}$ and $y_{{\gamma }_2}$ axes, respectively.