Observing Light-by-Light Scattering at the Large Hadron Collider

Elastic light-by-light scattering ($\gamma \gamma \to \gamma \gamma$) is open to study at the Large Hadron Collider thanks to the large quasireal photon fluxes available in electromagnetic interactions of protons ($p$) and lead (Pb) ions. The $\gamma \gamma \to \gamma \gamma$ cross sections for diphoton masses $m_{\gamma \gamma }>5\mathrm{GeV}$ amount to 12 fb, 26 pb, and 35 nb in $p\mathrm{\text{−}}p$, $p\mathrm{\text{−}}\mathrm{Pb}$, and Pb-Pb collisions at nucleon-nucleon center-of-mass energies $\sqrt{s_{\mathrm{NN}}}=14$, 8.8, and 5.5 TeV, respectively. Such a measurement has no substantial background in Pb-Pb collisions where one expects about 20 signal events per run, after typical detector acceptance and reconstruction efficiency selections.

Figure 1

Schematic diagram of elastic $\gamma \gamma \to \gamma \gamma$ collisions in electromagnetic proton and/or ion interactions at the LHC. The initial-state photons are emitted coherently by the protons and/or nuclei which survive the electromagnetic interaction.

Figure 2

Left: Cross sections for exclusive $\gamma \gamma \to \gamma \gamma$, with pair masses above 5 GeV, in ultraperipheral Pb-Pb (top curve), $p\mathrm{\text{−}}\mathrm{Pb}$ (middle) and $p\mathrm{\text{−}}p$ (bottom) collisions as a function of the nucleon-nucleon c.m. energy in the range $\sqrt{s_{\mathrm{NN}}}=1–20\mathrm{TeV}$. Right: Stacked diphoton yields as a function of invariant mass for elastic $\gamma \gamma$ and backgrounds (CEP $\gamma \gamma$ and QED $e^{+}{e}^{-}$) expected in $1{\mathrm{nb}}^{-1}$ Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.5\mathrm{TeV}$ after analysis cuts (see text). The three superimposed curves indicate the underlying individual LbyL, CEP, and QED distributions.