Light-by-light scattering

The elastic scattering of two photons into two photons. In vacuum QED there is no photon self-coupling at tree level; its leading scattering amplitude is the sum of six oriented charged-fermion box diagrams. The superficial degree of divergence is zero, but the photon Ward identities forbid the required local dimension-four $A^4$ counterterm. The complete one-loop Feynman diagram sum is consequently ultraviolet finite. This does not remove its finite four-momentum dependence or its physical thresholds.

The ATLAS experiment used lead ion collisions at the Large Hadron Collider to study the vacuum QED process. In an ultra-peripheral collision, the nuclei pass without an ordinary nuclear collision; their strong electromagnetic fields supply nearly real photons. Selecting two nearly back-to-back photons with little other detector activity isolated the rare channel. The 2017 result used $480\mu {\mathrm{b}}^{-1}$ at $\sqrt{s_{NN}}=5.02\mathrm{TeV}$ and found 13 candidates against an expected background of $2.6\pm 0.7$. This was evidence, with a reported significance of $4.4$ standard deviations.^[ref][ref]