Constraining Gluonic Quartic Gauge Coupling Operators with $gg \to \gamma \gamma$

Gluon-gluon to photon-photon scattering $gg \to \gamma\gamma$ offers to the LHC experiments a uniquely powerful probe of dimension-8 operators in the Standard Model Effective Field Theory (SMEFT) that are quadratic in both the electromagnetic and gluonic field-strength tensors, such as would appear in the Born-Infeld extension of the Standard Model (SM). We use 13-TeV ATLAS data on the production of isolated photon pairs to set lower limits on the scales of dimension-8 operators $M \gtrsim 1$~TeV, and discuss the prospective sensitivities of possible future hadron colliders.