On-Shell Calculation of Low-Energy Photon–Photon Scattering

Although photon–photon scattering does not exist at the tree level, this is no longer the case at loop order and was first calculated by Euler and Heisenberg. The existence of this phenomenon has now been confirmed experimentally by the ATLAS collaboration and plays a small but important role in the calculation of gμ-2. We show how the low-energy form of the γγ scattering amplitude can be determined via causal (on-shell) methods using Compton scattering helicity amplitudes as input for the case of charged S = 0, S = 1/2, and S = 1 intermediate state fields.