PHYSICAL REVIEW D
Light-by-light scattering sum rules based on general field theory principles relate cross sections with different helicities. In this paper the simplest sum rule is tested for the I = 0 and 2 channels for " real" photon-photon collisions. Important contributions come from the long-lived pseudoscalar mesons and from dimeson intermediate states. The latest amplitude analysis of gamma gamma ->pi pi, KK allows this contribution to be evaluated. However, we find that other multimeson contributions up to 2.5 GeV are required to satisfy the sum rules. While data on three-and four-pion cross sections exist, there is no information about their isospin and helicity decomposition. Nevertheless, we show the measured cross sections are sufficiently large to ensure the sum rules for the helicity differences are likely fulfilled.
Dai, Ling-Yun and Pennington, M. R., Pascalutsa-Vanderhaeghen light-by-light sum rule from photon-photon collisions (2017). PHYSICAL REVIEW D, 95(5).