Pascalutsa-Vanderhaeghen light-by-light sumrule from photon-photon collisions

Light-by-light scattering sumrules based on general field theory principles relate cross-sections with different helicities. In this paper the simplest sumrule 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 di-meson intermediate states. The latest Amplitude Analysis of $\gamma\gamma\to\pi\pi, \overline{K}K$ allows this contribution to be evaluated. However, we find that other multi-meson contributions up to 2.5 GeV are required to satisfy the sumrules. 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 sumrules for the helicity differences are likely fulfilled.