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

Abstract

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.

13 pages, 1 figure

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Cited by in corpus (4)

• Hadronic light-by-light scattering amplitudes from lattice QCD versus dispersive sum rules
• Data-driven dispersive analysis of the $\pi \pi$ and $\pi K$ scattering
• Two and Three Pseudoscalar Production in $e^{+}{e}^{-}$ annihilation and their contributions to $(g-2{)}_{\mu }$
• Amplitude analysis of the anomalous decay ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$