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Light-by-light scattering sum rules constraining meson transition form factors

Relating the forward light-by-light scattering to energy weighted integrals of the γ* γ-fusion cross sections, with one real photon (γ) and one virtual photon (γ*), we find two new exact super-convergence relations. They complement the known super-convergence relation based on the extension of the GDH sum rule to the light-light system. We also find a set of sum rules for the low-energy photon-photon interaction. All of the new relations are verified here exactly at leading order in scalar and spinor QED. The super-convergence relations, applied to the γ* γ-production of mesons, lead to intricate relations between the γγ-decay widths or the γ* γ-transition form factors for (pseudo-) scalar, axial-vector and tensor mesons. We discuss the phenomenological implications of these results for mesons in both the light-quark sector and the charm-quark sector.