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

TL;DR

This paper derives new exact sum rules linking light-by-light scattering, meson transition form factors, and decay widths, verified at leading order in QED, with implications for understanding meson properties across quark sectors.

Contribution

It introduces two new super-convergence relations and a set of sum rules for low-energy photon-photon interactions, extending the GDH sum rule to the light-light system.

Findings

Derived new super-convergence relations verified in QED.

Established relations between meson decay widths and transition form factors.

Discussed implications for mesons in light and charm quark sectors.

Abstract

Relating the forward light-by-light scattering to energy weighted integrals of the \gamma* \gamma -fusion cross sections, with one real photon (\gamma) and one virtual photon (\gamma*), 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 \gamma* \gamma -production of mesons, lead to intricate relations between the \gamma \gamma -decay widths or the \gamma* \gamma -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.