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

Abstract

Relating the forward light-by-light scattering to energy weighted integrals of the ${\ensuremath{\gamma}}^{*}\ensuremath{\gamma}$ fusion cross sections, with one real photon ($\ensuremath{\gamma}$) and one virtual photon (${\ensuremath{\gamma}}^{*}$), we find two new exact superconvergence relations. They complement the known superconvergence relation based on the extension of the Gerasimov-Drell-Hearn 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 superconvergence relations, applied to the ${\ensuremath{\gamma}}^{*}\ensuremath{\gamma}$ production of mesons, lead to intricate relations between the $\ensuremath{\gamma}\ensuremath{\gamma}$ decay widths or the ${\ensuremath{\gamma}}^{*}\ensuremath{\gamma}$ 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.