Longitudinal short-distance constraints for the hadronic light-by-light contribution to $(g-2)_\mu$ with large-$N_c$ Regge models

Understand

While the low-energy part of the hadronic light-by-light (HLbL) tensor can be constrained from data using dispersion relations, for a full evaluation of its contribution to the anomalous magnetic moment of the muon $(g-2)_\mu$ also mixed- and high-energy regions need to be estimated.

• Both can be addressed within the operator product expansion (OPE), either for configurations where all photon virtualities become large or one of them remains finite.
• Imposing such short-distance constraints (SDCs) on the HLbL tensor is thus a major aspect of a model-independent approach towards HLbL scattering.
• Here, we focus on longitudinal SDCs, which concern the amplitudes containing the pseudoscalar-pole contributions from $\pi^0$, $\eta$, $\eta'$.