Dispersion relation for hadronic light-by-light scattering: η and η′ poles
摘要
The pseudoscalar-pole contributions to hadronic light-by-light scattering are determined by the respective transition form factors (TFFs) into two virtual photons. These TFFs constitute complicated functions of the photon virtualities that, in turn, can be reconstructed in a dispersive approach from their discontinuities. In this work, we present such an analysis for the η(′) TFFs, implementing a number of constraints from both experiment and theory: normalizations from the η(′) → γγ decay widths, unitarity constraints from the η(′) → π+π−γ spectra, chiral symmetry for the η(′) → 2(π+π−) amplitudes, vector-meson couplings, singly-virtual data from e+e− → e+e−η(′), and the asymptotic behavior predicted by the light-cone expansion. In particular, we account for the leading left-hand-cut singularity by including effects from the a2 resonance, necessitating the solution of an inhomogeneous Muskhelishvili-Omnès problem via a carefully chosen path deformation. The resulting TFFs allow us to evaluate the η(′)-pole contributions to the anomalous magnetic moment of the muon,