$γ^\ast γ\to η, η^\prime$ transition form factors

Abstract

Using a continuum approach to the hadron bound-state problem, we calculate $γ^\ast γ\to η, η^\prime$ transition form factors on the entire domain of spacelike momenta, for comparison with existing experiments and in anticipation of new precision data from next-generation $e^{+}{e}^{-}$ colliders. One novel feature is a model for the contribution to the Bethe-Salpeter kernel deriving from the non-Abelian anomaly, an element which is crucial for any computation of $\hat{I}\cdot ,\hat{I}{\cdot }^{\prime }$ properties. The study also delivers predictions for the amplitudes that describe the light- and strange-quark distributions within the $\hat{I}\cdot ,\hat{I}{\cdot }^{\prime }$. Our results compare favourably with available data. Important to this at large-$Q^2$ is a sound understanding of QCD evolution, which has a visible impact on the $\hat{I}{\cdot }^{\prime }$ in particular. Our analysis also provides some insights into the properties of $\hat{I}\cdot ,\hat{I}{\cdot }^{\prime }$ mesons and associated observable manifestations of the non-Abelian anomaly.

16 pages, 7 figures, 3 tables