${\gamma }^{\ast }\gamma \to \eta ,{\eta }^{\prime }$ transition form factors

Abstract

Using a continuum approach to the hadron bound-state problem, we calculate ${\gamma }^{\ast }\gamma \to \eta ,{\eta }^{\prime }$ 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 $\eta ,{\eta }^{\prime }$ properties. The study also delivers predictions for the amplitudes that describe the light- and strange-quark distributions within the $\eta ,{\eta }^{\prime }$. 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 ${\eta }^{\prime }$ in particular. Our analysis also provides some insights into the properties of $\eta ,{\eta }^{\prime }$ mesons and associated observable manifestations of the non-Abelian anomaly.

arXiv comment16 pages, 7 figures, 3 tables

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