Dispersive analysis for $\eta \to \gamma {\gamma }^{\ast }$

Abstract

A dispersion integral is derived that connects data on $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ to the $\eta \to \gamma {\gamma }^{\ast }$ transition form factor. A detailed analysis of the uncertainties is provided. We find for the slope of the $\eta$ transition form factor at the origin $b_{\eta }=(2.05{}_{-0.10}^{+0.22}){\mathrm{GeV}}^{-2}$. Using an additional, plausible assumption, one finds for the corresponding slope of the ${\eta }^{\prime }$ transition form factor, $b_{{\eta }^{\prime }}=(1.58{}_{-0.08}^{+0.15}){\mathrm{GeV}}^{-2}$. Both values are consistent with all recent data, but differ from some previous theoretical analyses.

11 pages, 3 figures, 2 tables (with extended discussion of the isoscalar contribution to the transition form factor)

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