Dispersive analysis for $η\to γγ^*$

Abstract

A dispersion integral is derived that connects data on $η\to π^+π^-γ$ to the $η\to γγ^*$ transition form factor. A detailed analysis of the uncertainties is provided. We find for the slope of the $η$ transition form factor at the origin $b_η= (2.05 {}^{+0.22}_{-0.10})\, {\rm GeV}^{-2}$. Using an additional, plausible assumption, one finds for the corresponding slope of the $η'$ transition form factor, $b_{η'} = (1.58 {}^{+0.15}_{-0.08})\, {\rm GeV}^{-2}$. 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)