A dispersive analysis of varvec{eta 'rightarrow pi ^+pi ^-gamma } and varvec{eta 'rightarrow ell ^+ell ^-gamma }

Abstract

We present a dispersive representation of the eta ' transition form factor that allows one to account, in a consistent way, for the effects of rho –omega mixing in both the isoscalar and the isovector contributions. Using this formalism, we analyze recent data on eta 'rightarrow pi ^+pi ^-gamma to constrain the isovector part of the form factor, individually and in combination with data for the pion vector form factor, which suggests a tension in the rho –omega mixing parameter. As a first application, we use our results, in combination with the most recent input for the isoscalar part of the form factor, to predict the corresponding spectrum of eta 'rightarrow ell ^+ell ^-gamma , in particular we find the slope parameter b_{eta '}=1.455(24),text {GeV}^{-2}. With forthcoming data on the latter process, our results establish the necessary framework to improve the evaluation of the eta '-pole contribution to the anomalous magnetic moment of the muon using experimental input from both eta ' decay channels.