A dispersive analysis of [Formula: see text] and [Formula: see text]

We present a dispersive representation of the [Formula: see text] transition form factor that allows one to account, in a consistent way, for the effects of [Formula: see text] –[Formula: see text] mixing in both the isoscalar and the isovector contributions. Using this formalism, we analyze recent data on [Formula: see text] 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 [Formula: see text] –[Formula: see text] 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 [Formula: see text] , in particular we find the slope parameter [Formula: see text] . With forthcoming data on the latter process, our results establish the necessary framework to improve the evaluation of the [Formula: see text] -pole contribution to the anomalous magnetic moment of the muon using experimental input from both [Formula: see text] decay channels.