A dispersive analysis of and

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