Regular Article - Theoretical Physics
A dispersive analysis of and
Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115, Bonn, Germany
2 Forschungszentrum Jülich, Institute for Advanced Simulation, Institut für Kernphysik, and Jülich Center for Hadron Physics, 52425, Jülich, Germany
3 Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
4 Institute for Nuclear Theory, University of Washington, 98195-1550, Seattle, WA, USA
Accepted: 23 March 2022
Published online: 12 May 2022
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.
© The Author(s) 2022
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