https://doi.org/10.1140/epjc/s10052-022-10247-7
Regular Article - Theoretical Physics
A dispersive analysis of 
and 
1
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
Received:
15
February
2022
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
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
