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

Journal Article · 11 May 2022 · European Physical Journal. C, Particles and Fields (Online)

DOI: https://doi.org/10.1140/epjc/s10052-022-10247-7 · OSTI ID:1867523

Holz, Simon ; Hanhart, Christoph ; Hoferichter, Martin ; Kubis, Bastian

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

• Sponsoring Organization: USDOE
• Grant/Contract Number: FG02-00ER41132
• OSTI ID: 1867523
• Alternate ID(s): OSTI ID: 1904706; OSTI ID: 23157638
• Journal Information: European Physical Journal. C, Particles and Fields (Online), Journal Name: European Physical Journal. C, Particles and Fields (Online) Journal Issue: 5 Vol. 82; ISSN 1434-6052
• Publisher: Springer Science + Business MediaCopyright Statement
• Country of Publication: Germany
• Language: English