A dispersive analysis of $$\varvec{\eta '\rightarrow \pi ^+\pi ^-\gamma }$$ η ′ → π + π - γ and $$\varvec{\eta '\rightarrow \ell ^+\ell ^-\gamma }$$ η ′ → ℓ + ℓ - γ

Autor: Simon Holz, Christoph Hanhart, Martin Hoferichter, Bastian Kubis
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: European Physical Journal C: Particles and Fields, Vol 82, Iss 5, Pp 1-17 (2022)
Druh dokumentu: article
ISSN: 1434-6052
DOI: 10.1140/epjc/s10052-022-10247-7
Popis: Abstract We present a dispersive representation of the $$\eta '$$ η ′ transition form factor that allows one to account, in a consistent way, for the effects of $$\rho $$ ρ – $$\omega $$ ω mixing in both the isoscalar and the isovector contributions. Using this formalism, we analyze recent data on $$\eta '\rightarrow \pi ^+\pi ^-\gamma $$ η ′ → π + π - γ 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 $$\rho $$ ρ – $$\omega $$ ω 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 $$\eta '\rightarrow \ell ^+\ell ^-\gamma $$ η ′ → ℓ + ℓ - γ , in particular we find the slope parameter $$b_{\eta '}=1.455(24)\,\text {GeV}^{-2}$$ b η ′ = 1.455 ( 24 ) GeV - 2 . With forthcoming data on the latter process, our results establish the necessary framework to improve the evaluation of the $$\eta '$$ η ′ -pole contribution to the anomalous magnetic moment of the muon using experimental input from both $$\eta '$$ η ′ decay channels.
Databáze: Directory of Open Access Journals
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