Hadronic vacuum polarization and vector-meson resonance parameters from $$\varvec{e^+e^-\rightarrow \pi ^0\gamma }$$
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Regular Article - Theoretical Physics
Hadronic vacuum polarization and vector-meson resonance parameters from e+ e− → π 0 γ Bai-Long Hoid1,a , Martin Hoferichter2 , Bastian Kubis1 1 2
Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
Received: 29 July 2020 / Accepted: 13 October 2020 © The Author(s) 2020
Abstract We study the reaction e+ e− → π 0 γ based on a dispersive representation of the underlying π 0 → γ γ ∗ transition form factor. As a first application, we evaluate the contribution of the π 0 γ channel to the hadronic-vacuumpolarization correction to the anomalous magnetic moment π 0γ of the muon. We find aμ ≤1.35 GeV = 43.8(6) × 10−11 , in line with evaluations from the direct integration of the data. Second, our fit determines the resonance parameters of ω and φ. We observe good agreement with the e+ e− → 3π channel, explaining a previous tension in the ω mass between π 0 γ and 3π by an unphysical phase in the fit function. Combining both channels we find M¯ ω = 782.736(24) MeV and M¯ φ = 1019.457(20) MeV for the masses including vacuumpolarization corrections. The φ mass agrees perfectly with the PDG average, which is dominated by determinations from the K¯ K channel, demonstrating consistency with 3π and π 0 γ . For the ω mass, our result is consistent but more precise, exacerbating tensions with the ω mass extracted via isospinbreaking effects from the 2π channel.
1 Introduction The vector mesons ω and φ are narrow states compared to other hadronic resonances in the low-energy QCD spectrum. In the case of the ω, this is because two-body decays are either forbidden by G parity (2π ) or require electromagnetic interactions (π 0 γ , ηγ ), so that the dominant decay proceeds into 3π . In contrast, for the φ a G-parity conserving two-body decay into K¯ K is possible, but suppressed by very small phase space, while the decay into 3π is small due to the Okubo–Zweig–Iizuka rule [1–3]. Accordingly, the most precise information on the mass of the φ comes from e+ e− → K¯ K [4–8], which indeed dominates the PDG average [9]. For the determination of the ω mass, the reaction a e-mail:
e+ e− → 3π is the primary source of information [5,10], but here the three-particle nature of the decay complicates a reliable extraction of the resonance parameters. In particular, there is a significant tension with the mass determination from e+ e− → π 0 γ [11], which together with p¯ p → ωπ 0 π 0 [12] leads to a scale factor S = 1.9 in the PDG average. In this work, we consider the reaction e+ e− → π 0 γ using a dispersive representation of the π 0 → γ γ ∗ transition form factor (TFF), which together with our previous work on the 3π channel [13] allows us to present a combined determination of the ω and φ resonance parameters within the same framework consistent with the constraints from analytic
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