Extracting the chiral anomaly from $e^{+}{e}^{-}\to 3\pi$

Abstract

The strength of the interaction of three pions and a photon, $F_{3\pi }$ is predicted by the axial anomaly in terms of the pion decay constant, a relation that is frequently used to constrain low-energy radiative processes involving pions, but only tested experimentally at the $10\%$ level. Here, we present a new avenue to test this prediction, via a fit of a dispersive description of the ${\gamma }^{\ast }\to 3\pi$ amplitude to data for $e^{+}{e}^{-}\to 3\pi$. From the global fit to SND, CMD-2, and BaBar data we obtain $F_{3\pi }=33.1(1.7){\text{GeV}}^{-3}$, in agreement with the chiral prediction at the level of $5\%$. We also consider dispersive fits to the recent data by Belle II, in which case we observe tensions with the dispersive constraints, the width parameters of $\omega$ and $\varphi$, and the chiral anomaly.

17 pages, 1 figure; journal version

References in corpus (24)

• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order
• Towards a data-driven analysis of hadronic light-by-light scattering
• Dispersive analysis of omega --> 3pi and phi --> 3pi decays
• Dispersive analysis of the pion transition form factor
• Extracting the chiral anomaly from gamma pi --> pi pi
• Anomalous decay and scattering processes of the eta meson
• Kaon electromagnetic form factors in dispersion theory
• Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization
• Radiative resonance couplings in $\gamma \pi \to \pi \pi$
• A phenomenological estimate of isospin breaking in hadronic vacuum polarization
• Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• Dispersion relation for hadronic light-by-light scattering: subleading contributions
• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
• A dispersive analysis of ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ and ${\eta }^{\prime }\to {\ell }^{+}{\ell }^{-}\gamma$
• Dispersion relations for the hadronic VVA correlator
• Precision evaluation of the $\eta$- and ${\eta }^{\prime }$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Dispersive analysis of the Primakoff reaction $\gamma K\to K\pi$
• From pole parameters to line shapes and branching ratios
• Axion-meson mixing in light of recent lattice $\eta$-${\eta }^{\prime }$ simulations and their two-photon couplings within $U(3)$ chiral theory
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$
• Timelike form factor for the anomalous process ${\gamma }^{\ast }\pi \to \pi \pi$
• Polarizabilities from kaon Compton scattering

Cited by in corpus (1)

• The anomalous magnetic moment of the muon in the Standard Model: an update