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.

arXiv comment17 pages, 1 figure; journal version

References in corpus (69)

• The anomalous magnetic moment of the muon in the Standard Model
• The QCD axion, precisely
• The muon $g-2$ and $\alpha (M_Z^2)$: a new data-based analysis
• Refinements in electroweak contributions to the muon anomalous magnetic moment
• Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon g-2 and alpha(mZ) using newest hadronic cross-section data
• Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment revisited
• 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
• Two-pion contribution to hadronic vacuum polarization
• The electroweak contributions to (g-2)_μ after the Higgs boson mass measurement
• Remarks on higher-order hadronic corrections to the muon g-2
• Dispersion relation for hadronic light-by-light scattering: two-pion contributions
• The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD
• Three-pion contribution to hadronic vacuum polarization
• Dispersion relation for hadronic light-by-light scattering: pion pole
• Pseudoscalar-pole contribution to the $(g_{\mu }-2)$: a rational approach
• Short-distance constraints for the HLbL contribution to the muon anomalous magnetic moment
• Longitudinal short-distance constraints for the hadronic light-by-light contribution to $(g-2{)}_{\mu }$ with large-$N_c$ Regge models
• Dispersion relation for hadronic light-by-light scattering: theoretical foundations
• Towards a data-driven analysis of hadronic light-by-light scattering
• Dispersive approach to hadronic light-by-light scattering
• Pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Dispersive analysis of omega --> 3pi and phi --> 3pi decays
• Dispersive analysis of the pion transition form factor
• The anomalous chiral Lagrangian of order $p^6$
• omega --> pi0 gamma* and phi --> pi0 gamma* Transition form factors in dispersion theory
• Fitting Parton Distribution Data with Multiplicative Normalization Uncertainties
• A new Parameterization for the Pion Vector Form Factor
• Dispersive analysis for $\eta \to \gamma {\gamma }^{\ast }$
• Extracting the chiral anomaly from gamma pi --> pi pi
• Unified dispersive approach to real and virtual photon-photon scattering at low energy
• The decay pi0 to gamma gamma to next to leading order in Chiral Perturbation Theory
• Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Chiral expansions of the pi0 lifetime
• Electromagnetic corrections in the anomaly sector
• Anomalous decay and scattering processes of the eta meson
• Model-independent approach to eta -> pi+ pi- gamma and eta' -> pi+ pi- gamma
• Kaon electromagnetic form factors in dispersion theory
• On the transition form factors of the axial-vector resonance $f_1(1285)$ and its decay into $e^{+}{e}^{-}$
• The resonant ${\pi }^{+}\gamma \to {\pi }^{+}{\pi }^0$ amplitude from Quantum Chromodynamics
• A new parametrization for the scalar pion form factors
• Hadronic vacuum polarization and vector-meson resonance parameters from $e^{+}{e}^{-}\to {\pi }^0\gamma$
• Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization
• Radiative resonance couplings in $\gamma \pi \to \pi \pi$
• Time-like and space-like electromagnetic form factors of nucleons, a unified description
• Calculation of the anomalous $\gamma {\pi }^{\ast }\to \pi \pi$ form factor
• A phenomenological estimate of isospin breaking in hadronic vacuum polarization
• Towards an improved understanding of $\eta \to {\gamma }^{\ast }{\gamma }^{\ast }$
• Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
• Electromagnetic corrections to gamma pi(+) -> pi(0) pi(+)
• Dispersion relation for hadronic light-by-light scattering: subleading contributions
• The anomalous process gamma pi -> pi pi to two loops
• Leading logarithms in the anomalous sector of two-flavour QCD
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• Chiral Anomaly and $\gamma 3\pi$
• 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
• On the scalar $\pi K$ form factor beyond the elastic region
• A new determination of the $\gamma \pi \to \pi \pi$ anomalous amplitude via ${\pi }^{-}{e}^{-}\to {\pi }^{-}{e}^{-}{\pi }^0$ data
• Study of $\gamma \pi \to \pi \pi$ below 1 GeV using Integral Equation Approach
• 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
• Axial anomaly and the interplay of quark loops with pseudoscalar and vector mesons in the gamma* --> pi+ pi0 pi- process

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