The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations

Abstract

We propose a formalism to extract the $\gamma \pi \to \pi \pi$ chiral anomaly $F_{3\pi }$ from calculations in lattice QCD performed at larger-than-physical pion masses. To this end, we start from a dispersive representation of the ${\gamma }^{(\ast )}\pi \to \pi \pi$ amplitude, whose main quark-mass dependence arises from the $\pi \pi$ scattering phase shift and can be derived from chiral perturbation theory via the inverse-amplitude method. With parameters constrained by lattice calculations of the $P$-wave phase shift, we use this combination of dispersion relations and effective field theory to extrapolate two recent ${\gamma }^{(\ast )}\pi \to \pi \pi$ calculations in lattice QCD to the physical point. Our formalism allows us to extract the radiative coupling of the $\rho (770)$ meson and, for the first time, the chiral anomaly $F_{3\pi }=38(16)(11){\text{GeV}}^{-3}$. The result is consistent with the chiral prediction albeit within large uncertainties, which will improve in accordance with progress in future lattice-QCD computations.

arXiv comment29 pages, 5 figures; version published in JHEP: high-energy continuation of phase explained in more detail

References in corpus (99)

• The anomalous magnetic moment of the muon in the Standard Model
• Leading hadronic contribution to the muon magnetic moment from lattice QCD
• FLAG Review 2019
• The muon $g-2$ and $\alpha (M_Z^2)$: a new data-based analysis
• Complete Tenth-Order QED Contribution to the Muon g-2
• 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
• Lattice calculation of the pion transition form factor with $N_f=2+1$ Wilson quarks
• Scattering processes and resonances from lattice QCD
• Longitudinal short-distance constraints for the hadronic light-by-light contribution to $(g-2{)}_{\mu }$ with large-$N_c$ Regge models
• The inverse amplitude method in Chiral Perturbation Theory
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• Dispersion relation for hadronic light-by-light scattering: theoretical foundations
• Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis
• Coupled $\pi \pi ,K\overline{K}$ scattering in $P$-wave and the $\rho$ resonance from lattice QCD
• Hadronic vacuum polarization: $(g-2{)}_{\mu }$ versus global electroweak fits
• Towards a data-driven analysis of hadronic light-by-light scattering
• The muon $g$-2 and $\Delta \alpha$ connection
• Mesonic low-energy constants
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• A global fit of $\pi \pi$ and $\pi K$ elastic scattering in ChPT with dispersion relations
• 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
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Lattice QCD and Three-particle Decays of Resonances
• Constraints on the two-pion contribution to hadronic vacuum polarization
• Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon
• Consistency of hadronic vacuum polarization between lattice QCD and the R-ratio
• Multichannel one-to-two transition amplitudes in a finite volume
• Dispersive analysis of omega --> 3pi and phi --> 3pi decays
• Dispersive analysis of the pion transition form factor
• $I=1$ and $I=2$ $\pi -\pi$ scattering phase shifts from $N_{\mathrm{f}}=2+1$ lattice QCD
• KK bar scattering amplitude to one loop in chiral perturbation theory, its unitarization and pion form factors
• The $I=1$ pion-pion scattering amplitude and timelike pion form factor from $N_{\mathrm{f}}=2+1$ lattice QCD
• Chiral Perturbation Theory for Vector Mesons
• $P$-wave $\pi \pi$ scattering and the $\rho$ resonance from lattice QCD
• Rho resonance parameters from lattice QCD
• Extracting the chiral anomaly from gamma pi --> pi pi
• Hadronic light-by-light contribution to $(g-2{)}_{\mu }$ from lattice QCD: a complete calculation
• Unified dispersive approach to real and virtual photon-photon scattering at low energy
• The Inverse Amplitude Method and Adler Zeros
• $\rho$ and $K^{\ast }$ resonances on the lattice at nearly physical quark masses and $N_f=2$
• Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• The $\pi \pi \to \pi {\gamma }^{\star }$ amplitude and the resonant $\rho \to \pi {\gamma }^{\star }$ transition from lattice QCD
• Impact of correlations between $a_{\mu }$ and ${\alpha }_{QED}$ on the EW fit
• On the transition form factors of the axial-vector resonance $f_1(1285)$ and its decay into $e^{+}{e}^{-}$
• Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results
• The resonant ${\pi }^{+}\gamma \to {\pi }^{+}{\pi }^0$ amplitude from Quantum Chromodynamics
• The Low Energy Constants of $SU(2)$ Partially Quenched Chiral Perturbation Theory from $N_f=2+1$ Domain Wall QCD
• A dispersive estimate of scalar contributions to hadronic light-by-light scattering
• SU(2) chiral perturbation theory low-energy constants from 2+1 flavor staggered lattice simulations
• Lattice QCD at the physical point meets SU(2) chiral perturbation theory
• Hadronic vacuum polarization and vector-meson resonance parameters from $e^{+}{e}^{-}\to {\pi }^0\gamma$
• Asymptotic behavior of meson transition form factors
• The energy-dependent ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ scattering amplitude from QCD
• The two-loop perturbative correction to the (g-2)${}_{\mu }$ HLbL at short distances
• Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update
• Short-distance HLbL contributions to the muon anomalous magnetic moment beyond perturbation theory
• Radiative resonance couplings in $\gamma \pi \to \pi \pi$
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Scattering of two and three physical pions at maximal isospin from lattice QCD
• Studying the $\rho$ resonance parameters with staggered fermions
• The Inverse Amplitude Method in $\pi \pi$ Scattering in Chiral Perturbation Theory to Two Loops
• The $\pi \gamma \to \pi \pi$ transition and the $\rho$ radiative decay width from lattice QCD
• Electromagnetic Contributions to Vector Meson Masses and Mixings
• Study of the reaction $e^{+}{e}^{-}\to {\pi }^0\gamma$ with the SND detector at the VEPP-2M collider
• Vector Meson Masses in Chiral Perturbation Theory
• Effects of Longitudinal Short-Distance Constraints on the Hadronic Light-by-Light Contribution to the Muon $g-2$
• Pion scattering in the isospin I=2 channel from elongated lattices
• Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarisation
• Quark mass dependence of the pion vector form factor
• Electromagnetic form factor of the pion
• Two-loop analysis of the pion-mass dependence of the $\rho$ meson
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: The $\rho$-resonance
• The $\rho$-resonance with physical pion mass from $N_f=2$ lattice QCD
• Electromagnetic corrections to gamma pi(+) -> pi(0) pi(+)
• SU(2) Low-Energy Constants from Mixed-Action Lattice QCD
• Constraining $1+\mathcal{J}\to 2$ coupled-channel amplitudes in finite-volume
• Quark-mass dependence in $\omega \to 3\pi$ decays
• Leading logarithms in the anomalous sector of two-flavour QCD
• The anomalous process gamma pi -> pi pi to two loops
• Chiral Anomaly and $\gamma 3\pi$
• Solving integral equations in $\eta \to 3\pi$
• $I=0$ $\pi \pi$ $s$-wave scattering length from lattice QCD
• 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
• Dispersive analysis of the Primakoff reaction $\gamma K\to K\pi$

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