Lattice QCD calculation of ${\pi }^0\to e^{+}{e}^{-}$ decay

Abstract

We extend the application of lattice QCD to the two-photon-mediated, order ${\alpha }^2$ rare decay ${\pi }^0\to e^{+}{e}^{-}$. By combining Minkowski- and Euclidean-space methods we are able to calculate the complex amplitude describing this decay directly from the underlying theories (QCD and QED) which predict this decay. The leading connected and disconnected diagrams are considered; a continuum limit is evaluated and the systematic errors are estimated. We find $\mathrm{Re}\mathcal{A}=18.60(1.19)(1.04)$eV, $\mathrm{Im}\mathcal{A}=32.59(1.50)(1.65)$eV, a more accurate value for the ratio $\frac{\mathrm{Re}\mathcal{A}}{\mathrm{Im}\mathcal{A}}=0.571(10)(4)$ and a result for the partial width $\Gamma ({\pi }^0\to \gamma \gamma )=6.60(0.61)(0.67)$eV. Here the first errors are statistical and the second systematic. This calculation is the first step in determining the more challenging, two-photon-mediated decay amplitude that contributes to the rare decay $K\to {\mu }^{+}{\mu }^{-}$.

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Cited by in corpus (8)

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• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
• First-principle calculation of ${\eta }_c\to 2\gamma$ decay width from lattice QCD
• Precision evaluation of the $\eta$- and ${\eta }^{\prime }$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• First lattice QCD calculation of $J/\psi$ semileptonic decay containing $D$ and $D_s$ particles
• Improved Standard-Model prediction for $K_L\to {\ell }^{+}{\ell }^{-}$
• Radiative corrections to leptonic decays using infinite-volume reconstruction
• Workshop summary -- Kaons@CERN 2023