A phenomenological estimate of isospin breaking in hadronic vacuum polarization

Abstract

Puzzles in the determination of the hadronic-vacuum-polarization contribution currently impede a conclusive interpretation of the precision measurement of the anomalous magnetic moment of the muon at the Fermilab experiment. One such puzzle concerns tensions between evaluations in lattice QCD and using $e^{+}{e}^{-}\to \text{hadrons}$ cross-section data. In lattice QCD, the dominant isospin-symmetric part and isospin-breaking (IB) corrections are calculated separately, with very different systematic effects. Identifying these two pieces in a data-driven approach provides an opportunity to compare them individually and trace back the source of the discrepancy. Here, we estimate the IB component of the lattice-QCD calculations from phenomenology, based on a comprehensive study of exclusive contributions that can be enhanced via infrared singularities, threshold effects, or hadronic resonances, including, for the first time, in the $e^{+}{e}^{-}\to 3\pi$ channel. We observe sizable cancellations among different channels, with a sum that even suggests a slightly larger result for the QED correction than obtained in lattice QCD. We conclude that the tensions between lattice QCD and $e^{+}{e}^{-}$ data therefore cannot be explained by the IB contributions in the lattice-QCD calculations.

7 pages, 2 figures; journal version

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Cited by in corpus (21)

• The anomalous magnetic moment of the muon in the Standard Model: an update
• An optimized basis for hadronic light-by-light scattering
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• Dispersion relation for hadronic light-by-light scattering: subleading contributions
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• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
• Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
• Precision evaluation of the $\eta$- and ${\eta }^{\prime }$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Isospin breaking corrections in $2\pi$ production in tau decays and $e^{+}{e}^{-}$ annihilation: consequences for the muon $g-2$ and CVC tests
• Improved evaluation of the electroweak contribution to muon $g-2$
• Improved Standard-Model prediction for $K_L\to {\ell }^{+}{\ell }^{-}$
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$
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