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A phenomenological estimate of isospin breaking in hadronic vacuum polarization

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arxiv 2307.02532 v2 pith:7KCWNFM3 submitted 2023-07-05 hep-ph hep-exhep-latnucl-th

Martin Hoferichter , Gilberto Colangelo , Bai-Long Hoid , Bastian Kubis , Jacobo Ruiz de Elvira , Dominic Schuh , Dominik Stamen , Peter Stoffer This is my paper · ORCID
classification hep-phhep-exhep-latnucl-th
keywords latticecalculationscontributionsdatadifferenteffectsestimatehadronic
verification ladder T0 review T1 audit T2 compute T3 formal
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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 $e^+e^-\to3\pi$ 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.

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Cited by 4 Pith papers

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  1. Pion $\beta$ decay and $\tau\to\pi\pi\nu_\tau$ beyond leading logarithms

    hep-ph 2026-02 conditional novelty 7.0 of 10

    Pion β decay and τ→ππν short-distance radiative corrections are matched at NLL accuracy with evanescent-scheme dependence cancelled, giving Δ_RC^{πℓ}=0.03403(11) and a τ-HVP isospin-breaking shift of −0.07(4)×10^-10.

  2. Radiative return at NLOPS accuracy

    hep-ph 2026-01 conditional novelty 7.0 of 10

    First implementation of NLO corrections matched to a parton shower for the radiative processes e+e−→π+π−γ and e+e−→μ+μ−γ, including ISR, FSR and their interference.

  3. Comparison of the hadronic vacuum polarization between hadronic $\tau$-decay data and lattice QCD

    hep-ph 2026-05 unverdicted novelty 6.0 of 10

    Lattice QCD and tau-decay dispersive calculations of isospin-one HVP generally agree, except for a significant difference in the 2π−π+π0 four-pion mode contribution to window quantities.

  4. Isospin-violating vacuum polarization in the muon $(g-2)$ with SU(3) flavour symmetry from lattice QCD

    hep-lat 2025-05 conditional novelty 6.0 of 10

    First lattice QCD determination of the isospin-violating (3,8) hadronic vacuum polarization contribution to muon (g-2), giving 2 aµ^{HVP,38} = 21.8(3.1) × 10^{-11} at Mπ=MK≈416 MeV.

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