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Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization

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arxiv 2208.08993 v2 pith:2PZU43HC submitted 2022-08-18 hep-ph hep-exhep-latnucl-th

Gilberto Colangelo , Martin Hoferichter , Bastian Kubis , Peter Stoffer This is my paper · ORCID
classification hep-phhep-exhep-latnucl-th
keywords omegacontributionepsilongammatwo-pioncircdatadelta
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Isospin-breaking (IB) effects in the two-pion contribution to hadronic vacuum polarization (HVP) can be resonantly enhanced, if related to the interference of the $\rho(770)$ and $\omega(782)$ resonances. This particular IB contribution to the pion vector form factor and thus the line shape in $e^+e^-\to \pi^+\pi^-$ can be described by the residue at the $\omega$ pole - the $\rho$-$\omega$ mixing parameter $\epsilon_\omega$. Here, we argue that while in general analyticity requires this parameter to be real, the radiative channels $\pi^0\gamma$, $\pi\pi\gamma$, $\eta\gamma$ can induce a small phase, whose size we estimate as $\delta_\epsilon=3.5(1.0)^\circ$ by using a narrow-width approximation for the intermediate-state vector mesons. We then perform fits to the $e^+e^-\to \pi^+\pi^-$ data base and study the consequences for the two-pion HVP contribution to the anomalous magnetic moment of the muon, its IB part due to $\rho$-$\omega$ mixing, and the mass of the $\omega$ resonance. We find that the global fit does prefer a non-vanishing value of $\delta_\epsilon=4.5(1.2)^\circ$, close to the narrow-resonance expectation, but with a large spread among the data sets, indicating systematic differences in the $\rho$-$\omega$ region.

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Cited by 5 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.

  5. A dispersive method to study CP asymmetries in hadronic multi-body $B$ decays

    hep-ph 2026-07 conditional novelty 5.0 of 10

    The large localized CP asymmetry in B±→K±π+π− arises from a dip in the CP-conserving rate, not enhanced CP violation, and the non-resonant isospin-2 S-wave is essential — per a 13-parameter dispersive fit to LHCb's an...

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