The anomalous magnetic moment of the muon in the Standard Model: an update

Abstract

We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, $a_{\mu }$, updating the first White Paper (WP20) [1]. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two. The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%. Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads $a_{\mu }^{\text{SM}}=116592033(62)\times 10^{-11}$ (530 ppb). When compared against the current experimental average based on the E821 experiment and runs 1-6 of E989 at Fermilab, one finds $a_{\mu }^{\text{exp}}-a_{\mu }^{\text{SM}}=38(63)\times 10^{-11}$, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 (127 ppb) is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor.

arXiv comment188 pages, 83 figures; $a_{\mu }^{\text{exp}}$ updated to final result of the Fermilab experiment, SM prediction unchanged; journal version

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• Two-pion low-energy contribution to the muon $g-2$ with improved precision from analyticity and unitarity
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• Radiative corrections to $\tau \to \pi (K){\nu }_{\tau }[\gamma ]$: a reliable new physics test
• Dispersion relation for hadronic light-by-light scattering: subleading contributions
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• Muon-electron scattering at NLO
• Towards muon-electron scattering at NNLO
• Vector two-point functions in finite volume using partially quenched chiral perturbation theory
• Dispersion relations for hadronic light-by-light scattering in triangle kinematics
• Data-driven dispersive analysis of the $\pi \pi$ and $\pi K$ scattering
• Improved ${\pi }^0,\eta ,{\eta }^{\prime }$ transition form factors in resonance chiral theory and their $a_{\mu }^{\mathrm{HLbL}}$ contribution
• Hadronic light-by-light contribution to $(g-2{)}_{\mu }$ from lattice QCD with SU(3) flavor symmetry
• Dissecting the hadronic contributions to $(g-2{)}_{\mu }$ by Schwinger's sum rule
• Solving integral equations in $\eta \to 3\pi$
• Pion electromagnetic formfactor in the space-like region and $P$-phase ${\delta }_1^1(s)$ of $\pi \pi$ scattering from the value of the modulus of formfactor in the time-like region.
• The LBK theorem to all orders
• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
• $\tau$ data-driven evaluation of Euclidean windows for the hadronic vacuum polarization
• Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization
• Measurement of the integrated luminosity of data samples collected during 2019-2022 by the Belle II experiment
• The width difference of rho vector mesons
• Massive three-loop form factors: anomaly contribution
• Pseudoscalar transition form factors and the hadronic light-by-light contribution to the anomalous magnetic moment of the muon from holographic QCD
• Vacuum correlators at short distances from lattice QCD
• Dispersion relations for the hadronic VVA correlator
• Model-dependent radiative corrections to tau- -> pi- pi0 nu revisited
• Exploratory studies for the position-space approach to hadronic light-by-light scattering in the muon $g-2$
• Lattice QCD calculation of ${\pi }^0\to e^{+}{e}^{-}$ decay
• Sum rule for the Compton amplitude and implications for the proton-neutron mass difference
• Exclusive tensor meson photoproduction
• Model Independent Tests of the Hadronic Vacuum Polarization Contribution to the Muon $g$$-$$2$
• Hadronic vacuum polarization contributions to the muon $g$-2 in the space-like region
• Hadronic light-by-light scattering contribution to the muon g-2 on the lattice
• Search for direct production of the $f_1(1285)$ resonance in $e^{+}{e}^{-}$ collisions
• Two and Three Pseudoscalar Production in $e^{+}{e}^{-}$ annihilation and their contributions to $(g-2{)}_{\mu }$
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• One-loop determination of $\tau \to \pi (K){\nu }_{\tau }[\gamma ]$ branching ratios and new physics tests
• Scalar resonances in the hadronic light-by-light contribution to the muon $(g-2)$
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