Abstract
Following updates in the compilation of $e^+e^-\rightarrow{\rm hadrons}$ data, this work presents re-evaluations of the hadronic vacuum polarisation contributions to the anomalous magnetic moment of the electron ($a_e$), muon ($a_\mu$) and tau lepton ($a_\tau$), to the ground-state hyperfine splitting of muonium and also updates the hadronic contributions to the running of the QED coupling at the mass scale of the $Z$ boson, $\alpha(M_Z^2)$. Combining the results for the hadronic vacuum polarisation contributions with recent updates for the hadronic light-by-light corrections, the electromagnetic and the weak contributions, the deviation between the measured value of $a_\mu$ and its Standard Model prediction amounts to $\Delta a_{\mu} = (28.02 \pm 7.37) \times 10^{-10}$, corresponding to a muon $g-2$ discrepancy of $3.8\sigma$.
Highlights
For the charged leptons (l 1⁄4 e, μ, τ), the study of their anomalous magnetic moment, al 1⁄4 ðg − 2Þl=2, continues to serve as a long-standing test of the Standard Model (SM) and as a powerful indirect search for new physics
Combining the results for the hadronic vacuum polarization contributions with recent updates for the hadronic light-bylight corrections, the electromagnetic and the weak contributions, the deviation between the measured value of aμ and its Standard Model prediction amounts to Δaμ 1⁄4 ð28.02 Æ 7.37Þ × 10−10, corresponding to a muon g − 2 discrepancy of 3.8σ
The SM prediction of the anomalous magnetic moment is determined by summing the contributions from all sectors of the SM, such that aSl M 1⁄4 aQl ED þ aEl W þ ahl ad;vacuum polarization (VP) þ ahl ad;LbL; ð1:1Þ
Summary
For the charged leptons (l 1⁄4 e, μ, τ), the study of their anomalous magnetic moment, al 1⁄4 ðg − 2Þl=2, continues to serve as a long-standing test of the Standard Model (SM) and as a powerful indirect search for new physics. It is clear that the comparison of Δaτ 1⁄4 aeτxp − aSτ M is insignificant due to the current insufficient accuracy of aeτxp, the determination of aSτ M is an interesting undertaking and may prove useful, should experimental techniques improve to be able to better probe the anomaly of the τ lepton It follows that this work, denoted KNT19, will update the hadronic vacuum polarization contributions to al 1⁄4 ðg − 2Þl=2 for all l 1⁄4 e, μ, τ. A recent study of the three-pion contribution to the hadronic vacuum polarization based on a global fit function using analyticity and unitarity constraints [38] highlighted major differences arising in various determinations of aπμþπ−π0 These were attributed to the choice of cross section interpolation used in the prominent ω resonance region when integrating the data. The resulting KNT19 determination of the ω resonance in the πþπ−π0 channel and all contributing data are shown in
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