The muon $g-2$: a brief overview of hadronic cross section data

Abstract

The hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon, $a_{\mu}^{\rm had, VP}$ are evaluated dispersively via a combination of experimentally measured $e^+e^-\rightarrow {\rm hadrons}$ cross section data. Many experiments have dedicated programmes to precisely measure these final states, meaning that a vast amount of data is now available and that, in some cases, overall precision has reached the sub-percent level. However, data tensions are evident between measurements of the same hadronic channels from different experiments, which reduces the overall quality of the data combinations used to determine $a_{\mu}^{\rm had, \, VP}$. The inclusion of these data in the KNT18 analysis results in $a_{\mu}^{\rm had, \, LO \, VP} = (693.26 \pm 2.46)\times 10^{-10}$ and $a_{\mu}^{\rm had, \, NLO \, VP} = (-9.82 \pm 0.04)\times 10^{-10}$. The corresponding new estimate for the Standard Model prediction is found to be $a_{\mu}^{\rm SM} = (11\ 659 \ 182.04 \pm 3.56) \times 10^{-10}$, which is $3.7\sigma$ below the current experimental measurement.