The hadronic vacuum polarisation contributions to the muon $g-2$

Abstract

The hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon, $a_{\mu}^{\rm had, VP}$ have been re-evaluated from the combination of $e^+e^-\rightarrow {\rm hadrons}$ cross section data. Focus has been placed on the development of a new data combination method, which fully incorporates all correlated statistical and systematic uncertainties in a bias free approach. Using these combined data have resulted in estimates of the hadronic vacuum polarisation contributions to $g-2$ of the muon of $a_{\mu}^{\rm had, \, LO \, VP} = (693.27 \pm 2.46)\times 10^{-10}$ and $a_{\mu}^{\rm had, \, NLO \, VP} = (-9.82 \pm 0.04)\times 10^{-10}$. The new estimate for the Standard Model prediction is found to be $a_{\mu}^{\rm SM} = (11\ 659 \ 182.05 \pm 3.56) \times 10^{-10}$, which is $3.7\sigma$ below the current experimental measurement. In addition, the prediction for the hadronic contribution to the QED coupling at the $Z$ boson mass has been calculated to be $\Delta\alpha_{\rm had}^{(5)}(M_Z^2)= (276.11 \pm 1.11)\times 10^{-4}$, resulting in $\alpha^{-1}(M_Z^2) = 128.946 \pm 0.015$.