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

The hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon, $a_{\mu }^{\mathrm{h}\mathrm{a}\mathrm{d},\mathrm{V}\mathrm{P}}$ have been re-evaluated from the combination of $e^{+}{e}^{-}\to \mathrm{h}\mathrm{a}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{n}\mathrm{s}$ 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 $a_{\mu }^{\mathrm{h}\mathrm{a}\mathrm{d},\mathrm{L}\mathrm{O}\mathrm{V}\mathrm{P}}=(693.27\pm 2.46)\times {10}^{-10}$ and $a_{\mu }^{\mathrm{h}\mathrm{a}\mathrm{d},\mathrm{N}\mathrm{L}\mathrm{O}\mathrm{V}\mathrm{P}}=(-9.82\pm 0.04)\times {10}^{-10}$. The new estimate for the Standard Model prediction is found to be $a_{\mu}^{\rm SM} = (11\ 659 \ 182.05 \pm 3.56) \times 10^{-10}$,whichis$3.7\sigma$ 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 $\mathrm{\Delta }{\alpha }_{\mathrm{h}\mathrm{a}\mathrm{d}}^{(5)}(M_Z^2)=(276.11\pm 1.11)\times {10}^{-4}$, resulting in ${\alpha }^{-1}(M_Z^2)=128.946\pm 0.015$.