Dispersive estimation of the LO hadronic contribution to the muon ${g-2}$: fitting incompatible ${e^+e^-}$ data

Abstract

Using an up-to-date compilation of $\sigma_{\mathrm{tot}}(e^+e^- \to hadrons)$ data we estimated the LO hadronic contribution to the muon anomalous magnetic moment, $a_\mu(had,LO)$. Incompatibilities between $\sigma_{\mathrm{tot}}(e^+e^- \to hadrons)$ measurements by independent experiments are mitigated by extra systematic uncertainties estimated using as a guideline a requirement of uniformity of $\chi^2$ distribution over degrees of freedom in joint fits of $\sigma_{\mathrm{tot}}$. Tensions in the $e^+e^-$ input data translate into an expanded uncertainty of the $a_\mu(had,LO) = (697.7 \pm {9.8}_{e^+e^-} \pm 3.6_{sys}) \times 10^{-10}$. Given this, we obtain the SM prediction for the muon anomaly $a_\mu^{\mathrm{SM}} = 11659185.5(10.6) \times 10^{-10}$, below the experimental world average $a_\mu^{\mathrm{exp}}$ at $2\sigma$ level.