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 $a_{\mu }^{\exp }$ at $2\sigma$ level.

11 pages, 5 figures