A comment on the impact of CMD-3 $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ cross section measurement on the SM $g_{\mu }-2$ value

Abstract

We estimated an impact of the recent CMD-3 measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ total cross section at $0.3<\sqrt{s}<1.2$ GeV on the leading order hadronic contribution $a_{\mu }^{had,LO}$ to the muon anomalous magnetic moment $a_{\mu }=(g_{\mu }-2)/2$, in presence of comparably precise ISR measurements of the cross section by BaBar and KLOE experiments being in significant tension with the CMD-3. Assuming that all the experiments are affected by yet unidentified systematic effects, to account for the latter, we scaled the experimental uncertainties following the PDG prescription, thus facilitating a consistent joint fit of the world data on the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ total cross section. The same procedure was applied in all $e^{+}{e}^{-}\to hadrons$ channels contributing to the dispersive estimate of $a_{\mu }^{had,LO}$. Despite an inclusion of the new CMD-3 ${\pi }^{+}{\pi }^{-}$ data, our estimate $a_{\mu }^{had,LO}(e^{+}{e}^{-})=(696.2\pm 2.9)\times 10^{-10}$ is consistent with $a_{\mu }^{had,LO}(e^{+}{e}^{-})$ values obtained by other authors before publication of the CMD-3 result. Including our $a_{\mu }^{had,LO}$ value into the SM prediction for $a_{\mu }$, we obtain $a_{\mu }^{SM}=(11659184\pm 4_{\mathrm{tot}})\times 10^{-10}$ which is by $4.7\sigma$ smaller than the world average for the experimental value $a_{\mu }^{exp}=(11659205.9\pm 2.2)\times 10^{-10}$. We confirm the observation by the CMD-3 authors that their $\sigma (e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-})$ measurement, when taken alone, implies the $a_{\mu }^{SM}$ prediction consistent with the $a_{\mu }^{exp}$ at $\sim 1\sigma$ level.

Comments: The note contains a comprehensive bibliography on the total e+e- --> hadrons cross section measurements at sqrt(s) < 12 GeV