The SM prediction of g-2 of the muon

TL;DR

The paper addresses the precision SM prediction of the muon anomalous magnetic moment $a_\mu$ by refining the hadronic vacuum polarization contribution $a_\mu^{\rm had,LO}$. It adopts a data-driven approach that combines all available $e^+e^- \to {\rm hadrons}$ cross-sections (both exclusive and inclusive), applies a nonlinear $\chi^2$ clustering to merge datasets, and uses QCD sum rules to resolve a notable discrepancy in the $1.43<\sqrt{s}<2$ GeV region. The main result is $a_\mu^{\rm had,LO} = (683.1 \pm 5.9_{\rm exp} \pm 2.0_{\rm rad}) \times 10^{-10}$, which leads to $a_\mu^{\rm SM} = (11659166.9 \pm 7.4) \times 10^{-10}$, about $3.3\sigma$ below the world-average $a_\mu^{\rm exp}$. The work also discusses agreement with independent SM predictions and outlines future prospects for reducing uncertainties via low-energy $e^+e^-$ data from ISR programs at multiple facilities, potentially improving the precision by roughly $1\times 10^{-10}$.

Abstract

We calculate (g-2)/2 of the muon, by improving the determination of the hadronic vacuum polarisation contribution, a_mu^{had,LO}, and its uncertainties. The different e+e- data sets for each exclusive (and the inclusive) channel are combined in order to obtain the optimum estimate of the cross sections and their uncertainties. QCD sum rules are evaluated in order to resolve an apparent discrepancy between the inclusive data and the sum of the exclusive channels. We conclude a_mu^{had,LO}=(683.1 +- 5.9_{exp} +- 2.0_{rad}) 10^{-10} which, when combined with the other contributions to (g-2)/2, is about 3 sigma below the present world average measurement.

Figures (2)

• Figure 1: $e^+e^- \rightarrow \pi^+\pi^-$ data up to 1.2 GeV, where the shaded band shows the result of clustering. The second plot is an enlargement of the $\rho$-$\omega$ interference region.
• Figure 2: The inclusive and the sum of exclusive channel values of $R$, after the data have been clustered.