Muon g-2 Theory: the Hadronic Part

Abstract

I present a status report of the hadronic vacuum polarization effects for the muon $g-2$, to be considered as an update of [1]. The update concerns recent new inclusive $R$ measurements from KEDR in the energy range 1.84 to 3.72 GeV. For the leading order contributions I find $a_{\mu }^{\mathrm{had}(1)}=(688.07\pm 4.14)[688.77\pm 3.38]\times 10^{-10}$ based on $e^{+}{e}^{-}$data [incl. $\tau$ data], $a_{\mu }^{\mathrm{had}(2)}=(-9.93\pm 0.07)\times 10^{-10}$ (NLO) and $a_{\mu }^{\mathrm{had}(3)}=(1.22\pm 0.01)\times 10^{-10}$ (NNLO). Collecting recent progress in the hadronic light-by-light scattering I adopt ${\pi }^0,\eta ,{\eta }^{\prime }$ [$95\pm 12$] + axial--vector [$8\pm 3$] + scalar [$-6\pm 1$] + $\pi ,K$ loops [$-20\pm 5$] + quark loops [$22\pm 4$] + tensor [$1\pm 0$] + NLO [$3\pm 2$] which yields $a_{\mu }^{(6)}(\mathrm{lbl},\mathrm{had})=(103\pm 29)\times 10^{-11}.$ With these updates I find $a_{\mu }^{\exp }-a_{\mu }^{\mathrm{the}}=(31.3\pm 7.7)\times 10^{-10}$ a 4.1 $\sigma$ deviation. Recent lattice QCD results and future prospects to improve hadronic contributions are discussed.

Comments: 17 pages, 26 figures