Leading-order hadronic contribution to the electron and muon g-2

Abstract

I present a new data driven update of the hadronic vacuum polarization effects for the muon and the electron $g-2$. For the leading order contributions I find $a_{\mu }^{\mathrm{had}(1)}=(686.99\pm 4.21)[687.19\pm 3.48]\times 10^{-10}$ based on $e^{+}{e}^{-}$data [incl. $\tau$ data], $a_{\mu }^{\mathrm{had}(2)}=(-9.934\pm 0.091)\times 10^{-10}$ (NLO) and $a_{\mu }^{\mathrm{had}(3)}=(1.226\pm 0.012)\times 10^{-10}$ (NNLO) for the muon, and $a_e^{\mathrm{had}(1)}=(184.64\pm 1.21)\times 10^{-14}$ (LO), $a_e^{\mathrm{had}(2)}=(-22.10\pm 0.14)\times 10^{-14}$ (NLO) and $a_e^{\mathrm{had}(3)}=(2.79\pm 0.02)\times 10^{-14}$ (NNLO) for the electron. A problem with vacuum polarization undressing of cross-sections (time-like region) is addressed. I also add a comment on properly including axial mesons in the hadronic light-by-light scattering contribution. My estimate here reads $a_{\mu }[a_1,f_1^{\prime },f_1]\sim (7.51\pm 2.71)\times 10^{-11}.$ With these updates $a_{\mu }^{\exp }-a_{\mu }^{\mathrm{the}}=(32.73\pm 8.15)\times 10^{-10}$ a 4.0 $\sigma$ deviation, while $a_e^{\exp }-a_e^{\mathrm{the}}=(-1.10\pm 0.82)\times 10^{-12}$ shows no significant deviation.

Comments: 10 pages, 21 figures, including updated BESIII results arXiv:1507.08188v3, results slightly go down