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 $a_\mu[a_1,f_1',f_1] \sim ({ 7.51 \pm 2.71}) \times 10^{-11}\,.$ With these updates $a_\mu^{\rm exp}-a_\mu^{\rm the}=(32.73\pm 8.15)\times 10^{-10}$ a 4.0 $\sigma$ deviation, while $a_e^{\rm exp}-a_e^{\rm the}=(-1.10\pm 0.82)\times 10^{-12}$ shows no significant deviation.