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We perform a new calculation of the hadronic contributions, $a({\rmHadronic})$ to the anomalous magnetic moment of the muon, $a_\mu$. For the lowenergy contributions of order $\alpha^2$ we carry over an analysis of the pionform factor $F_\pi(t)$ using recent data both on $e^+e^-\to\pi^+\pi^-$ and$\tau^+\to \bar{\nu}_\tau \pi^+\pi^0$. In this analysis we take into accountthat the phase of the form factor is equal to that of $\pi\pi$ scattering. Thisallows us to profit fully from analyticity properties so we can use alsoexperimental information on $F_\pi(t)$ at spacelike $t$. At higher energy weuse QCD to supplement experimental data, including the recent measurements of$e^+e^-\to {\rm hadrons}$ both around 1 GeV and near the $\bar{c}c$ threshold.This yields a precise determination of the $O(\alpha^2)$ and$O(\alpha^2)+O(\alpha^3)$ hadronic part of the photon vacuum polarizationpieces, $$10^{11}\times a^{(2)}({\rm h.v.p.})=6 909\pm64;\quad 10^{11}\timesa^{(2+3)}({\rm h.v.p.})=7 002\pm66$$ As byproducts we also get the masses andwidths of the $\rho^0, \rho^+$, and very accurate values for the charge radiusand second coefficient of the pion. Adding the remaining order $\alpha^3$hadronic contributions we find $$10^{11}\times a^{\rm theory}(\hbox{Hadronic})=6 993\pm69\quad(e^+e^- + \tau + {\rm spacel.})$$ The figures given are obtainedincluding $\tau$ decay data. This is to be compared with the recentexperimental value, $$10^{11}\times a^{\rm exp.}(\hbox{Hadronic})=7174\pm150.$$Comment: Plain TeX file. Published version. Correct value for light-by-light  include

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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Precision determination of the pion form factor and calculation of the muong−2