Precision determination of the pion form factor and calculation of the muon g-2

We perform a new calculation of the hadronic contributions, a(Hadronic), to the anomalous magnetic moment of the muon, a_μ. For the low-energy contributions of order α² we carry over an analysis of the pion form factor F_π(t) using recent data both on e⁺e^-→π⁺π^- and τ⁺→ν̅ _τπ⁺π⁰. In this analysis we take into account that the phase of the form factor is equal to that of ππ scattering. This allows us to profit fully from analyticity properties so we can also use experimental information on F_π(t) at spacelike t. At higher energy we use QCD to supplement experimental data, including the recent measurements of e⁺e^-→hadrons both around 1 GeV and near the c̅ c threshold. This yields a precise determination of the O(α²) and O(α²)+O(α³) hadronic part of the photon vacuum polarization 10¹¹×a⁽²⁾(h.v.p.)=6909±64; 10¹¹×a⁽²⁺³⁾(h.v.p.)=7002±66. As by-products we also get the masses and widths of the ρ⁰,ρ⁺, and very accurate values for the charge radius and second coefficient of the pion. Adding the remaining order α³ hadronic contributions we find 10¹¹×a^theory(hadronic)=6993±69 (e⁺e^-+τ+spacel). The error above includes statistical, systematic, and estimated theoretical errors. The figures given are obtained including τ decay data; if we restrict ourselves to e⁺e^- data, slightly lower values and somewhat higher errors are found. This is to be compared with the figure obtained by subtracting pure electroweak contributions from the recent experimental value, obtained from measurements of the muon gyromagnetic ratio (g-2), which reads 10¹¹×a^expt(hadronic)=7174±150.