Precision Determination of the Pion Form Factor and Calculation of the Muon $g-2$

Abstract

We perform a new calculation of the hadronic contributions, $a(\mathrm{Hadronic})$ to the anomalous magnetic moment of the muon, $a_{\mu }$. For the low energy contributions of order ${\alpha }^2$ we carry over an analysis of the pion form 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 account that the phase of the form factor is equal to that of $\pi \pi$ scattering. This allows us to profit fully from analyticity properties so we can use also experimental information on $F_{\pi }(t)$ at spacelike $t$. At higher energy we use QCD to supplement experimental data, including the recent measurements of $e^{+}{e}^{-}\to \mathrm{hadrons}$ 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 polarization pieces, $$10^{11}\times a^{(2)}(h.v.p.)=6909\pm 64;10^{11}\times a^{(2+3)}(h.v.p.)=7002\pm 66$$ As byproducts we also get the masses and widths of the ${\rho }^0,{\rho }^{+}$, and very accurate values for the charge radius and second coefficient of the pion. Adding the remaining order ${\alpha }^3$ hadronic contributions we find $$10^{11}\times a^{\mathrm{theory}}(Hadronic)=6993\pm 69(e^{+}{e}^{-}+\tau +spacel.)$$ The figures given are obtained including $\tau$ decay data. This is to be compared with the recent experimental value, $$10^{11}\times a^{exp.}(Hadronic)=7174\pm 150.$$

Plain TeX file. Published version. Correct value for light-by-light included

References in corpus (4)

• ππscattering
• Precise Measurement of the Positive Muon Anomalous Magnetic Moment
• Muon and tau anomalies updated
• Electroweak Measurements on the Z Resonance

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