Final report of the E821 muon anomalous magnetic moment measurement at BNL

We present the final report from a series of precision measurements of the muon anomalous magnetic moment, ${a}_{\ensuremath{\mu}}=(g\ensuremath{-}2)/2$. The details of the experimental method, apparatus, data taking, and analysis are summarized. Data obtained at Brookhaven National Laboratory, using nearly equal samples of positive and negative muons, were used to deduce ${a}_{\ensuremath{\mu}}(\mathrm{\text{Expt}})=11659208.0(5.4)(3.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, where the statistical and systematic uncertainties are given, respectively. The combined uncertainty of 0.54 ppm represents a 14-fold improvement compared to previous measurements at CERN. The standard model value for ${a}_{\ensuremath{\mu}}$ includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, $\ensuremath{\approx}0.55\text{ }\text{ }\mathrm{ppm}$, is associated with first-order hadronic vacuum polarization. Present standard model evaluations, based on ${e}^{+}{e}^{\ensuremath{-}}$ hadronic cross sections, lie 2.2--2.7 standard deviations below the experimental result.