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We present a lattice calculation of the hadronic vacuum polarization and thelowest-order hadronic contribution to the muon anomalous magnetic moment, a_\mu= (g-2)/2, using 2+1 flavors of improved staggered fermions. A precise fit tothe low-q^2 region of the vacuum polarization is necessary to accuratelyextract the muon g-2. To obtain this fit, we use staggered chiral perturbationtheory, including the vector particles as resonances, and compare these topolynomial fits to the lattice data. We discuss the fit results and associatedsystematic uncertainties, paying particular attention to the relativecontributions of the pions and vector mesons. Using a single lattice spacingensemble (a=0.086 fm), light quark masses as small as roughly one-tenth thestrange quark mass, and volumes as large as (3.4 fm)^3, we find a_\mu^{HLO} =(713 \pm 15) \times 10^{-10} and (748 \pm 21) \times 10^{-10} where the erroris statistical only and the two values correspond to linear and quadraticextrapolations in the light quark mass, respectively. Considering systematicuncertainties not eliminated in this study, we view this as agreement with thecurrent best calculations using the experimental cross section for e^+e^-annihilation to hadrons, 692.4 (5.9) (2.4)\times 10^{-10}, and including theexperimental decay rate of the tau lepton to hadrons, 711.0 (5.0)(0.8)(2.8)\times 10^{-10}. We discuss several ways to improve the currentlattice calculation.Comment: 44 pages, 4 tables, 17 figures, more discussion on matching the chpt  calculation to lattice calculation, typos corrected, refs added, version to  appear in PR

Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks