Bottomonium Precision Tests From Full Lattice Qcd: Hyperfine Splitting, Upsilon Leptonic Width, And B Quark Contribution To E(+)E(-) -> Hadrons

We calculate the mass difference between the Upsilon and eta b, and the Upsilon leptonic width from lattice QCD using the highly improved staggered quark formalism for the b quark and including u, d, s and c quarks in the sea. We have results for lattices with lattice spacing as low as 0.03 fm and multiple heavy quark masses, enabling us to map out the heavy quark mass dependence and determine values at the b quark mass. Our results are M-Upsilon - M-eta b = 57.5(2.3)(1.0) MeV (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay constants, f(eta b) = 724(12) MeV and f(Upsilon) = 677.2(9.7) MeV, giving Gamma((eta b) -> e(+) e(-)) = 1.292(37)(3) keV. The hyperfine splitting and leptonic width are both in good agreement with experiment, and provide the most accurate lattice QCD results to date for these quantities by some margin. At the same time results for the time moments of the vector-vector correlation function can be compared to values for the b quark contribution to sigma(e(+) e(-) -> hadrons) determined from experiment. Moments 4-10 provide a 2% test of QCD and yield a h quark contribution to the anomalous magnetic moment of the muon of 0.300(15) x 10(-10). Our results, covering a range of heavy quark masses, may also be useful to constrain QCD-like composite theories for beyond the Standard Model physics.