As tests of QCD in the bottomonium system, we give the most accurate results to date for the ground-state hyperfine splitting and the Ξ₯ leptonic width from full lattice QCD. These quantities are both accurately known from experiment, so can provide a good test of π physics, but previous lattice results have been rather imprecise. We also test the impact on these quantities of the π quark's electric charge. Our results are: π Ξ₯ β π π π = 57.5(2.3) (1.0) MeV (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay constants, π π π = 724(12) MeV and π Ξ₯ = 677.2(9.7) MeV, giving Ξ(Ξ₯ β π + π β ) = 1.292(37) (3) keV. We also give a new determination of the ratio of the masses for π and π quarks that is completely nonperturbative in lattice QCD and includes the calculation of QED effects for the first time. This gives a result for the π quark mass of π π (π π , π π = 5) = 4.202(21) GeV.
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