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The bottomonium spectrum is computed in dynamical 2+1 flavor lattice QCD,using NRQCD for the b quarks. The main calculations in this work are based ongauge field ensembles generated by the RBC and UKQCD collaborations with theIwasaki action for the gluons and a domain-wall action for the sea quarks.Lattice spacing values of approximately 0.08 fm and 0.11 fm are used, andsimultaneous chiral extrapolations to the physical pion mass are performed. Asa test for gluon discretization errors, the calculations are repeated on twoensembles generated by the MILC collaboration with the Luscher-Weisz gaugeaction. Gluon discretization errors are also studied in a lattice potentialmodel using perturbation theory for four different gauge actions. Thenonperturbative lattice QCD results for the radial and orbital bottomoniumenergy splittings obtained from the RBC/UKQCD ensembles are found to be inexcellent agreement with experiment. To get accurate results for spinsplittings, the spin-dependent order-v^6 terms are included in the NRQCDaction, and suitable ratios are calculated such that most of the unknownradiative corrections cancel. The cancellation of radiative corrections isverified explicitly by repeating the calculations with different values of thecouplings in the NRQCD action. Using the lattice ratios of the S-wave hyperfineand the 1P tensor splitting, and the experimental result for the 1P tensorsplitting, the 1S hyperfine splitting is found to be60.3+-5.5(stat)+-5.0(syst)+-2.1(exp) MeV, and the 2S hyperfine splitting ispredicted to be 23.5+-4.1(stat)+-2.1(syst)+-0.8(exp) MeV.

Bottomonium spectrum at order v^6 from domain-wall lattice QCD: precise results for hyperfine splittings