Bottomonium spectrum at order v6 from domain-wall lattice QCD: Precise results for hyperfine splittings

The bottomonium spectrum is computed in dynamical 2 + 1 flavor lattice QCD, using nonrelativistic QCD for the b quarks. The main calculations in this work are based on gauge field ensembles generated by the RBC and UKQCD Collaborations with the Iwasaki 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, and simultaneous chiral extrapolations to the physical pion mass are performed. As a test for gluon-discretization errors, the calculations are repeated on two ensembles generated by the MILC Collaboration with the Luscher-Weisz gauge action. Gluon-discretization errors are also studied in a lattice potential model using perturbation theory for four different gauge actions. The nonperturbative lattice QCD results for the radial and orbital bottomonium energy splittings obtained from the RBC/UKQCD ensembles are found to be in excellent agreement with experiment. To get accurate results for spin splittings, the spin-dependent order-v(6) terms are included in the nonrelativistic QCD action, and suitable ratios are calculated such that most of the unknown radiative corrections cancel. The cancellation of radiative corrections is verified explicitly by repeating the calculations with different values of the couplings in the nonrelativistic QCD action. Using the lattice ratios of the S-wave hyperfine and the 1P tensor splitting, and the experimental result for the 1P tensor splitting, the 1S hyperfine splitting is found to be 60.3 +/- 5.5(stat) +/- 5.0(syst) +/- 2.1(exp) MeV, and the 2S hyperfine splitting is predicted to be 23.5 +/- 4.1(stat) +/- 2.1(syst) +/- 0.8(exp) MeV.