Bottomonium spectrum from lattice QCD with 2+1 flavors of domain wall fermions

Recently, realistic lattice QCD calculations with $2+1$ flavors of domain wall fermions and the Iwasaki gauge action have been performed by the RBC and UKQCD Collaborations. Here, results for the bottomonium spectrum computed on their gauge configurations of size ${24}^{3}\ifmmode\times\else\texttimes\fi{}64$ with a lattice spacing of approximately 0.11 fm and four different values for the light quark mass are presented. Improved lattice nonrelativistic QCD is used to treat the $b$ quarks inside the bottomonium. The results for the radial and orbital energy splittings are found to be in good agreement with experimental measurements, indicating that systematic errors are small. The calculation of the $\ensuremath{\Upsilon}(2S)\ensuremath{-}\ensuremath{\Upsilon}(1S)$ energy splitting provides an independent determination of the lattice spacing. For the most physical ensemble it is found to be ${a}^{\ensuremath{-}1}=1.740(25)(19)\text{ }\text{ }\mathrm{GeV}$, where the first error is statistical/fitting and the second error is an estimate of the systematic errors due to the lattice nonrelativistic QCD action.