The Upsilon spectrum and the determination of the lattice spacing from lattice QCD including charm quarks in the sea

We give results for the Upsilon spectrum from lattice QCD using an improved version of the nonrelativistic QCD action for b quarks which includes radiative corrections to kinetic terms at O(v^4) in the velocity expansion. We also include for the first time the effect of up, down, strange and charm quarks in the sea using “second generation” gluon field configurations from the MILC Collaboration. Using the Upsilon 2S-1S splitting to determine the lattice spacing, we are able to obtain the 1P-1Sbar splitting to 1.4% and the 3S-1S splitting to 2.4%. Our improved result for M(Υ)−M(ηb) is 70(9) MeV and we predict M(Υ′)−M(η′b)=35(3)MeV. We also calculate π, K and ηs correlators using the highly improved staggered quark action and perform a chiral and continuum extrapolation to give values for Mηs(0.6893(12)GeV) and fηs(0.1819(5) GeV) that allow us to tune the strange quark mass as well as providing an independent and consistent determination of the lattice spacing. Combining the nonrelativistic QCD and highly improved staggered quark analyses gives mb/ms=54.7(2.5) and a value for the heavy quark potential parameter of r1=0.3209(26)fm.