Υ spectrum and mb from full lattice QCD -: art. no. 094507

We show results for the Upsilon spectrum calculated in lattice QCD including for the first time vacuum polarization effects for light u and d quarks as well as s quarks. We use gluon field configurations generated by the MILC collaboration. The calculations compare the results for a variety of u and d quark masses, as well as making a comparison to quenched results (in which quark vacuum polarization is ignored) and results with only u and d quarks. The b quarks in the Upsilon are treated in lattice Nonrelativistic QCD through NLO in an expansion in the velocity of the b quark. We concentrate on accurate results for orbital and radial splittings where we see clear agreement with experiment once u, d and s quark vacuum polarization effects are included. This now allows a consistent determination of the parameters of QCD. We demonstrate this consistency through the agreement of the Upsilon and B spectrum using the same lattice bare b quark mass. A one-loop matching to continuum QCD gives a value for the b quark mass in full lattice QCD for the first time. We obtain m(b) ((MS) over bar) (m(b)((Ms) over bar))=4.4(3) GeV. We are able to give physical results for the heavy quark potential parameters, r(0)=0.469(7) fm and r(1)=0.321(5) fm. Results for the fine structure in the spectrum and the Upsilon leptonic width are also presented. We predict the Upsilon-eta(b) splitting to be 61(14) MeV, the Upsilon(')-eta(b)(') splitting as 30(19) MeV and the splitting between the h(b) and the spin-average of the chi(b) states to be less than 6 MeV. Improvements to these calculations that will be made in the near future are discussed.