The Upsilon spectrum and m_b from full lattice QCD

A. Gray, I. Allison, C. T. H. Davies, E. Gulez, G. P. Lepage, J. Shigemitsu, M. Wingate

Published 2005-07-13, updated 2005-09-16Version 2

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 polarisation 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 polarisation 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^{\bar{MS}}(m_b^{\bar{MS}}) = 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^{\prime} - eta_b^{\prime} 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.