ImprovedΥspectrum with dynamical Wilson fermions

We present results for the $b\overline{b}$ spectrum obtained using an ${O(M}_b{v}^6)$-correct nonrelativistic lattice QCD action, where $M_b$ denotes the bare $b$-quark mass and $v^2$ is the mean-squared quark velocity. Propagators are evaluated on SESAM’s three sets of dynamical gauge configurations generated with two flavors of Wilson fermions at $\beta =5.6\mathrm{}$. These results, obtained with dynamical Wilson fermions, are compared to a quenched analysis at equivalent lattice spacing $\beta =6.0\mathrm{}$. Using our three sea-quark values, we perform the “chiral” extrapolation to $m_{\mathrm{eff}}{=m}_s/3\mathrm{}$, where $m_s$ denotes the strange quark mass. The light quark mass dependence is found to be small in relation to the statistical errors. Comparing the full QCD result to our quenched simulation, we find better agreement of our dynamical data with experimental results in the spin-independent sector, but observe no unquenching effects in hyperfine splittings. To pin down the systematic errors we have also compared quenched results in different “tadpole” schemes as well as using a lower-order action. We find that spin splittings with an ${O(M}_b{v}^4)$ action are $O$(10%) higher compared to ${O(M}_b{v}^6)$ results. Relative to the results obtained with the plaquette method, the Landau gauge mean-link tadpole scheme raises the spin splittings by about the same margin so that our two improvements are opposite in effect.