Υspectrum andmbfrom full lattice QCD

Abstract

We show results for the $\ensuremath{\Upsilon}$ 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 $\ensuremath{\Upsilon}$ 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 $\ensuremath{\Upsilon}$ 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 ${m}_{b}^{\overline{\mathrm{MS}}}({m}_{b}^{\overline{\mathrm{MS}}})=4.4(3)\text{ }\text{ }\mathrm{GeV}$. We are able to give physical results for the heavy quark potential parameters, ${r}_{0}=0.469(7)\text{ }\text{ }\mathrm{fm}$ and ${r}_{1}=0.321(5)\text{ }\text{ }\mathrm{fm}$. Results for the fine structure in the spectrum and the $\ensuremath{\Upsilon}$ leptonic width are also presented. We predict the $\ensuremath{\Upsilon}\ensuremath{-}{\ensuremath{\eta}}_{b}$ splitting to be 61(14) MeV, the ${\ensuremath{\Upsilon}}^{\ensuremath{'}}\ensuremath{-}{\ensuremath{\eta}}_{b}^{\ensuremath{'}}$ splitting as 30(19) MeV and the splitting between the ${h}_{b}$ and the spin-average of the ${\ensuremath{\chi}}_{b}$ states to be less than 6 MeV. Improvements to these calculations that will be made in the near future are discussed.