标题： 精确的$Υ$和$J/Ψ$光谱学与格点NRQCD 显示英文标题

标题： Precision $Υ$ and $J/Ψ$ spectroscopy with lattice NRQCD

摘要： 我们利用格点非相对论QCD（NRQCD）给出了关于$\Upsilon$和$J/\Psi$谱学的新结果。 在淬火近似下，特征粲偶素（charmonium）在$\beta$= 5.7 的结果与实验结果一致，系统误差在已知范围内。 我们比较了底重子束缚态在淬火近似下 $\beta$ 值为6.0和5.7的结果，并表明只要对格点胶子场配置中固有的 $\cal{O}$$(a^{2})$ 误差进行修正，$1P-1S$ 能级劈裂会随 $\Lambda_V$ 缩放。在淬火近似中，粲重子束缚态和底重子束缚态的结果存在明显的尺度差异。 我们将底重子束缚态在淬火近似下 $\beta$ 值为6.0的结果与在 $\beta$ 值为5.6的HEMCGC构型上使用两种轻夸克 flavour 的动力学夸克计算的结果进行了比较。 我们表明，外推到 \($n_f$= 3 \) 时，$2S-1S$ 裂分与 $1P-1S$ 裂分的比值与实验结果一致。 我们提取了外推到 \($n_f$= 3 \) 时的 \($\Upsilon$-$\eta_b$\) 裂分值。 显示英文摘要

摘要： We present new results on $\Upsilon$ and $J/\Psi$ spectroscopy using Lattice NRQCD. Charmonium results at quenched $\beta$ = 5.7 show agreement with experiment within understood systematic errors. We compare bottomonium results at quenched $\beta$s 6.0 and 5.7 and show that the $1P-1S$ splitting scales with $\Lambda_V$, provided a correction is applied for the $\cal{O}$$(a^{2})$ errors inherent in the gluon field configurations. There is a clear scale difference between charmonium and bottomonium results in the quenched approximation. We compare quenched results at $\beta$=6.0 for bottomonium with those obtained on HEMCGC configurations at $\beta$=5.6 using 2 light flavours of dynamical quarks. We show that extrapolations to $n_f$ = 3 are consistent with experiment for the ratio of the $2S-1S$ splitting to that of the $1P-1S$. We extract a value for the $\Upsilon$-$\eta_b$ splitting extrapolated to $n_f$ = 3.