Precision $\Upsilon$ and $J/\Psi$ spectroscopy with lattice NRQCD

Abstract

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.