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

TL;DR

This paper uses lattice NRQCD to study $$ and $J/ $ spectroscopy, showing agreement with experimental results and analyzing the effects of quenching and dynamical quarks on the spectra.

Contribution

It provides new lattice NRQCD results for quarkonium spectra, compares quenched and unquenched configurations, and explores scale setting and systematic errors.

Findings

Charmonium results agree with experiment within systematic errors.

The $1P-1S$ splitting scales with $_V$ after corrections.

Extrapolations to $n_f=3$ are consistent with experimental data.

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.