Prediction of the bottomonium D-wave spectrum from full lattice QCD

TL;DR

This study uses advanced lattice QCD techniques to accurately predict the D-wave bottomonium spectrum, including fine structure, with results consistent with experimental data and new theoretical predictions.

Contribution

First lattice QCD calculation of the full D-wave bottomonium spectrum using improved NRQCD and second-generation gluon configurations, providing precise predictions.

Findings

^3D_2 - 1S splitting determined to 2.3% accuracy

Predicted masses for ^3D_3 and ^3D_1 states at 10.181 GeV and 10.147 GeV

Agreement with experimental measurements for the 2S-1S splitting

Abstract

We calculate the full spectrum of D-wave states in the Upsilon system in lattice QCD for the first time, using an improved version of NonRelativistic QCD on coarse and fine "second generation" gluon field configurations from the MILC collaboration that include the effect of up, down, strange and charm quarks in the sea. Taking the 2S-1S splitting to set the lattice spacing, we determine the ^3D_2 - 1S splitting to 2.3%, and find agreement with experiment. Our prediction of the fine structure relative to the ^3D_2 gives the ^3D_3 at 10.181(5) GeV and the ^3D_1 at 10.147(6) GeV. We also discuss the overlap of ^3D_1 operators with ^3S_1 states.