Non-Relativistic QCD for Heavy Quark Systems

TL;DR

This paper uses nonrelativistic QCD on lattice configurations to study heavy quark-antiquark states, confirming rotational invariance restoration and analyzing mass splittings with high accuracy.

Contribution

It provides lattice QCD calculations of heavy quarkonium states and hybrids using NRQCD, demonstrating invariance restoration and insensitivity of S-P splitting to quark mass variations.

Findings

D wave masses from different lattice orientations agree, indicating rotational invariance.

S-P splitting remains stable across a range of quark masses.

Signals for hybrid states were detected.

Abstract

We employ a nonrelativistic version of QCD (NRQCD) to study heavy quark-antiquark bound states in the lowest approximation without fine structure. We use gluon configurations on a 16^3 by 48 lattice at beta=6.2 from the UKQCD collaboration. For quark masses in the vicinity of the b we obtain bound state masses for S, P and both types of D wave. We also detect signals for two types of hybrids (quark,antiquark,gluon states). The results are sufficiently accurate to confirm that the values of the D wave mass from both lattice D waves coincide indicating that the cubical invariance of the lattice is restored to full rotational invariance at large distance. Our results also show that the S-P splitting is indeed insensitive to variations in the bare quark mass from Ma=1.0 to Ma=1.9.