Mass dependence of the heavy quark potential and its effects on quarkonium states

TL;DR

This paper investigates how the mass of heavy quarks influences the potential between quark-antiquark pairs, combining perturbative QCD and lattice results to derive quarkonium spectra and estimate quark masses.

Contribution

It introduces a method to match perturbative and lattice QCD potentials for heavy quarks, enabling accurate quarkonium spectrum predictions with minimal free parameters.

Findings

Matched perturbative and lattice potentials at intermediate distances.

Derived quarkonium spectra consistent with empirical data.

Estimated charm and bottom quark masses.

Abstract

The heavy quark-antiquark potential is accessible in perturbative QCD and in lattice simulations. The perturbative short-distance part of the potential is contructed via a restricted Fourier transform, covering the momentum region where perturbative QCD is applicable. We show that for the leading order static term as well as for the mass dependent corrections, the perturbative part can be matched at intermediate distances with results from lattice QCD. From these matched potentials, quarkonium spectra with a single free parameter (the heavy quark mass) are derived and compared with empirical spectra. Furthermore, charm and bottom quark masses are deduced.