Gluons, Heavy and Light Quarks in the QCD Vacuum

TL;DR

This paper explores the properties of the QCD vacuum using the Instanton Liquid Model, highlighting its success in describing light hadron physics and its implications for heavy and light quark interactions.

Contribution

It extends the Instanton Liquid Model to include heavy quark interactions and discusses the role of instantons in nonperturbative QCD effects across different quark systems.

Findings

The dynamical quark mass is approximately 360 MeV, confirmed by lattice evaluations.

Gluon-instanton interactions are significant, with a dynamical gluon mass around 360 MeV.

Heavy quark-instanton interaction contributes about 70 MeV to the quark mass shift.

Abstract

We are discussing the properties of the QCD vacuum which might be important especially for the understanding of hadrons with small quark core size $\sim0.3\,fm.$ We assume that at these distances the QCD vacuum can be described by the Instanton Liquid Model (ILM). At larger distances, where confinement is important, ILM should be extended to Dyons Liquid Model (DLM). The ILM has only two free parameters, average instanton size $\rho\approx0.3\,fm$ and average inter-instanton distance $R\approx1\,fm$, and can successfully describe the key features of light hadron physics. One of the important conceptual results was prediction of the momentum dependent dynamical quark mass $M\sim(packing\,\,fraction)^{1/2}\,\,\rho^{-1}\approx360\,MeV$, later confirmed numerically by evaluations in the lattice. The estimates show that gluon-instanton interaction strength is also big and is controlled by the value of dynamical gluon mass $M_{g}\approx M$. Heavy quarks interact with instantons much weaker. The heavy quark-instanton interaction strength is given by $\Delta m_{Q}\sim packing\,\,fraction\,\,\rho^{-1}\approx70\,MeV.$ Nevertheless, the direct instanton contribution to the colorless heavy-heavy quarks potential is sizable and must be taken into account. At small distances, where one-gluon exchange contribution to this potential is dominated, we have to take into account dynamical gluon mass $M_{g}$. Also, instantons are generating light-heavy quarks interactions and allow to describe the nonperturbative effects in heavy-light quarks systems.