Dynamical gluon mass in the instanton vacuum model

M Musakhanov,O Egamberdiev

doi:10.1016/j.physletb.2018.01.080

Abstract

We consider the modifications of gluon properties in the instanton liquid model (ILM) for the QCD vacuum. Rescattering of gluons on instantons generates the dynamical momentum-dependent gluon mass Mg(q). First, we consider the case of a scalar gluon, no zero-mode problem occurs and its dynamical mass Ms(q) can be found. Using the typical phenomenological values of the average instanton size ρ=1/3 fm and average inter-instanton distance R=1 fm we get Ms(0)=256 MeV. We then extend this approach to the real vector gluon with zero-modes carefully considered. We obtain the following expression Mg2(q)=2Ms2(q). This modification of the gluon in the instanton media will shed light on nonperturbative aspect on heavy quarkonium physics.

Highlights

INTRODUCTIONWithout any doubt instantons represent a very important topologically nontrivial component of the QCD vacuum
We consider the modifications of gluon properties in the instanton liquid model (ILM) for the QCD vacuum
The main parameters of the QCD instanton vacuum developed in the instanton liquid model (ILM) are the average instanton size ρ and inter-instanton distance R

Summary

INTRODUCTION

Without any doubt instantons represent a very important topologically nontrivial component of the QCD vacuum. The main parameters of the QCD instanton vacuum developed in the instanton liquid model (ILM) are the average instanton size ρ and inter-instanton distance R (see, for example, following reviews [1, 2]). The dynamical quark mass M is expressed as (packing parameter)1/2ρ−1 ∼ 365 MeV [1] while the instanton contribution to the heavy quark mass is given as ∆M ∼ (packing parameter)ρ−1 ∼ 70 MeV [12] We see that these specific packing parameter dependencies explain the values of M and ∆M. These factors define the coupling between the light-light, heavy-light and heavy-heavy quarks induced by the instantons from the QCD vacuum. We aim at investigating the dynamical gluon mass within the ILM, extending the method developed in Ref. [16], where the formulae for the quark correlators were derive

SCALAR ”GLUON” PROPAGATOR

REAL GLUON PROPAGATOR

CONCLUSION