# Dynamical gluon mass in the instanton vacuum model

## TL;DR

This paper investigates how instanton effects in the QCD vacuum induce a momentum-dependent dynamical mass for gluons, with potential implications for heavy quarkonium physics.

## Contribution

It introduces a model for the dynamical gluon mass in the instanton liquid framework, including scalar and vector gluons, with specific mass estimates.

## Key findings

- Scalar gluon mass at zero momentum: 256 MeV
- Vector gluon mass squared is twice the scalar gluon mass squared
- Modification of gluon properties could impact heavy quarkonium physics

## Abstract

We are considering the modifications of gluon properties in Instanton Liquid Model (ILM) for the QCD vacuum. Re-scattering of a gluons on an instantons leads to the dynamical momentum-dependent gluon mass $M_g(q).$ First, we considered scalar "gluon", since there are no zero-modes problem and found its dynamical mass $M_s(q)$. At the typical phenomenological values of the average instanton size $\rho=1/3\,\,fm$ and average inter-instanton distance $R=1\,\, fm$ we got $M_s(0)=256\,\,MeV$. Further, we extended this approach to the real vector gluon with careful consideration of zero-modes and got $M^2_g(q)=2M^2_s(q).$ This modification of the gluon in the instanton media might be important for the heavy quarkonium physics at least.