Dynamical gluon mass in the instanton vacuum model

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 $M_g\left(q\right)$. First, we consider the case of a scalar gluon, no zero-mode problem occurs and its dynamical mass $M_s\left(q\right)$ can be found. Using the typical phenomenological values of the average instanton size $\rho =1/3\text{fm}$ and average inter-instanton distance $R=1\text{fm}$ we get $M_s\left(0\right)=256\text{MeV}$. We then extend this approach to the real vector gluon with zero-modes carefully considered. We obtain the following expression $M_g^2\left(q\right)=2M_s^2\left(q\right)$. This modification of the gluon in the instanton media will shed light on nonperturbative aspect on heavy quarkonium physics.