Dynamical gluon mass at non-zero temperature in instanton vacuum model

Abstract

In the framework of the instanton liquid model (ILM), we consider thermal modifications of the gluon properties in different scenarios of temperature $T$ dependence of the average instanton size $\bar{\rho}(T)$ and the instanton density $n(T)$ known from the literature. Due to interactions with instantons, the gluons acquire the dynamical temperature dependent "electric" gluon mass $M_{el}(q,T).$ We found that at small momenta and zero temperature $M_{el}(0,0)\approx362\,{\rm MeV}$ at the phenomenological values of $\bar{\rho}(0)=1/3\,{\rm fm}$ and $n(0)=1\,{\rm fm}^{-4}$, however the $T$-dependence of the mass is very sensitive to the temperature dependence of the instanton vacuum parameters $\bar{\rho}(T),\,n(T)$: it is very mild in case of the lattice-motivated dependence and decreases steeply in the whole range with theoretical parametrization. We see that in region $0<T<T_{c}$ ILM is able to reproduce lattice results for the dynamical "electric" gluon mass.