Dynamical gluon mass at nonzero temperature in instanton vacuum model

In the framework of the instanton liquid model (ILM), we consider thermal modifications of gluon properties in different scenarios of temperature ($T$) dependence of the average instanton size $\overline{\ensuremath{\rho}}(T)$ and instanton density $n(T)$ known from the literature. Due to interactions with instantons, the gluons acquire the dynamical temperature-dependent ``electric'' gluon mass ${M}_{\mathrm{el}}(q,T)$. We find that at small momenta and zero temperature ${M}_{\mathrm{el}}(0,0)\ensuremath{\approx}362\text{ }\text{ }\mathrm{MeV}$ for the phenomenological values of $\overline{\ensuremath{\rho}}(0)=1/3\text{ }\text{ }\mathrm{fm}$ and $n(0)=1\text{ }\text{ }{\mathrm{fm}}^{\ensuremath{-}4}$. However, the $T$ dependence of the mass is very sensitive to the temperature dependence of the instanton vacuum parameters $\overline{\ensuremath{\rho}}(T)$ and $n(T)$: it is very mild in the case of the lattice-motivated dependence and decreases steeply in the whole range with theoretical parametrization. We find that the region $0<T<{T}_{c}$ ILM is able to reproduce lattice results for the dynamical gluon mass.

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