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

TL;DR

This paper studies how the gluon mass varies with temperature within the instanton liquid model, showing that the mass's temperature dependence is highly sensitive to the instanton parameters and can match lattice results.

Contribution

It introduces a temperature-dependent gluon mass in the instanton liquid model and analyzes its sensitivity to instanton parameters, aligning with lattice data.

Findings

At zero temperature, the gluon mass is approximately 362 MeV.

The temperature dependence of the gluon mass varies significantly with different instanton parameter models.

The model reproduces lattice results for the gluon mass in the temperature range 0 to T_c.

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.