established.

As most of our lattice data for the finite temperature quark anti-quark free energies do not reach distances smaller than $0.1$ fm we use in the following the Cornell form deduced in (\[t=0ansatz\]) as reference to the zero temperature heavy quark potential.

Quark anti-quark free energy {#secfreee}
============================

We will analyze here the temperature dependence of the change in free energy due to the presence of a heavy (static) quark anti-quark pair in a 2-flavor QCD heat bath. The static quark sources are described by the Polyakov loop, $$\begin{aligned}
L(\vec{x})&=&\frac{1}{3}{{\rm Tr}}W(\vec{x})\;,\label{pol}\end{aligned}$$ with $$\begin{aligned}
W(\vec{x}) = \prod_{\tau=1}^{N_\tau} U_0(\vec{x},\tau)\;,\label{loop}\end{aligned}$$ where we already have used the lattice formulation with $U_0(\vec{x},\tau) \in
SU(3)$ being defined on the lattice link in time direction. The change in free energy due to the presence of the static color sources in color singlet ($F_1$) and color octet ($F_8$) states can be calculated in terms of Polyakov loop correlation functions [@McLerran:1981pb; @Philipsen:2002az; @Nadkarni:1986as; @Nadkarni:1986cz], $$\begin{aligned}
e^{-F_1(r)/T+C}&=&\frac{1}{3} {{\rm Tr}}\langle  W(\vec{x}) W^{\dagger}(\vec{y}) \rangle 
\label{f1}\;,\\
e^{-F_8(r)/T+C}&=&\frac{1}{8}\langle {{\rm Tr}}W(\vec{x}) {{\rm Tr}}W^{\dagger}(\vec{y})\rangle- \nonumber \\
&&
                \frac{1}{24} {{\rm Tr}}\langle W(\vec{x}) W^{\dagger}(\vec{y}) \rangle\; ,
\label{f8}\end{aligned}$$ where $r=|\vec{x}-\vec{y}|$. As it stands, the correlation functions for the color singlet and octet free energies are gauge dependent quantities 