configurations used at each $\beta$-value. The pseudo critical coupling for this action is $\beta_c=3.649(2)$ [@Allton:2002zi]. To set the physical scale we use the string tension, $\sigma a^2$, measured in units of the lattice spacing, obtained from the large distance behavior of the heavy quark potential calculated from smeared Wilson loops at zero temperature [@Karsch:2000kv]. This is also used to define the temperature scale and $a\sqrt{\sigma}$ is used for setting the scale for the free energies and the physical distances. For the conversion to physical units, $\sqrt{\sigma}=420$MeV is used. For instance, we get $T_c=202(4)$ MeV calculated from $T_c/\sqrt{\sigma}=0.48(1)$ [@Karsch:2000kv]. In parts of our analysis of the quark anti-quark free energies we are also interested in the flavor and finite quark mass dependence. For this reason we also compare our $2$-flavor QCD results to the todays available recent findings in quenched ($N_f$=0) [@Kaczmarek:2002mc; @Kaczmarek:2004gv] and $3$-flavor QCD ($m_\pi/m_\rho\simeq0.4$ [@Peterpriv]) [@Petreczky:2004pz]. Here we use $T_c=270$ MeV for quenched and $T_c=193$ MeV [@Petreczky:2004pz] for the $3$-flavor case.

Our results for the color singlet quark anti-quark free energies, $F_1$, and color averaged free energies, $F_{av}$, are summarized in Fig. \[fes\] as function of distance at several temperatures close to the transition. At distances much smaller 