and plasma freq}\end{aligned}$$ The number of colors $N_{c}$ is fixed at $3$. The numbers of light quarks $N_{q}=2$ and one strange quark, $N_{s}=1$, are chosen as in the lattice calculations [@Kar07].

Properties of HTL self-energies and dispersion relations
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The real and the imaginary parts of the HTL self-energies (\[eq:HTL PiT\]) and (\[eq:HTL Sigmapm\]) are [@LeB96]$$\begin{aligned}
{\text{Re}}\Pi_{T}=\frac{m_{D}^{2}}{2}\left(1+\frac{\omega^{2}\!-\! k^{2}}{k^{2}}{\text{Re}}{\Pi_\text{L}}(\omega,k)\right)\!, &  & {\text{Im}}\Pi_{T}=\frac{1}{2}m_{D}^{2}\frac{\omega^{2}\!-\! k^{2}}{k^{2}}\frac{\omega}{2k}\pi\Theta\left(k^{2}\!-\!\omega^{2}\right)\varepsilon(k),\label{eq:Im PiT}\\
{\text{Re}}\Pi_{L}=m_{D}^{2}\left(1-\frac{\omega}{2k}\ln\left|\frac{\omega+k}{\omega-k}\right|\right)\!, &  & {\text{Im}}\Pi_{L}=m_{D}^{2}\frac{\omega}{2k}\pi\Theta\left(k^{2}-\omega^{2}\right)\varepsilon(k),\label{eq:Im PiL}\\
{\text{Re}}\Sigma_{\pm}=\frac{\hat{M}^{2}}{k}\left(1-\frac{\omega\mp k}{2k}\ln\left|\frac{\omega+k}{\omega-k}\right|\right)\!, &  & {\text{Im}}\Sigma_{\pm}=\frac{\hat{M}^{2}}{k}\frac{\omega\mp k}{2k}\pi\Theta\left(k^{2}-\omega^{2}\right)\varepsilon(k),\label{eq:Im Sigmapm}\end{aligned}$$ where ${\varepsilon}(k)$ is the sign function. The real parts are symmetric with respect to $\omega$, while the imaginary parts are antisymmetric and differ from zero only for $|\omega|<k$, i.e. below the light cone. The real and imaginary parts for $k=0.5T$ are shown in Figure \[fig:gluon se\]. Analogously, the quark self-energies fulfill the parity relations ${\text{Re}}\Sigma_{+}(-\omega)={\text{Re}}\Sigma_{-}(\omega)$ and ${\text{Im}}\Sigma_{+}(-\omega)=-{\text{Im}}\Sigma_{-}(\omega)$ as shown for $k=0.5T$ in Figure \[fig:quark se\].

![The real and imaginary parts of the retarded transverse (left) and longitudinal (right) gluon self-energies scaled by the Debye mass squared are shown as functions of the energy $\omega$ scaled by the momentum $k$ which is fixed at $k=0.5T$. \[fig:gluon se\]](PiTGraph2.eps "fig:")        ![The real and imaginary parts of the retarded transverse (left) and longitudinal (right) gluon self-energies scaled by the 