to adjust the eQP to lattice data, they can be modified to accomodate lattice restmasses $m_{i}$ using a prescription from [@Pis93]: $m_{i,\infty}^{2}\rightarrow m_{i}^{2}+2m_{i}m_{i,\infty}+2m_{i,\infty}^{2}$. Additionally neglecting Landau damping, i.e. assuming vanishing imaginary parts of the self-energies, and contributions from collective excitations, i.e. plasmons and (anti)plasminos, leads to the eQP. As collective excitations are exponentially suppressed[^2] and the effect of Landau damping is small at vanishing chemical potential the eQP seemed to be sufficient.

However, as previous studies of the flow equation [@Pes02; @Blu04a] have shown the characteristic curves emerging at $T\approx T_{c}$ cross each other in some region of finite values of $\mu$ for parameters adjusted to lattice QCD results (cf. dashed lines in Figure \[fig:HTL characteristics\] below). This unfortunate feature prevents an unambiguous extrapolation of thermodynamic quantities into the full $T$-$\mu$-plane. Romatschke [@RR03] has shown for the $2$ flavor case that these crossings can be avoided by using the full HTL model. We are going to extend his line of arguing to the physically interesting case of $2+1$ flavors.

Investigation of the full HTL QPM\[sec:fullHTL\]
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Adjustment to lattice data at $\mu=0$
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While the eQP is able to accommodate arbitrary lattice restmasses by means of a modified asymptotic dispersion 