Recently I saw a talk stating that the hadron resonance gas model, which is basically all the known hadrons put together as ideal gases, describes lattice QCD "data" really well.

Like in this paper:
http://arxiv.org/abs/hep-ph/0303108
In this paper Fig. 1 is what I am looking at.

I tried that out myself, and computed energy densities:
$$\epsilon = \frac{g}{2 \pi^2} \int_{m}^{\infinity} \frac{ \sqrt{E^2-m^2}E^2 dE}{exp(E/T)+a}$$

where a = -1 for bosons and +1 for fermions and usual, then even if I only take the pion contribution, with the physical pion mass approx. 140GeV, and g = 3, than at 0.5TC ~ 85 GeV I get $$\epsilon / T^4$$ roughly 1, instead of 0 which is seen in Fig. 1 of that article. Where is the difference?

One thing I can think of is that they don't use a physical pion mass in the lattice calculation, but higher, and so get the lower value, which they also use in the thermodynamic model, but in that case wouldn't they have to measure all the other hadron resonance masses in the lattice calculation?

Can someone more well-versed in this topic tell me what happens?