Hadron Resonance Gas: Exploring QCD Data & Thermodynamic Model

[evilcman]

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?

Thanks in advance.

 

[AndyW]

Thank you for bringing up this interesting topic. The Hadron Resonance Gas (HRG) model is indeed a powerful tool for describing the thermodynamic properties of hadronic matter. However, as you have pointed out, there are some discrepancies between the results obtained from the HRG model and lattice QCD calculations.

Firstly, it is important to note that the HRG model is an effective model and does not take into account the full complexity of QCD. It is based on the assumption that hadrons can be treated as non-interacting ideal gases, which may not be accurate at high temperatures and densities. On the other hand, lattice QCD calculations take into account the strong interactions between quarks and gluons, which are responsible for the formation of hadrons.

One possible reason for the difference in results is the treatment of the pion mass. In the HRG model, the physical pion mass is used, while in lattice QCD calculations, a heavier pion mass is often used to simulate the effects of the quark masses. This can lead to differences in the thermodynamic properties, as you have observed.

Additionally, the HRG model assumes that all hadrons are in thermal equilibrium, but in reality, this may not be the case. In lattice QCD calculations, only a limited number of hadrons are included, and their masses and interactions are determined by fitting to experimental data. Therefore, the results may not be directly comparable to the HRG model, which includes all known hadrons.

In summary, the HRG model provides a good description of the thermodynamic properties of hadronic matter, but it is not a perfect model and may not be suitable for all temperature and density regimes. Lattice QCD calculations, on the other hand, take into account the full complexity of QCD but also have their limitations. More research is needed to better understand the differences between these two approaches and to improve our understanding of the properties of hadronic matter. I hope this helps to answer your question.