QCD Equation of State and Hadron Resonance Gas

TL;DR

This paper evaluates how well the hadron resonance gas (HRG) describes QCD thermodynamics from lattice QCD. It shows that lattice discretization and heavier quark masses distort the hadron spectrum, but adjusting HRG masses to reflect these artifacts brings HRG into good agreement with lattice fluctuations and the trace anomaly up to the chiral crossover. The authors construct interpolating QCD equations of state by matching a lattice-based high-T trace anomaly to HRG at low T, yielding several parametrizations (e.g., s95p-v1, s95n-v1, s90f-v1) that are smooth and practical for hydrodynamic modeling. Hydrodynamic simulations with these EoS show that elliptic flow is relatively robust to the precise EoS choice, while spectra and proton v2 can be sensitive to freeze-out conditions, underscoring the importance of consistent EoS implementation in heavy-ion phenomenology.

Abstract

We compare the trace anomaly, strangeness and baryon number fluctuations calculated in lattice QCD with expectations based on hadron resonance gas model. We find that there is a significant discrepancy between the hadron resonance gas and the lattice data. This discrepancy is largely reduced if the hadron spectrum is modified to take into account the larger values of the quark mass used in lattice calculations as well as the finite lattice spacing errors. We also give a simple parametrization of QCD equation of state, which combines hadron resonance gas at low temperatures with lattice QCD at high temperatures. We compare this parametrization with other parametrizations of the equation of state used in hydrodynamical models and discuss differences in hydrodynamic flow for different equations of state.

Figures (17)

• Figure 1: The quadratic splittings of non-Goldstone pseudo-scalar mesons in the seven different multiplets calculated with asqtad action bazavov09 at different lattice spacings. The lines show the parametrization given by Eq. (\ref{['delta_ps']}). The open symbols refer to the lattice data obtained with the stout action BW_Tc_09.
• Figure 2: Baryon number fluctuations calculated with asqtad action on the $N_{\tau}=6$ lattices compared with HRG model with physical value of the baryon masses (solid line) and with HRG model with baryon masses calculated according Eqs. (\ref{['mV']})-(\ref{['mXi']}), $m_{cut}^B=1.8$GeV and $m_{cut}^B=2.5$GeV (dashed lines). Also shown are the lattice results for the p4 action.
• Figure 3: The strangeness fluctuations calculated on $N_{\tau}=8$ lattices for asqtad and p4 actions and compared with the prediction of the HRG model with physical (solid line) and modified (dashed lines) hadron masses. The upper (lower) dashed line corresponds to $m_{cut}^B=1.8(2.5)$GeV. The doted lines show the prediction of the HRG with modified hadron masses for $N_{\tau}=12$.
• Figure 4: The trace anomaly calculated in lattice QCD compared with the HRG model with physical hadron masses (solid line) and modified hadron masses (dashed lines). The upper (lower) dashed line corresponds to $m_{cut}^B=1.8(2.5)$GeV.
• Figure 5: The trace anomaly calculated in lattice QCD with p4 and asqtad actions on $N_{\tau}=6$ and $8$ lattices compared with the parametrization given by Eqs. (\ref{['e-3p_high']}) and (\ref{['e-3p_low']}). The solid, dotted and dashed lines correspond to parametrizations $s95p{\rm -v1}$, $s95n{\rm -v1}$ and $s90f\rm{-v1}$ respectively, as discussed in the text.