Hadron Resonance Mass Spectrum and Lattice QCD Thermodynamics

TL;DR

The paper addresses how QCD thermodynamics and the deconfinement transition depend on quark mass by combining lattice results with a hadron resonance gas (HRG) description and an MIT bag-model-inspired quark-mass dependence of hadron masses. It demonstrates that for $T$ up to $T_c$, the lattice equation of state in (2+1) flavor QCD can be described by an HRG containing thousands of resonances, and it extends this HRG to arbitrary quark masses using a phenomenological mass scaling $M(x)/\sqrt{\sigma}$ calibrated to bag-model results. The study finds that the transition temperature aligns with lines of constant energy density $\epsilon/T_c^4$ in the HRG framework, with glueball contributions required at heavier quarks; allowing for possible glueball mass reductions near $T_c$ improves agreement with lattice data. These results point to a density-driven deconfinement mechanism and provide a bridge between lattice QCD thermodynamics and hadronic resonance gas phenomenology, with implications for heavy-ion theory and percolation pictures.

Abstract

We confront lattice QCD results on the transition from the hadronic phase to the quark--gluon plasma with hadron resonance gas and percolation models. We argue that for T < T_c the equation of state derived from Monte--Carlo simulations of (2+1) quark--flavor QCD can be well described by a hadron resonance gas. We examine the quark mass dependence of the hadron spectrum on the lattice and discuss its description in terms of the MIT bag model. This is used to formulate a resonance gas model for arbitrary quark masses which can be compared to lattice calculations. We finally apply this model to analyze the quark mass dependence of the critical temperature obtained in lattice calculations. We show that the value of T_c for different quark masses agrees with lines of constant energy density in a hadron resonance gas. For large quark masses a corresponding contribution from a glueball resonance gas is required.

Figures (5)

• Figure 1: The left--hand figure shows the energy density $\epsilon$ in units of $T^4$ calculated on the lattice with (2+1) quark flavors as a function of the $T/T_c$ ratio. The vertical lines indicate the position of the critical temperature. The right--hand figure represents the corresponding results for the interaction measure $(\epsilon -3P)/T^4$. The full--lines are the results of the hadron resonance gas model that accounts for all mesonic and baryonic resonances.
• Figure 2: Dependence of different hadron masses $m_h$ on the pion mass $m_\pi$. Both $m_h$ and $m_\pi$ are expressed in the units of the string tension $\sqrt\sigma$. Curves are the MIT bag model results (see text for details). The filled circles represent the PC--PACS lattice results from data1. The filled diamonds are the $N_f=3$ whereas the open--diamonds are $N_f=2$ flavor results from peikert1. The filled--boxes are quenched QCD results data3. All other points are from reference data6. Both the lattice data and the bag model results are shifted in $m_h$--direction by a constant factors indicated in the figure.
• Figure 3: The transition temperature in 2 (filled squares) and 3 (circles) flavor QCD versus $m_{PS}/\sqrt{\sigma}$ using an improved staggered fermion action (p4-action). Also shown are results for 2-flavor QCD obtained with the standard staggered fermion action (open squares). The dashed band indicates the uncertainty on $T_c/\sqrt{\sigma}$ in the quenched limit. The straight line is the fit given in Eq. \ref{['tcfit']}.
• Figure 4: The transition temperature vs. pion mass obtained in lattice calculations and lines of constant energy density calculated in a resonance gas model. The left hand figure shows a comparison of constant energy density lines at 1.2 (upper), 0.8(middle) and 0.4(lower) GeV/fm$^3$ with lattice results for 2-flavor QCD obtained with improved staggered karsch1 as well as improved Wilson BernardAliEdwards fermion formulations. $T_c$ as well as $m_{PS}$ are expressed in terms of the corresponding vector meson mass. The right hand figure shows results for 2 and 3 flavor QCD compared to lines of constant energy density of 0.8 GeV/fm$^3$. Here $T_c$ and $m_{PS}$ are expressed in units of $\sqrt{\sigma}$. For a detailed description see text.
• Figure 5: The transition temperature in 3-flavor QCD compared to lines of constant energy density ($\epsilon = 0.8$ GeV/fm$^3$) in a hadronic resonance gas (upper curve), a hadronic resonance gas with 15 glueball states added (middle curve) and a hadronic resonance gas with 15 glueball states with a 40% reduced mass (lower curve).