New scenarios for hard-core interactions in a hadron resonance gas

The equation of state of baryon-symmetric hadronic matter with hard-sphere interactions is studied. It is assumed that mesons $M$ are pointlike, but baryons $B$ and antibaryons $\overline{B}$ have the same hard-core radius $r_B$. Three possibilities are considered: (1) the $BB$ and $B\overline{B}$ interactions are the same; (2) baryons do not interact with antibaryons; (3) the $B\overline{B}, MB$, and $M\overline{B}$ interactions are negligible. By choosing the parameter $r_B=0.3–0.6$ fm, we calculate the nucleon to pion ratio as a function of temperature and perform the fit of hadron yields measured in central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. New nontrivial effects in the interacting hadron resonance gas at temperatures $150–200$ MeV are found.

Figure 1

The $N/\pi$ ratio as a function of temperature in the $N\overline{N}\pi$ matter with pointlike pions and equal numbers of nucleons and antinucleons. The solid, dashed, and dash-dotted lines correspond to nucleon hard-core radii $r_N=0.3$, 0.4, and $0.5\mathrm{fm}$, respectively. The dotted line is obtained in the ideal gas limiting case $r_N=0$.

Figure 2

The $N/\pi$ ratio as a function of temperature in the $N\overline{N}\pi$ matter with equal numbers of nucleons and antinucleons. The thick solid, dashed, and dash-dotted lines are calculated by using the NDEM with nucleon hard-core radii $r_N=0.3$, 0.4, and $0.5\mathrm{fm}$, respectively. Thin lines give corresponding results obtained within the DEM. The dotted line is calculated in the ideal gas limit $r_N=0$.

Figure 3

The $N/\pi$ ratio as a function of temperature in the $N\overline{N}\pi$ matter with equal numbers of nucleons and antinucleons. The thick solid, dashed, and dash-dotted lines are calculated by using the CSM with nucleon hard-core radii $r_N=0.3$, 0.4, and $0.5\mathrm{fm}$, respectively. Thin lines give corresponding results obtained within the EVM. The dotted line is calculated assuming $r_N=0$.

Figure 4

The $N/\pi$ ratio as a function of temperature in the $N\overline{N}\pi$ matter with equal numbers of nucleons and antinucleons. The thick lines are calculated using the CS approximation of compressibility and disregarding the $N\overline{N}$ interactions. Thin lines give corresponding results with inclusion of the $N\overline{N}$ repulsion. The dotted line is calculated in the ideal gas limit $r_N=0$.

Figure 5

The $N/\pi$ ratio as a function of temperature in $B\overline{B}M$ matter with pointlike mesons. Thick lines show the CSM results for the full set of hadrons with inclusion of feeding from strong decays of resonances (the CI model). Thin lines are calculated for the $N\overline{N}\pi$ matter. The dotted lines represent the ideal gas limiting case.

Figure 6

Scaled densities ${\overline{n}}_N/T^3$ and ${\overline{n}}_{\pi }/T^3$ in $B\overline{B}M$ matter with pointlike mesons. Thick lines show the CSM results for the full set of hadrons (the CI model). Thin lines are calculated for $N\overline{N}\pi$ matter. All calculations correspond to hard-core radius $r_B=0.3\mathrm{fm}$. The dotted lines represents the ideal gas limiting case.

Figure 7

The $N/\pi$ ratio as a function of temperature in $B\overline{B}M$ matter (the full set of hadrons) with pointlike mesons. Thick (thin) lines show the CSM results within the CII (CI) model. The dotted line represents the ideal gas limiting case. Shading shows experimental bounds for the $N/\pi$ ratio obtained [28] for 0–5% central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. The cross represents the $N/\pi$ value in the ideal gas at $T=156\mathrm{MeV}$.

Figure 8

Scaled pressure as a function of temperature in $B\overline{B}M$ matter (the full set of hadrons) with pointlike mesons. Thick (thin) lines show the CSM results within the CII (CI) model. The dotted line represents the ideal gas limiting case. The lower solid curve gives the (anti)baryon part of pressure calculated in the CII model with $r_B=0.3\mathrm{fm}$. Open dots show the results of lattice QCD calculation [1].

Figure 9

The ratio $N/\pi$ as a function of temperature in $B\overline{B}M$ matter (the full set of hadrons) with pointlike mesons. Thick (thin) lines show the CSM results within the CIII (CII) model. The dotted line represents the ideal gas limiting case. Shading shows experimental bounds for the $N/\pi$ ratio obtained [28] for 0–5% central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$.

Figure 10

Scaled pressure as a function of temperature in $B\overline{B}M$ matter (the full set of hadrons) with pointlike mesons. Thick (thin) lines show the CSM results within the CIII (CII) model. The dotted line represents the ideal gas limiting case. Open dots show the results of lattice QCD calculation [1].

Figure 11

The temperature dependence of ${\chi }^2/N_{\mathrm{dof}}$ for fitting the ALICE data on hadron yields in 0–5% central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. The dashed, dash-dotted, and solid curves correspond, respectively, to the models CI, CII, and CIII. The dotted lines are calculated in the ideal gas limit $r_B=0$.