Hybrid model approach for strange and multistrange hadrons in $2.76A$ TeV $\text{Pb}+\text{Pb}$ collisions

Using the VISHNU hybrid model, we calculate the multiplicity, spectra, and elliptic flow of $\Lambda ,\Xi$, and $\Omega$ in $2.76A$ TeV Pb + Pb collisions. Comparisons between our calculations and the ALICE measurements show that the model generally describes the soft hadron data of these strange and multistrange hadrons at several centrality bins. Mass ordering of elliptic flow among $\pi ,K,p,\Lambda ,\Xi$, and $\Omega$ has also been studied and discussed. With a nice description of the particle yields, we explore chemical and thermal freeze-out of various hadrons species at the Large Hadron Collider within the framework of the VISHNU hybrid model.

Figure 1

Centrality dependence of the multiplicity density per participant pair, $(dN/dy)/(N_{\mathrm{part}}/2)$, for $\Lambda ,\Xi$, and $\Omega$ in $2.76A$ TeV Pb + Pb collisions. Inset: $(dN/dy)/(N_{\mathrm{part}}/2)$ for $\pi ,K,p$ and for all charged hadrons. Experimental data are from the ALICE Collaboration [19, 20, 45, 46]. Theoretical curves are calculated with the VISHNU hybrid model, using MC-KLN initial conditions, $\eta /s=0.16$, and $T_{sw}=165\mathrm{MeV}$.

Figure 2

Transverse momentum spectra of $\Lambda ,\Xi$, and $\Omega$ at various centralities in $2.76A$ TeV Pb + Pb collisions. Experimental data are taken from ALICE [19, 20]. Theoretical curves are calculated with VISHNU with the same inputs as for Fig. 1. From top to bottom the curves correspond to 0–10% $(\times {10}^4)$, 10–20% $(\times {10}^3)$, 20–40% $(\times {10}^2)$, 40–60% $(\times {10}^1)$, and 60-80% $(\times 1)$ centrality, respectively, where the factors in parentheses are the multipliers applied to the spectra for clear separation. Spectra of $\Lambda$ start from 0–5% $(\times {10}^5)$ and 5–10% $(\times {10}^4)$, instead of 0–10%.

Figure 3

Differential elliptic flow of strange hadrons $\Lambda$ and multistrange hadrons $\Xi$ and $\Omega$ at 10–20%, 30–40% and 50–60% centralities in $2.76A$ TeV Pb + Pb collisions. Experimental data are from ALICE [21], theoretical curves are calculated from VISHNU with the same inputs as for Figs. 1 and 2.

Figure 4

Differential elliptic flow of $\pi ,K,p,\Lambda ,\Xi$, and $\Omega$ at 10–20% and 40–50% centralities in $2.76A$ TeV Pb + Pb collisions. Left panels (a) and (c) are plotted with $v_2$ from ALICE [21], right panels (b) and (d) are plotted with $v_2$ from VISHNU.

Figure 5

Left panels (a)–(f): time evolution of relative particle yield density $\frac{dN}{dy}\left(t\right)/\frac{dN}{dy}\left(0\right)$ for $\pi ,K,p,\Lambda ,\Xi$, and $\Omega$ during the UrQMD expansion of VISHNU. Right panels (g) and (h): time evolution of the changing rate for the corresponding particle yield density. Solid/dashed lines denote the VISHNU simulations with/without $B-\overline{B}$ annihilations in the most central $2.76A$ TeV Pb + Pb collisions.

Figure 6

Similar to Fig. 5, but for 70–80% centrality bin.

Figure 7

Thermal freeze-out time distributions for $\pi ,K,p,\Lambda ,\Xi$, and $\Omega$ in the most central Pb + Pb collisions, calculated from hydrodynamics (green), hydrodynamics + resonance decay (blue), and VISNU without $\mathit{B}-\overline{B}$ annihilations (red) and with $\mathit{B}-\overline{B}$ annihilations (black).

Figure 8

Comparisons of the thermal freeze-out time distributions for $\pi ,K,p,\Lambda ,\Xi$, and $\Omega$ between the most central and peripheral Pb + Pb collisions, calculated from VISHNU with $\mathit{B}-\overline{B}$ annihilations.

Figure 9

Thermal freeze-out time distributions for $\pi ,K,p,\Lambda ,\Xi$, and $\Omega$ in the most central Pb + Pb collisions, calculated from VISHNU with $\mathit{B}-\overline{B}$ annihilations.