Freezeout hypersurface at energies available at the CERN Large Hadron Collider from particle spectra: Flavor and centrality dependence

We extract the freezeout hypersurface in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2760$ GeV at the CERN Large Hadron Collider by analyzing the data on transverse momentum spectra within a unified model for chemical and kinetic freezeout. The study is done within two schemes of freezeout: single freezeout, where all the hadrons freeze out together, versus double-freezeout, where those hadrons with nonzero strangeness content have different freezeout parameters compared to the nonstrange ones. We demonstrate that the data are better described within the latter scenario. We obtain a strange freezeout hypersurface which is smaller in volume and hotter compared to the nonstrange freezeout hypersurface for all centralities, with a reduction in ${\chi }^2/N_{\mathrm{df}}$ around $40\%$. We observe from the extracted parameters that the ratio of the transverse size to the freezeout proper time is invariant under expansion from the strange to the nonstrange freezeout surfaces across all centralities. Moreover, except for the most peripheral bins, the ratio of the nonstrange-to-strange freezeout proper times is close to 1.3.

Figure 1

Plots of ${\chi }^2/N_{\mathrm{df}}$ in the 1FO and 2FO schemes. The left plot shows the total ${\chi }^2/N_{\mathrm{df}}$ of both FHs, while the middle and right plots show the ${\chi }^2/N_{\mathrm{df}}$ for nonstrange and strange FHs respectively. Centrality bin numbers 1, 2, 3, 4, 5, and 6 refer to the (0–5)%, (5–10)%, (10–20)%, (20–40)%, (40–60)%, and (60–80)% centrality bins, respectively.

Figure 2

Plots of the different freezeout parameters in the 1FO and 2FO schemes. The left panel shows a plot of $T$, while the middle and right plots show the geometric parameters ${\tau }^f$ and ${\rho }^{\text{max}}$. Centrality bin numbers 1, 2, 3, 4, 5, and 6 refer to the (00–05)%, (05–10)%, (10–20)%, (20–40)%, (40–60)%, and (60–80)% centrality bins, respectively.

Figure 3

Plots of ${\pi }^{+}$ spectra as obtained in 1FO (left) vs 2FO (right). While the top panels show a comparison of the $p_T$ spectra between data [33] and model, the lower panels plot the data/model ratio for the different centrality bins.

Figure 4

Plots of $K^{+}$ spectra as obtained in 1FO (left) vs 2FO (right). While the top panels show a comparison of the $p_T$ spectra between data [33] and model, the lower panels plot the data/model ratio for the different centrality bins.

Figure 5

Plots of $p$ spectra as obtained in 1FO (left) vs 2FO (right). While the top panels show comparison of the $p_T$ spectra between data [33] and model, the lower panels plot the data/model ratio for the different centrality bins.

Figure 6

Plots of $\mathrm{\Lambda }$ spectra as obtained in 1FO (left) vs 2FO (right). While the top panels show a comparison of the $p_T$ spectra between data [34] and model, the lower panels plot the data/model ratio for the different centrality bins.

Figure 7

Plots of ${\mathrm{\Xi }}^{-}$ (top) and $\mathrm{\Omega }$ (bottom) spectra as obtained in 1FO (left) vs 2FO (right). In each plot, the top panels show a comparison of the $p_T$ spectra between data [35] and model and the lower panels plot the data/model ratio for the different centrality bins.

Figure 8

Plots of $K^{*}$ spectra as obtained in 1FO (left) vs 2FO (right). While the top panels show a comparison of the $p_T$ spectra between data [36] and model, the lower panels plot the data/model ratio for the different centrality bins.

Figure 9

Plots of $\varphi$ spectra as obtained in 1FO (left) vs 2FO (right). While the top panels show a comparison of the $p_T$ spectra between data [36] and model, the lower panels plot the data/model ratio for the different centrality bins.

Figure 10

Comparison of ${\chi }^2/N_{df}$ for different parameter sets in 2FO with 1FO. The last two peripheral bins in the case of the fit with 2FO and four parameters are not shown, as $\frac{{\tau }_{\mathrm{ns}}}{{\tau }_s}=1.3$ does not hold for these centralities. For the most peripheral bin 6, (60–80)%, the model fits are becoming worse, indicating that the model should be improved for peripheral collisions.

Figure 11

Nonstrange and strange freezeout hypersurfaces as obtained in the 1FO and 2FO schemes from fits to the data on $p_T$ spectra for the (0–5)% centrality bin. Freezeout is assumed to occur at a fixed invariant time ${\tau }^f$, and ${\rho }^{\text{max}}$ is the edge of the freezeout cylinder.