Hadron production and quark-gluon plasma hadronization in Pb-Pb collisions at $\sqrt{s_{\mathit{NN}}}=2.76$ TeV

We show that all central rapidity hadron yields measured in Pb-Pb collisions at $\sqrt{s_{\mathit{NN}}}=2.76$ TeV are well described by the chemical nonequilibrium statistical hadronization model (SHM), where the chemically equilibrated quark-gluon plasma source breaks up directly into hadrons. SHM parameters are obtained as a function of centrality of colliding ions, and we compare CERN Large Hadron Collider (LHC) results with Brookhaven National Laboratory Relativistic Heavy Ion Collider (RHIC) results. We predict yields of unobserved hadrons and address antimatter production. The physical properties of the quark-gluon plasma fireball particle source show universality of hadronization conditions at LHC and RHIC.

Figure 1

SHM fit to experimental data measured by the ALICE experiment in Pb-Pb collisions at $\sqrt{s_{\mathit{NN}}}=2.76$ TeV for 0%–20% centrality [panels (a) and (b) on the left-hand side] and for 1/4 of this range, 5%–10% [panels (c) and (d) on the right-hand side]. The input set of particle types is the same as can be seen in particle listing on the ordinates of panels (b) and (d); in panel (d) also particle yield ratios are used. In the panels (b) and (d) comparison of SHM chemical nonequilibrium fit (horizontal line) with data is shown. The experimental data are shown as solid squares; in the panel (d) the interpolated experimental data are shown with open symbols (see Appendix for details). Panels (a) and (c) show the ratio of model values to experimental data for the three SHM variants and present the key parameter values for chemical nonequilibrium (solid squares), chemical semiequilibrium (solid circles), and chemical equilibrium (solid triangles). For readability, antiparticles are omitted in panels (a) and (c).

Figure 2

Total ${\chi }^2$ as a function of centrality, as indicated in the figure, for the total equilibrium (${\gamma }_q={\gamma }_s=1,\mathrm{ndf}=11$), for the semiequilibrium (${\gamma }_q=1,{\gamma }_s\ne 1,\mathrm{ndf}=10$), and for chemical nonequilibrium (${\gamma }_q\ne 1,{\gamma }_s\ne 1,\mathrm{ndf}=9$) SHM. Open symbols represent the total ${\chi }^2$ for the 0%–20% centrality bin depicted in Figs. 1a and 1b The number of degrees of freedom for the three cases, respectively, is $\mathrm{ndf}=11,10,9$. (The value of equilibrium SHM in the 0%–20% bin has been shifted down by 20 to fit in the figure.)

Figure 3

Experimental charged-particle yield pseudorapidity density $dN/d\eta$ (blue squares), and geometric model relating to charged-particle rapidity density $dN/dy$ of only primary particles (violet circles) and including feed from strongly decaying resonances (red triangles) per participant pairs $N_{\mathrm{part}}/2$.

Figure 4

Fraction of primary hadrons produced, normalized by their final yield, which consists of primary produced hadrons and the feed from strong decaying resonances, for particles indicated in the right margin, as a function of hadronization temperature in single freeze-out model.

Figure 5

${\chi }^2/\mathrm{ndf}$ profile as a function of ${\gamma }_q$ for all studied centralities.

Figure 6

Solid symbols are the experimental data points. Open symbols represent the outcome for our chemical nonequilibrium SHM fit to LHC2760 as a function of centrality, i.e., $N_{\mathrm{part}}$. Dashed lines are the outcome of our data interpolation of experimental yields available (see Appendix). Dotted lines connecting $\Lambda$, $K^{*}$, and $\varphi$ SHM output values are presented to guide the eye; because ratios of these particles were used in our fit, the data are shown in Fig. 7.

Figure 7

Solid symbols, experimental data with errors for $K^{*}/K$, $\varphi /K$, and $\Lambda /\pi$ as a function of centrality, i.e., number of participants $N_{\mathrm{part}}$. Lines are the interpolation (respectively, extrapolation) except for the case $\varphi /K$, where dotted line guides the eye. Open circles represent the resulting fit value for each ratio. The (blue) shaded band shows the error input used obtaining the interpolated values of $K^{*}/K$ ratio.

Figure 8

Particles predicted by the chemical nonequilibrium SHM fits. Predictions for hadron yields (solid symbols) are above antinuclei yield predictions (open symbols), which have been multiplied by suitable factors. Lines guide the eye; points are actual predictions for each of the nine centralities we analyzed.

Figure 9

SHM parameters as a function of centrality, i.e., number of participants $N_{\mathrm{part}}$, presented for the three different levels of chemical equilibrium, and compared to the chemical nonequilibrium SHM RHIC62 results (open symbols, dashed lines). All lines guide the eye. From top to bottom: (a) $dV/dy$ (note that the volume for both equilibrium and semiequilibrium SHM variants is so close that symbols overlap); (b) $T$, the chemical freeze-out temperature (semiequilibrium symbols are offset to separate them from equilibrium); (c) phase-space occupancies ${\gamma }_s^{\left(\mathrm{neq}\right)}$, ${\gamma }_q^{\left(\mathrm{neq}\right)}$, and for comparison with equilibrium ${\gamma }_s^{\left(\mathrm{seq}\right)}$; we also present ${\gamma }_s^{\left(\mathrm{neq}\right)}/{\gamma }_q^{\left(\mathrm{neq}\right)}$.

Figure 10

Scatter plot of fitted chemical potentials. The dashed line shows net baryon number over entropy $b/S$ scaled with 5000.

Figure 11

(a) Data and SHM description of $p/\pi$ ratio fitted together with all other data within the three SHM approaches as a function of centrality. (b) Resulting ${\chi }_{\mathrm{total}}^2$ for the three variants. See Sec. 3b for details.

Figure 12

Solid symbols, antiproton annihilation event path $L_{\mathrm{event}}$ for the three SHM models as a function of centrality; open symbols, fireball size scale $\langle L\rangle$. The shaded error band represents error margin originating from the uncertainty of $T$ (semi)equilibrium SHM. For readability, we omit much smaller error bands for nonequilibrium SHM.

Figure 13

Bulk properties of the fireball as a function of centrality. From top to bottom, energy density $\varepsilon$ (purple triangles), the entropy density $\sigma$ (red) circles, scaled down by factor 10, and the hadronization pressure $3P$ (blue) squares; LHC2760 values are shown with solid symbols, RHIC62 values are shown with open symbols for comparison. Shaded areas show our estimate of systematic error arising from the uncertainty of ${\gamma }_s$.

Figure 14

Entropy yield $dS/dy$ at LHC2760 and at RHIC62 as a function of centrality showing power-law fit parameters in the legend. The colored band represents uncertainty based on ${\gamma }_s$ fit uncertainty. Error bars arise from error in the volume $dV/dy$.

Figure 15

(a) Strangeness per entropy $s/S$ content of the fireball at LHC2760 (solid squares) and at RHIC62 (open squares) as a function of centrality; (b) the thermal energy cost to make a strange-antistrange quark pair. Colored bands represent uncertainty based on ${\gamma }_s$ uncertainty.

Figure 16

Phase diagram showing current lattice value of critical temperature $T_c$ calculated by two groups [25, 27] and results of this work, as well as our previous results (blue circles) [7, 40, 52] and results of other groups [6, 15, 53, 54, 55, 56, 57, 58]. Solid circles refer to chemical nonequilibrium; all other symbols refer to fit results with chemical equilibrium of light quarks.