Production and ratio of $\pi$, $K$, $p$, and $\Lambda$ in Pb + Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV

The particle production and their ratios for $\pi$, $K$, $p$, and $\Lambda$ are studied in Pb + Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV based on a blast-wave model with thermal equilibrium mechanism. The transverse momentum spectra of the above-mentioned particles at the kinetic freeze-out stage are discussed. The modification of the inverse slope of pion transverse momentum spectrum due to resonance decay has also been investigated. In addition, we found that the antiparticles-to-particles ratio as well as the kaons-to-pions ratio agree with the data by the LHC-ALICE Collaboration reasonably well, while the $p/\pi$ ratio is overestimated by a factor of 1.5, similar to those from other thermal model calculations. It is found that the ratios of $p/\pi$ and $K/\pi$ are dominated by the radial flow but slightly affected by the baryon chemical potential. Our study thus constrains the parameters at the chemical and kinetic freeze-out stages within the framework of thermal model in Pb + Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV, and will help us better understand the properties of the dense and hot matter created in high-energy heavy-ion collisions at freeze-out stage.

Figure 1

Transverse momentum ($p_T$) distribution of $\pi$, $K$, $p$, and $\Lambda$ in central and peripheral collisions. Lines: model calculations with ${\mu }_B=0.1$ MeV, ${\mu }_S=0.001$ MeV, and $T_{\mathrm{ch}}=160$ MeV for central collisions and $T_{\mathrm{ch}}=150$ MeV for peripheral collisions. Symbols: ALICE data [8, 21, 22, 23], collision centrality 0–5% (left column) and 70–80% (right column) for ${\pi }^{-}$, $K^{-}$, and $p$, and 0–10% (left column) and 60–80% (right column) for $\Lambda$. $T_{\mathrm{kin}}$ is in MeV and ${\rho }_0$ is dimensionless.

Figure 2

Local slopes of the $p_T$ distributions for $\pi$, $K$, $p$, and $\Lambda$ including their antiparticles as a function of $p_T$ in central and peripheral collisions. Lines: model calculations with ${\mu }_B=0.1$ MeV, ${\mu }_S=0.001$ MeV, and $T_{\mathrm{ch}}=160$ MeV for central collisions and $T_{\mathrm{ch}}=150$ MeV for peripheral collisions. Shadow: the ALICE data [8] for collision centrality 0–5% (left column) and 70–80% (right column). $T_{\mathrm{kin}}$ is in MeV and ${\rho }_0$ is dimensionless.

Figure 3

Comparing the pion $p_T$ spectrum from direct production and resonance decay from model calculations with $(T_{\mathrm{ch}},{\mu }_B,{\mu }_S,T_{\mathrm{kin}},{\rho }_0)=(160,0.1,0.001,99,1)$ (all in MeV except that ${\rho }_0$ is dimensionless) for central collisions and $(T_{\mathrm{ch}},{\mu }_B,{\mu }_S,T_{\mathrm{kin}},{\rho }_0)=(150,0.1,0.001,140,0.78)$ for peripheral collisions. Left: Pion spectra from direct production and total yield in central and peripheral collisions. Right: The ratios of pions from resonance decay and direct production to the total yield as a function of $p_T$ in central and peripheral collisions.

Figure 4

Ratio of inclusive yields of particles to ${\pi }^{+}$ compared with the LHC-ALICE data for central ($0-5\%$) collisions [21, 25]. $T_{\mathrm{ch}}$, ${\mu }_B$, and ${\mu }_S$ are all in MeV.

Figure 5

Ratios of $p/\pi$ [stands for $(p+\overline{p})/({\pi }^{+}+{\pi }^{-})$] and $K/\pi$ [stands for $(K^{+}+K^{-})/({\pi }^{+}+{\pi }^{-})$] as a function of $p_T$ in central and peripheral collisions. Lines: model calculations with ${\mu }_S=0.001$ MeV, $T_{\mathrm{ch}}=160$ MeV, and $T_{\mathrm{kin}}=99$ MeV for central collisions, and $T_{\mathrm{ch}}=150$ MeV and $T_{\mathrm{kin}}=140$ MeV for peripheral collisions. Shadow: the ALICE data [8] for collision centrality 0–5% (left column) and 70–80% (right column). ${\rho }_0$ is dimensionless and ${\mu }_B$ is in MeV.