Spectra and elliptic flow for identified hadrons in $2.76A$ TeV Pb + Pb collisions

Using the vishnu hybrid model that couples (2+1)-dimensional viscous hydrodynamics to a microscopic hadronic transport model, we calculate the multiplicity, $p_T$ spectra, and elliptic flow for pions, kaons, and protons in 2.76$A$ TeV Pb+Pb collisions, using mc-kln initializations with smoothed initial conditions, obtained by averaging over a large number of events. The results from our calculations are compared to data from the ALICE Collaboration, showing nice agreement over several centrality bins. Using the same inputs, we predict the $p_T$ spectra and elliptic flow for $\varphi$ mesons and explore their flow development in the strong and weak coupling limits through hydrodynamic calculations with different decoupling temperatures. In addition we study the influence of baryon and antibaryon annihilation processes on common observables and demonstrate that, by including annihilation processes below a switching temperature of 165 MeV, vishnu provides a good description of the multiplicity and $p_T$ spectra for pions, kaons, and protons measured by PHENIX and ALICE at both the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC).

Figure 1

Centrality dependence of the rapidity density per participant pair $(d{N}_{\mathrm{ch}}/dy)/(N_{\mathrm{part}}/2)$ for pions, kaons, and protons in 2.76$A$ TeV Pb+Pb collisions. Experimental data are from ALICE [32]. Theoretical curves are from vishnu calculations with mc-kln initializations, $\eta /s=0.16$ and a switching temperature $T_{\mathrm{sw}}=165$ MeV.

Figure 2

Upper panels: $p_T$ spectra for pions, kaons and protons in 2.76$A$ TeV Pb+Pb collisions. Experimental data are from ALICE [32]. Theoretical curves are from vishnu. From top to bottom the curves correspond to 0–5% ($\times 1000$), 5–10% ($\times 100$), 10–20% ($\times 10$), 20–30%, 30–40% ($\times 0.1$), 40–50% ($\times 0.01$), 50–60% ($\times 0.001$), 60–70% ($\times {10}^{-4}$), 70–80% ($\times {10}^{-5}$) centrality, respectively, where the factors in parentheses indicate the multipliers applied to the spectra for clearer presentation. Lower panels: the ratio of the experimental and theoretical $p_T$ spectra for pions, kaons, and protons for 0–5%, 30–40% and 70–80% centralities.

Figure 3

Differential elliptic flow $v_2\left(p_T\right)$ for pions, kaons, and protons in 2.76$A$ TeV Pb+Pb collisions. Experimental data are from ALICE [29]. Theoretical curves are from vishnu. See text for details.

Figure 4

A prediction for the $\varphi$ meson $p_T$ spectra for 2.76$A$ TeV Pb+Pb collisions at different centralities as indicated, using vishnu simulations with the same inputs as in Figs. 1, 2, 3.

Figure 5

A prediction for the $\varphi$ elliptic flow for 2.76$A$ TeV Pb+Pb collisions using vishnu simulations with the same inputs as in Figs. 1, 2, 3.

Figure 6

$p_T$ spectra and differential elliptic flow $v_2\left(p_T\right)$ for pions, protons, and $\varphi$ mesons from the hybrid code vishnu, compared with results for $\varphi$ mesons from pure viscous hydrodynamics VISH2+1 with resonance decays. The freeze-out temperature for VISH2+1 is set to 165 and 100 MeV, and the switching temperature for vishnu is 165 MeV. See text for details.

Figure 7

Centrality dependence of the rapidity density per participant pair $(d{N}_{\mathrm{ch}}/dy)/(N_{\mathrm{part}}/2)$ for pions, kaons, and protons in 2.76$A$ TeV Pb+Pb collisions (left) and in 200$A$ GeV Au+Au collisions (right). Experimental data are from ALICE [32], STAR [39], and PHENIX [40]. Theoretical curves are from vishnu, with $B\text{−}\overline{B}$ annihilation turned on (solid lines) or off (dashed lines). The left panel is similar to Fig. 1, except for the addition of the theoretical lines without $B\text{−}\overline{B}$ annihilation.

Figure 8

$p_T$ spectra in most central collisions for pions kaons and protons in 2.76$A$ TeV Pb+Pb collisions (left) and 200$A$ GeV Au+Au collisions (right). Experimental data are from from ALICE [32], STAR [39, 41], and PHENIX [40], respectively. Same illustration for theoretical and experimental lines as in Fig. 7. All proton spectra were divided by 5 for improved clarity of the plots.