Hydrodynamic predictions for Pb+Pb collisions at 5.02 TeV

Predictions and comparisons of hadronic flow observables for Pb+Pb collisions at 2.76 and 5.02 TeV are presented using a hydrodynamics + hadronic cascade hybrid approach. Initial conditions are generated via a new formulation of the IP-Glasma model and then evolved using relativistic viscous hydrodynamics and finally fed into transport cascade in the hadronic phase. The results of this work show excellent agreement with the recent charged hadron anisotropic flow measurements from the ALICE Collaboration of Pb+Pb collisions at 5.02 TeV. Event-by-event distributions of charged hadron $v_n$, flow event-plane correlations, and flow factorization breaking ratios are compared with existing measurements at 2.76 TeV, and are predicted at 5.02 TeV. Further predictions of identified hadron observables (for both light and multistrange hadrons), such as $p_T$-spectra and anisotropic flow coefficients, are presented.

Figure 1

The centrality dependence of the event plane resolution factor $R_n$ for $n=2,3,4$ in Pb+Pb collisions at 5.02 TeV.

Figure 2

The centrality dependence of charged hadron multiplicity in Pb+Pb collisions compared with the ALICE measurements at 2.76 TeV [48] and 5.02 TeV [49].

Figure 3

The centrality dependence of charged hadron anisotropic flow coefficients in Pb+Pb collisions at 2.76 TeV (a) and 5.02 TeV (b). The integrated $p_T$ range for the two particle cumulant $v_n\left\{2\right\}$ is from 0.2 to 3.0 GeV. Theoretical results are compared with the recent ALICE measurements at both collision energies [3, 50].

Figure 4

Charged hadron $p_T$-differential $v_n$ in 0–5% (a,c) and 30–40% (b,d) centrality bins in Pb+Pb collisions at 2.76 (a,b) and 5.02 (c,d) TeV. The reference flow vector is the charged hadron $v_n$ integrated from 0.2 to 3.0 GeV. At both collision energies, theoretical results are compared with the ALICE measurements [3, 50].

Figure 5

(a) Identified particle averaged momentum, $\langle p_T\rangle$, as functions of centrality in Pb+Pb collisions at 2.76 TeV compared with the ALICE data [57]. (b) Predictions of ${\pi }^{+},K^{+}$, and $p$ mean $p_T$ in Pb+Pb collisions at 5.02 TeV. (c) Identified particle yields as functions of centrality compared to the ALICE data.

Figure 6

(a,c) Light hadrons $p_T$-differential spectra in 0–5% and 30–40% Pb+Pb collisions at 2.76 TeV compared with the ALICE measurements [57]. (b,d) Predictions of ${\pi }^{+},K^{+}$, and $p$ spectra in Pb+Pb collisions at 5.02 TeV.

Figure 7

(a,c) Multistrange hadrons $p_T$-differential spectra in 0–10% and 20–40% Pb+Pb collisions at 2.76 TeV compared with the ALICE measurements [60, 61, 62]. (b,d) Predictions of $\varphi ,\mathrm{\Lambda },{\mathrm{\Xi }}^{-}$, and $\mathrm{\Omega }$ spectra in Pb+Pb collisions at 5.02 TeV.

Figure 8

(a,c) The elliptic flow coefficients $v_2$ of identified particles in 5–10% and 30–40% Pb+Pb collisions at 2.76 TeV compared with the ALICE measurements [64]. The reference flow vector is the charged hadron $v_2$ integrated from 0.2 to 3.0 GeV. (b,d) Predictions of the $v_2\left(p_T\right)$ for ${\pi }^{+},K^{+}$, and $p$ in Pb+Pb collisions at 5.02 TeV.

Figure 9

Higher order anisotropic flow coefficients, $v_{3,4}\left\{2\right\}\left(p_T\right)$, for ${\pi }^{+},K^{+}$, and $p$ in Pb+Pb collisions at 2.76 and 5.02 TeV. The reference flow vector is the charged hadron $v_n$ integrated from 0.2 to 3.0 GeV. The ALICE measurements at 2.76 TeV [67] are shown for comparison.

Figure 10

(a,c) The elliptic flow coefficients $v_2$ of multistrange hadrons $\varphi ,\mathrm{\Lambda }+\overline{\mathrm{\Lambda }}$, and ${\mathrm{\Xi }}^{-}+{\overline{\mathrm{\Xi }}}^{+}$ in 5–10% and 30–40% Pb+Pb collisions at 2.76 TeV compared with the ALICE measurements [64]. The reference flow vector is the charged hadron $v_2$ integrated from 0.2 to 3.0 GeV. (b,d) Predictions of the $v_2\left(p_T\right)$ for $\varphi ,\mathrm{\Lambda }+\overline{\mathrm{\Lambda }}$, and ${\mathrm{\Xi }}^{-}+{\overline{\mathrm{\Xi }}}^{+}$ in Pb+Pb collisions at 5.02 TeV.

Figure 11

The normalized distributions of event-by-event charged hadron anisotropic flow coefficients are compared with the measurements from the ATLAS Collaboration in 0–5% (a–c), 20–25% (d–f), and 40–45% (g–i) centralities in Pb+Pb collisions at 2.76 TeV [47]. The charged hadron $v_n$ in every event are integrated from 0.5 to 3.0 GeV in transverse momentum. The normalized distributions of initial eccentricities at the end of the IP-Glasma phase $({\tau }_0=0.4$ fm) are shown as dashed lines.

Figure 12

Predictions of event-by-event charged hadron $v_n$ distributions in 0–5%, 20–25%, and 40–50% Pb+Pb collisions at 5.02 TeV.

Figure 13

The charged hadron event-plane correlations are compared with the ATLAS measurements [74] using the scalar-product method in Pb+Pb collisions at 2.76 TeV. The values of $N_{part}$ at different centrality bins are estimated using the MC-Glauber model according to Table I in Ref. [74].

Figure 14

Predictions of charged hadron event-plane correlations in Pb+Pb collisions at 5.02 TeV.

Figure 15

The charged hadron flow factorization breaking ratio $r_n$ are compared with the CMS measurements [77] in Pb+Pb collisions at 2.76 TeV.

Figure 16

The effect of hadronic rescatterings on the flow factorization breaking ratios $r_2$ and $r_3$.

Figure 17

Predictions of charged hadron flow factorization breaking ratio in Pb+Pb collisions at 5.02 TeV.

Figure 18

Identified particle spectra with and without $\delta f$ corrections from shear and bulk viscosities.

Figure 19

Identified particle $p_T$-differential $v_2\left(p_T\right)$ and $v_3\left(p_T\right)$ with and without the shear and bulk $\delta f$ corrections.

Figure 20

The effect of shear and bulk $\delta f$ on the flow factorization breaking ratios $r_2$ and $r_3$.