Effects of bulk viscosity and hadronic rescattering in heavy ion collisions at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider

We describe ultrarelativistic heavy ion collisions at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider with a hybrid model using the IP-Glasma model for the earliest stage and viscous hydrodynamics and microscopic transport for the later stages of the collision. We demonstrate that within this framework the bulk viscosity of the plasma plays an important role in describing the experimentally observed radial flow and azimuthal anisotropy simultaneously. We further investigate the dependence of observables on the temperature below which we employ the microscopic transport description.

Figure 1

The temperature dependence of the bulk viscosity to entropy density ratio used in this study. The QGP side of the $\zeta /s$ is taken from Karsch et al. 2008 [14] and the hadronic (HG) side is taken from Noronha-Hostler et al. 2009 [17].

Figure 2

Integrated $v_n$ (upper), midrapidity multiplicity ${dN/dy|}_{y=0}$ (middle), and mean $p_T$ (lower) as functions of centrality. The ratio of the shear viscosity to entropy density $\eta /s$ is determined to fit the ALICE data on $v_n$ [65]. The left-hand panels include bulk viscosity as shown in Fig. 1, while the right-hand panels were computed with $\zeta /s=0$. The nonzero bulk viscosity alters the favored value of $\eta /s$. The ALICE data [66] for ${dN/dy|}_{\left|y\right|<0.5}$ and $\langle p_T\rangle$ are also shown.

Figure 3

Midrapidity multiplicity ${\left.dN/dy\right|}_{\left|y\right|<0.5}$ (left) and mean $p_T$ (right) of pions, kaons, and protons as functions of the switching temperature $T_{\mathrm{sw}}$. The most central Pb-Pb collisions with $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ are considered. The ALICE data [66] are shown as the bands.

Figure 4

Midrapidity multiplicity ${\left.dN/dy\right|}_{\left|y\right|<0.5}$ (left) and mean $p_T$ (right) of $\mathrm{\Lambda }$, $\mathrm{\Xi }$, and $\mathrm{\Omega }$ baryons as functions of the switching temperature $T_{\mathrm{sw}}$. The most central Pb-Pb collisions with $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ are considered.

Figure 5

Midrapidity multiplicity (left panel) and mean $p_T$ (right panel) of identified particles as functions of centrality.

Figure 6

(a) Midrapidity multiplicity ${\left.dN/dy\right|}_{\left|y\right|<0.5}$ and mean $p_T$ of pions, kaons, and protons and (b) charged hadron momentum anisotropy, as functions of centrality, for Au-Au collisions with $\sqrt{s_{NN}}=200\mathrm{GeV}$. The value of $T_{\mathrm{sw}}$ is set to $165\mathrm{MeV}$ so as to provide the a good description of the proton multiplicity, while $\eta /s=0.06$ was adjusted to describe the momentum anisotropies. Measurements from STAR [67, 68, 69] are also shown.

Figure 7

(a) Midrapidity charged hadron $v_2\left\{2\right\}$ with and without hadronic rescattering, as a function of $T_{\mathrm{sw}}$ for Au-Au collisions with $\sqrt{s_{NN}}=200\mathrm{GeV}$ (left) and for Pb-Pb collisions with $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ (right).

Figure 8

$p_T$ differential $v_n\left\{2\right\}$ ($n=2$, 3, and 4) of charged hadrons for centrality classes $0–5\%$, $10–20\%$, $20–30\%$, and $30–40\%$ of Pb-Pb collisions with $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. The statistical errors in the calculation are shown as the bands around the curves. The ALICE data [65] and CMS [70, 71] data are also shown for comparison.

Figure 9

$p_T$ spectra of identified hadrons for centrality classes $0–5\%$, $10–20\%$, $20–30\%$, and $30–40\%$ of Pb-Pb collisions with $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. The solid curves and the dashed curves correspond to full urqmd and urqmd without collisions, respectively. The statistical errors in the calculation are shown as the bands around the curves. The ALICE data [66] are shown for comparison.

Figure 10

$p_T$ differential $v_2\left\{2\right\}$ of identified hadrons for centrality classes $0–5\%$, $10–20\%$, $20–30\%$, and $30–40\%$ of Pb-Pb collisions with $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. The solid curves and the dashed curves correspond to full urqmd and urqmd without collisions, respectively. The statistical errors in the calculation are shown as the bands around the curves. The ALICE data [72] are shown for comparison.

Figure 11

$p_T$ spectra (upper) and $p_T$ differential $v_2\left\{2\right\}$ (lower) of strange baryons of Pb-Pb collisions with $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. The solid curves and the dashed curves correspond to full urqmd and urqmd without collisions, respectively. The statistical errors in the calculation are shown as the bands around the curves.

Figure 12

$p_T$ differential $v_3\left\{2\right\}$ of pions, kaons, and antiprotons for centrality classes $0–5\%$, $10–20\%$, $20–30\%$, and $30–40\%$ of Pb-Pb collisions with $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. The statistical errors in the calculation are shown as the bands around the curves. Measurements are from [81].

Figure 13

$p_T$ differential $v_4\left\{2\right\}$ of pions, kaons, and antiprotons for centrality classes $0–5\%$, $10–20\%$, $20–30\%$, and $30–40\%$ of Pb-Pb collisions with $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. The statistical errors in the calculation are shown as the bands around the curves. Measurements are from [81].

Figure 14

$p_T$ differential $v_2\left\{4\right\}$ and $v_n\left\{2\right\}$ ($n=3$ and 4) of charged hadrons for centrality classes $10–20\%$ (left) and $30–40\%$ (right) of Au-Au collisions with $\sqrt{s_{NN}}=200\mathrm{GeV}$. The statistical errors in the calculation are shown as the bands around the curves. The PHENIX [82] and STAR [83] data are shown for comparison.

Figure 15

$p_T$ spectra of identified hadrons for centrality classes $0–5\%$, $10–20\%$, $20–30\%$, and $30–40\%$ of Au-Au collisions with $\sqrt{s_{NN}}=200\mathrm{GeV}$. The solid curves and the dashed curves correspond to full urqmd and urqmd without collisions, respectively. The statistical errors in the calculation are shown as the bands around the curves. The PHENIX [84] data are shown for comparison.

Figure 16

$p_T$ differential $v_2\left\{2\right\}$ (right panels) of identified hadrons for centrality classes $0–5\%$, $10–20\%$, $20–30\%$, and $30–40\%$ of Au-Au collisions with $\sqrt{s_{NN}}=200\mathrm{GeV}$. The solid curves and the dashed curves correspond to full urqmd and urqmd without collisions, respectively. The statistical errors in the calculation are shown as the bands around the curves. The STAR [67] and PHENIX [85] data are shown for comparison.

Figure 17

$p_T$ spectra (upper) and $p_T$ differential $v_2\left\{2\right\}$ (lower) of strange baryons in Au-Au collisions with $\sqrt{s_{NN}}=200\mathrm{GeV}$. The solid curves and the dashed curves correspond to full urqmd and urqmd without collisions, respectively. The statistical errors in the calculation are shown as the bands around the curves. The STAR data on $p_T$ spectra [86] and $v_2\left(p_T\right)$ [87] are shown for comparison.

Figure 18

Effect of $\delta f_{\mathrm{shear}}$ on (a) the average transverse momentum of thermally emitted (Cooper-Frye) pions, kaons, and protons, and (b) the $p_T$-integrated $v_2$, $v_3$, and $v_4$ of charged hadrons, as a function of centrality, for Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV.

Figure 19

Effect of $\delta f_{\mathrm{bulk}}$ on the pion, kaon, and proton $dN/dy$ as a function of centrality, for Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. Panel (a) is for thermal (Cooper-Frye) hadrons, (b) is after hadronic decays.

Figure 20

Effect of $\delta f_{\mathrm{bulk}}$ on the average transverse momentum of pions, kaons, and protons as a function of centrality, for Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. Panel (a) is for thermal (Cooper-Frye) hadrons, (b) is after hadronic decays.