Anisotropic hydrodynamic modeling of 2.76 TeV Pb-Pb collisions

We compare phenomenological results from $3+1\mathrm{D}$ quasiparticle anisotropic hydrodynamics (aHydroQP) with experimental data collected in the CERN Large Hadron Collider 2.76 TeV Pb-Pb collisions. In particular, we present comparisons of particle spectra, average transverse momentum, elliptic flow, and Hanbury Brown–Twiss radii. The aHydroQP model relies on the introduction of a single temperature-dependent quasiparticle mass which is fit to lattice QCD data. By taking moments of the resulting Boltzmann equation, we obtain the dynamical equations used in the hydrodynamic stage which include the effects of both shear and bulk viscosities. At freeze-out, we use anisotropic Cooper-Frye freeze-out performed on a fixed-energy-density hypersurface to convert to hadrons. To model the production and decays of the hadrons we use therminator2 which is customized to sample from ellipsoidal momentum-space distribution functions. Using smooth Glauber initial conditions, we find very good agreement with many heavy-ion collision observables.

Figure 1

In (a), we show the bulk viscosity scaled by the entropy density obtained using the quasiparticle model (black solid line) [31, 71] compared with $\zeta /s=15\eta /s{(1/3-c_s^2)}^2$, which is a frequently used small-mass limit result (red dashed line). In (b), we show $m/T$ extracted by fitting to LQCD results for the entropy density [70].

Figure 2

Transverse momentum spectra of ${\pi }^{\pm }$, $K^{\pm }$, and $p+\overline{p}$ for six centrality classes. All results are for 2.76 TeV Pb-Pb collisions and data shown are from the ALICE collaboration [76].

Figure 3

The charged-hadron multiplicity in different centrality classes as a function of pseudorapidity. Results are for 2.76 TeV Pb-Pb collisions and data are from the ALICE collaboration [77, 78].

Figure 4

The average transverse momentum of ${\pi }^{\pm }$, $K^{\pm }$, and $p+\overline{p}$ as a function of centrality for 2.76 TeV Pb-Pb collisions. Data are from the ALICE collaboration [76].

Figure 5

The integrated $v_2$ for charged hadrons as a function of centrality ($0.2<p_T<3$ GeV, $\eta <0.8$). All results are for 2.76 TeV Pb-Pb collisions and data are from the ALICE collaboration [79].

Figure 6

The elliptic flow coefficient for identified hadrons as a function of $p_T$ for four centrality classes as shown in each panel. All results and data are for 2.76 TeV Pb-Pb collisions. Data shown are from the ALICE collaboration and were extracted using the scalar product method [80].

Figure 7

The pseudorapidity dependence of the elliptic flow $v_2$ for charged hadrons in different centrality classes where we take $0<p_T<100$ GeV. All results are for 2.76 TeV Pb-Pb collisions and data are from the ALICE collaboration [81].

Figure 8

The femtoscopic (HBT) radii as a function of the pair mean transverse momentum $\left(k_T\right)$ for ${\pi }^{+}{\pi }^{+}$ in the $0\text{–}5\%$, $5\text{–}10\%$, $10\text{–}20\%$, and $20\text{–}30\%$ centrality classes. The left, middle, and right panels show $R_{\mathrm{out}}$, $R_{\mathrm{side}}$, and $R_{\mathrm{long}}$, respectively. All results are for 2.76 TeV Pb-Pb collisions where data shown are for ${\pi }^{\pm }{\pi }^{\pm }$ obtained by the ALICE collaboration [83].

Figure 9

The ratios of femtoscopic (HBT) radii as a function of the pair mean transverse momentum $\left(k_T\right)$ for ${\pi }^{+}{\pi }^{+}$ in the $0\text{–}5\%$, $5\text{–}10\%$, $10\text{–}20\%$, and $20\text{–}30\%$ centrality classes. The left, middle, and right panels show $R_{\mathrm{out}}/R_{\mathrm{side}}$, $R_{\mathrm{out}}/R_{\mathrm{long}}$, and $R_{\mathrm{side}}/R_{\mathrm{long}}$, respectively. All results are for 2.76 TeV Pb-Pb collisions where data shown are for ${\pi }^{\pm }{\pi }^{\pm }$ obtained by the ALICE collaboration [83].