Event-by-Event Anisotropic Flow in Heavy-ion Collisions from Combined Yang-Mills and Viscous Fluid Dynamics

Anisotropic flow coefficients $v_1–v_5$ in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time Glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The Glasma dynamics, as realized in the impact parameter dependent Glasma (IP-Glasma) model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic subnucleon scale color charge fluctuations; the preequilibrium flow of matter is then matched to the music algorithm describing viscous hydrodynamic flow and particle production at freeze-out. The IP-$\mathrm{\text{Glasma}}+\mathrm{MUSIC}$ model describes well both transverse momentum dependent and integrated $v_n$ data measured at the Large Hadron Collider and the Relativistic Heavy Ion Collider. The model also reproduces the event-by-event distributions of $v_2$, $v_3$ and $v_4$ measured by the ATLAS Collaboration. The implications of our results for better understanding of the dynamics of the Glasma and for the extraction of transport properties of the quark-gluon plasma are outlined.

Figure 1

Gluon multiplicity distribution in the IP-Glasma model.

Figure 2

Identified particle transverse momentum spectra including all resonances up to 2 GeV compared to experimental data from the ALICE Collaboration [34].

Figure 3

Root-mean-square anisotropic flow coefficients $⟨v_n^2{⟩}^{1/2}$ as a function of transverse momentum, compared to experimental data by the ATLAS Collaboration using the event plane (EP) method [4] (points). 200 events. Bands indicate statistical errors. Experimental error bars are smaller than the size of the points.

Figure 4

Root-mean-square anisotropic flow coefficients $⟨v_n^2{⟩}^{1/2}$, computed as a function of centrality, compared to experimental data of $v_n\{2\}$, $n\in \{2,3,4\}$, by the ALICE Collaboration [3] (points). Results are for 200 events per centrality with bands indicating statistical errors.

Figure 5

Comparison of $v_n(p_T)$ using two different switching times ${\tau }_{\mathrm{switch}}=0.2\mathrm{fm}/c$ (wide) and $0.4\mathrm{fm}/c$ (narrow). Experimental data by the ATLAS Collaboration using the EP method [4] (points). Bands indicate statistical errors.

Figure 6

Comparison of $v_n(p_T)$ using constant $\eta /s=0.2$ and a temperature dependent $(\eta /s)(T)$ as parametrized in Ref. 38. Experimental data by the ATLAS Collaboration using the EP method [4] (points). Bands indicate statistical errors.

Figure 7

Comparison of $v_n(p_T)$ at RHIC using constant $\eta /s=0.12$ and a temperature dependent $(\eta /s)(T)$ as parametrized in Ref. 38. Experimental data by the PHENIX [1] (open symbols) and STAR [40] (preliminary, filled symbols) Collaborations. Bands indicate statistical errors.

Figure 8

$v_1(p_T)$ compared to experimental data from the ALICE [43] and ATLAS [45] Collaborations.

Figure 9

Scaled distributions of $v_2$, $v_3$, and $v_4$ (from top to bottom) compared to experimental data from the ATLAS Collaboration [37, 46]. 1300 events. Bands are systematic experimental errors.