Elliptic and triangular flow of heavy flavor in heavy-ion collisions

We investigate the elliptic and the triangular flow of heavy mesons in ultrarelativistic heavy-ion collisions at the BNL Relativistic Heavy-Ion Collider and the CERN Large Hadron Collider (LHC) . The dynamics of heavy quarks is coupled to the locally thermalized and fluid dynamically evolving quark-gluon plasma. The elliptic flow of $D$ mesons and the centrality dependence measured at the LHC is well reproduced for purely collisional and bremsstrahlung interactions. Due to the event-by-event fluctuating initial conditions from the EPOS2 model, the $D$ meson triangular flow is predicted to be nonzero at $\sqrt{s}=200$ GeV and $\sqrt{s}=2.76$ TeV. We study the centrality dependence and quantify the contributions stemming from flow of the light bulk event and the hadronization process. The flow coefficients as responses to the initial eccentricities behave differently for heavy mesons than for light hadrons due to their inertia. Higher-order flow coefficients of heavy flavor become important in order to quantify the degree of thermalization.

Figure 1

Event-averaged initial eccentricities ${\epsilon }_2$ (red circles) and ${\epsilon }_3$ (blue triangles) in the EPOS2 model for Pb + Pb collisions at $\sqrt{s}=2.76$ TeV (upper panel) and in Au + Au collisions at $\sqrt{s}=200$ GeV (lower panel) as a function of centrality.

Figure 2

Event-averaged initial temperature weighted by the energy density (left) and the average initial overlap area (right), for which $T_{\mathrm{ini}}>0.155$ GeV in the $x\text{−}y$ plane, in the EPOS2 model of Pb + Pb collisions at $\sqrt{s}=2.76$ TeV as a function of centrality.

Figure 3

$D$ meson elliptic (solid) and triangular (dashed) flow in Pb + Pb collisions at $\sqrt{s}=2.76$ TeV (upper row) and in Au + Au collisions at $\sqrt{s}=200$ GeV (lower row) for different centralities. Both interaction mechanisms, purely collisional (orange, light) and collisional + radiative (LPM) (black, dark), are shown. Experimental data are taken from [16] for $D^0$. The last two data points for the 30–50% most central collisions at the LHC are outside the range of $v_n$ values shown. Simulation results at RHIC suffer from larger statistical fluctuations for $p_T\gtrsim 4$ GeV.

Figure 4

Centrality dependence of the ratios $v_n/{\epsilon }_n$ for $n=2,3$ in the collisional + radiative (LPM) energy loss model at $\sqrt{s}=2.76$ TeV collision energies for the light charged hadron and the $D$ and $B$ meson flow. The bulk flow is obtained as $v_n(2,|\Delta \eta |>1)$ from the full EPOS2 model [20].

Figure 5

Contribution of hadronization to the $D$ meson elliptic (solid) and triangular (dashed) flow (left plot) and the contribution of the bulk flow to the charm quark elliptic (solid) and triangular (dashed) flow (right plot) for 30–50% most central Pb + Pb collisions at $\sqrt{s}=2.76$ TeV.