Jet quenching effects on the direct, elliptic, and triangular flow at energies available at the BNL Relativistic Heavy Ion Collider

In this paper we investigate how the energy and momentum deposited by partonic dijets in the quark-gluon plasma (QGP) may affect the direct, elliptic, and triangular flow of low (and intermediate) $p_T$ hadrons in central $\mathrm{Au}+\mathrm{Au}$ collisions at the BNL Relativistic Heavy Ion Collider. The dijets are modeled as external sources in the energy-momentum conservation equations for hydrodynamics, which are solved on an event-by-event basis within the ideal-fluid approximation. We focus our investigation at midrapidity and solve the hydrodynamic equations by imposing boost invariance. Differential anisotropic flow coefficients for $p_T\gtrsim 1\mathrm{GeV}$ are found to be significantly enhanced if the dijets deposit on average more than 12 GeV in the QGP (or more than 6 GeV per jet). Because this extra energy and momentum added to the medium perturbs the geometry-induced hydrodynamic expansion, the correlation between the $v_2$ and $v_3$ coefficients (for $p_T\gtrsim 1\mathrm{GeV}$) and their corresponding initial eccentricities are considerably weakened. In addition, we argue that the extra amount of direct flow induced by dijets may be quantified by comparing the azimuthal dependence of dihadron correlations in dijet events with the corresponding quantity obtained in events without dijets. This comparison could be used to give a rough estimate of the magnitude of the effective coupling between the jets and the medium.

Figure 1

Hydrodynamic evolution, in the transverse plane at midrapidity, of a single event with (lower panels) and without (upper panels) the influence of the dijet. The initial energy density distribution corresponds to a randomly chosen central $\text{Au}+\text{Au}$ collision at $200A$ GeV computed using an implementation of the Monte Carlo Glauber model [39, 40]. The initial position of the dijet (lower panels) is indicated by the back-to-back arrows. In this computation, ${dE/dl|}_0=20$ GeV/fm.

Figure 2

Distribution of the dijet initial distance, $r_0^{jet}$ (at $\tau ={\tau }_0$), with respect to the origin for 250 events (generated by the Monte Carlo Glauber model [39, 40]) normalized to one.

Figure 3

Jet yield per event as a function of the jet transverse energy, $E_T^{jet}$, for proton-proton collisions scaled by the number of binary collisions in $\text{Au}+\text{Au}$ collisions at $200A$ GeV in the 0%–10% centrality window. The dashed line was obtained from RHIC data [41]. The solid line corresponds to the ensemble of 250 events used in this paper.

Figure 4

Average energy deposited in the medium, around midrapidity, by the dijet, $\langle E_d^{jet}\rangle$, in the 0%–5% centrality window, as a function of the reference energy loss rate ${dE/dl|}_0$ (using the jet ensemble).

Figure 5

Distribution of the ratio $\delta E=E_d^{jet}/E_T^{jet}$ for four values of the parameter ${dE/dl|}_0$. The respective average value $\langle \delta E\rangle$ is shown on the plot.

Figure 6

Transverse momentum dependence of the $v_n$ coefficients ($n=1,2,3$) for four values of the parameter ${dE/dl|}_0$. The left panels correspond to the event-plane method. On the right panels we show the same observables computed using ${\Psi }_n={\Psi }_n\left(p_T\right)$, i.e., the phase is computed for each $p_T$ bin [23]. The panels labeled “mixed” correspond to an ensemble of 1000 events that includes 750 events without and 250 events with dijets. The panels labeled “jet” correspond to an ensemble of 250 events that includes only events with dijets.

Figure 7

Correlation between the eccentricity ${\varepsilon }_{2,2}$ and the flow coefficient $v_2$ for three values of the parameter ${dE/dl|}_0$. The dashed lines correspond to linear fits computed using the mixed ensemble (black and light dots). The solid lines were computed by using the jet ensemble (black dots). Three ranges of transverse momentum are presented. $\lambda$ is the linear correlation coefficient.

Figure 8

Correlation between the eccentricity ${\varepsilon }_{2,3}$ and the flow coefficient $v_3$ for three values of the parameter ${dE/dl|}_0$. The dashed lines correspond to linear fits computed using the mixed ensemble (black and light dots). The solid lines were computed by using the jet ensemble (black dots). Three ranges of transverse momentum are presented. $\lambda$ is the linear correlation coefficient.

Figure 9

Distribution of the phase difference ${\delta }_2={\Psi }_2-{\Phi }_{2,2}$ for three values of the parameter ${dE/dl|}_0$. The dashed lines correspond to the mixed ensemble and the solid lines to the jet ensemble. Three ranges of transverse momentum are presented. Note that ${\Psi }_2$ is rotated by $\pi /2$ in order to achieve the smallest angular difference with respect to the angle ${\Phi }_{2,2}$. All distributions are normalized to unity.

Figure 10

Distribution of the phase difference ${\delta }_3={\Psi }_3-{\Phi }_{2,3}$, for three values of the parameter ${dE/dl|}_0$. The dashed lines correspond to the mixed ensemble and the solid lines to the jet ensemble. Three ranges of transverse momentum are presented. Note that ${\Psi }_3$ is rotated by $\pi /3$ in order to achieve the smallest angular difference with respect to the angle ${\Phi }_{2,3}$. All distributions are normalized to unity.

Figure 11

Azimuthal component of the dihadron correlation function $C\left(\Delta \varphi \right)$ for three values of the parameter ${dE/dl|}_0$. The dashed lines correspond to the mixed ensemble and the solid lines to the jet ensemble. Three ranges of transverse momentum of the associated particles are presented. The range in transverse momentum for the triggers is defined as $3<p_T^{\mathbf{trigg}}<5$ GeV.

Figure 12

Azimuthal component of the background-subtracted dihadron correlation function $R\left(\Delta \varphi \right)$ for three values of the parameter ${dE/dl|}_0$. The dashed lines correspond to the mixed ensemble and the solid lines to the jet ensemble. Three ranges of transverse momentum of the associated particles are presented. The range in transverse momentum for the triggers is defined as $3<p_T^{\mathbf{trigg}}<5$ GeV.