Reaction plane correlated triangular flow in $\text{Au}+\text{Au}$ collisions at $\sqrt{s_{NN}}=3$ GeV

We measure triangular flow relative to the reaction plane at 3 GeV center-of-mass energy in $\text{Au}+\text{Au}$ collisions at the BNL Relativistic Heavy Ion Collider. A significant $v_3$ signal for protons is observed, which increases for higher rapidity, higher transverse momentum, and more peripheral collisions. The triangular flow is essentially rapidity-odd with a slope at midrapidity, $d{v}_3{/dy|}_{(y=0)}$, opposite in sign compared to the slope for directed flow. No significant $v_3$ signal is observed for charged pions and kaons. Comparisons with models suggest that a mean field potential is required to describe these results, and that the triangular shape of the participant nucleons is the result of stopping and nuclear geometry.

Figure 1

Cartoon of a noncentral heavy-ion collision illustrating the triangular shape correlated with the event plane (the $x\text{−}z$ plane). The forces on the particles resulting from the triangular geometry are perpendicular to the sides of the yellow triangles, opposite to the direction of $v_1$. Note that the triangular regions are composed primarily of participants.

Figure 2

$p_T$ vs. $y_{\mathrm{c}.\mathrm{m}.}$ density plots for ${\pi }^{\pm }, K^{\pm }$, and $p$ measured by the STAR in $\text{Au}+\text{Au}$ collisions at $\sqrt{s_{NN}}=3.0$ GeV. The red dashed line represents the target rapidity and the solid red line represents midrapidity. The solid and dashed black boxes mark acceptance regions used for flow calculations in various cases explained in the text.

Figure 3

Event plane resolution for $v_3\left\{{\mathrm{\Psi }}_1\right\}$ as a function of centrality from $\sqrt{s_{NN}}=3$ GeV $\text{Au}+\text{Au}$ collisions at STAR. The points are the average of the resolutions from the three configurations discussed in Sec. 3d, and the systematic uncertainties are the maximum difference between the configurations and the average (taken as a symmetric uncertainty in the opposite direction as well). Vertical lines are statistical uncertainties and open brackets are systematic uncertainties.

Figure 4

$v_3\left\{{\mathrm{\Psi }}_1\right\}$ vs. centrality for ${\pi }^{+}, {\pi }^{-}$, and protons using the event plane method. Protons show a clear negative $v_3\left\{{\mathrm{\Psi }}_1\right\}$ while pions remain near zero. Statistical uncertainties are shown as lines while systematic uncertainties are denoted by open square brackets.

Figure 5

$v_3\left\{{\mathrm{\Psi }}_1\right\}$ vs. centrality for $K^{+}$ and $K^{-}$ using the event plane method. The values for $K^{+}$ are slightly shifted horizontally for visual clarity. More statistics are required to fully understand if this signal is present for kaons. Statistical uncertainties are shown as lines while systematic uncertainties are shown as open square brackets.

Figure 6

$v_3\left\{{\mathrm{\Psi }}_1\right\}$ vs. rapidity for protons in three large centrality bins from a symmetric acceptance across midrapidity. Protons exhibit an increasingly negative slope going towards more peripheral collisions. Statistical uncertainties are shown as lines while systematic uncertainties are denoted by open square brackets.

Figure 7

$v_3\left\{{\mathrm{\Psi }}_1\right\}$ vs. rapidity for protons in three large centrality bins from only the backward region (solid markers) along with mirrored points across midrapidity (open markers). Note that the $p_{\mathrm{T}}$ acceptance extended to a lower limit than in Fig. 6. Statistical uncertainties are represented as lines while systematic uncertainties are denoted by open square brackets.

Figure 8

$v_3\left\{{\mathrm{\Psi }}_1\right\}$ vs. $p_{\mathrm{T}}$ for protons in three large centrality bins. $v_3\left\{{\mathrm{\Psi }}_1\right\}$ becomes increasingly negative as $p_{\mathrm{T}}$ and centrality increase. Statistical uncertainties are shown as lines while systematic uncertainties are denoted by open square brackets.

Figure 9

$v_1$ vs. rapidity (left) and $v_2$ vs. $p_{\mathrm{T}}$ (right) for protons and ${\pi }^{+}$ in 3 GeV center of mass “minimum bias” $\text{Au}+\text{Au}$ collisions as given by the JAM model in cascade mode.

Figure 10

$v_3\left\{{\mathrm{\Psi }}_1\right\}$ for protons in several centralities in the JAM model (top) and SMASH model (bottom) as compared to the data. Cuts used in the model are identical to the data, where centrality is defined by cuts in impact parameter as described in the text.

Figure 11

The top two rows show fits of JAM [top row, (a)–(c)] and SMASH [second row, (d)–(f)] to the $v_3\left\{{\mathrm{\Psi }}_1\right\}$ data vs. rapidity (first column), $p_{\mathrm{T}}$ (second column), and centrality (third column). The fits to distributions vs. rapidity and $p_{\mathrm{T}}$ (a), (b), (d), (e) are fits to protons, for three centrality bins. Hollow points in (a), (d) are reflected around the mid-rapidity as explained in the text. Fits to centrality (c), (f) show protons, ${\pi }^{+}$, and ${\pi }^{-}$. The bottom row (g)–(i) depicts ${\epsilon }_3$ in the JAM simulation for protons at $t=20$ fm/$c$ vs rapidity, $p_{\mathrm{T}}$, and centrality.

Figure 12

Illustration of the triangular geometry of participants as discussed in the text. (a) Side view. Red nucleus is moving towards positive rapidity, blue nucleus to negative rapidity. The collision bifurcates the participants as indicated by the dotted line, where the nucleus from one half must penetrate through a thicker portion of the other nucleus, thereby experiencing more stopping and creating half-moon, triangular shapes. The red triangle [more easily visualized in (b)] moves towards positive rapidity, blue triangle towards negative rapidity. The eye indicates the beam view as shown in (b). (b) Beam view; positive rapidity is out of the page. The familiar almond shape formed by the participants resulting in $v_2$, primarily at midrapidity, is evident. However, at higher rapidity, the nucleons forming the half-moon shape with nonzero triangular component from the red nucleus penetrates through the thin tip of the blue nucleus, while the remainder of the nucleons from the red nucleus which participate in the collision, are stopped by the blue nucleus. The triangular shape emerges from the usual almond-shaped collision region, half of which is obstructed by the opposing nucleus. The lines in the red triangle portray the pressure gradients along the directions of the red arrows, resulting in a negative $v_3\left\{{\mathrm{\Psi }}_1\right\}$.

Figure 13

Illustration of the $x$ vs. $y$ position of protons from JAM at $t=50$ fm/$c$ for particles with rapidity $0.6<y<0.85$ and $0<p_{\mathrm{T}}<2\mathrm{GeV}/c$ (avoiding spectators) illustrating the half-moon, “triangular” shape. Note that the high density region is centered at $x\approx 7$ fm. The arrows depict the vector field obtained by dividing the collision region into cells. The average momentum in each cell is superimposed on the original plot. The length of each arrow represents the magnitude of the average momentum in each cell. The white dot indicates the $x=0, y=0$ position.

Figure 14

Total energy per nucleon for the potential used in the models. The relatively hard Skyrme potential with $K=380$ MeV used in the SMASH model is shown as the blue-solid line. The relativistic mean field potential with parameter set MD2 used in the JAM model is shown as the dashed red line [35].