Heavy-quark production and elliptic flow in Au + Au collisions at $\sqrt{s_{NN}}=62.4$ GeV

We present measurements of electrons and positrons from the semileptonic decays of heavy-flavor hadrons at midrapidity ($\left|y\right|<$ 0.35) in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=62.4$ GeV. The data were collected in 2010 by the PHENIX experiment that included the new hadron-blind detector. The invariant yield of electrons from heavy-flavor decays is measured as a function of transverse momentum in the range $1<p_T^e<5$ GeV/$c$. The invariant yield per binary collision is slightly enhanced above the $p+p$ reference in $\mathrm{Au}+\mathrm{Au}$ 0%–20%, 20%–40%, and 40%–60% centralities at a comparable level. At this low beam energy this may be a result of the interplay between initial-state Cronin effects, final-state flow, and energy loss in medium. The $v_2$ of electrons from heavy-flavor decays is nonzero when averaged between $1.3<p_T^e<2.5$ GeV/$c$ for 0%–40% centrality collisions at $\sqrt{s_{NN}}=62.4$ GeV. For 20%–40% centrality collisions, the $v_2$ at $\sqrt{s_{NN}}=62.4$ GeV is smaller than that for heavy-flavor decays at $\sqrt{s_{NN}}=200$ GeV. The $v_2$ of the electrons from heavy-flavor decay at the lower beam energy is also smaller than $v_2$ for pions. Both results indicate that the heavy quarks interact with the medium formed in these collisions, but they may not be at the same level of thermalization with the medium as observed at $\sqrt{s_{NN}}=200$ GeV.

Figure 1

The PHENIX detector configuration for the 2010 data-taking period. The upper panel is the beam view and the lower panel is the side view.

Figure 2

For centralities (a) 0%–20% (most central), (b) 20%–40%, (c) 40%–60%, and (d) MB events, shown are the shapes of the HBD charge distribution (black dashed curves), the swapped HBD charge distribution (red dotted curves), and the subtracted HBD charge distribution (blue solid curves). The swapped HBD distribution can statistically estimate the randomly matched HBD charges.

Figure 3

The shape of the HBD charge distribution (black dashed curves), the swapped HBD charge distribution (red dotted curves), and the subtracted HBD charge distribution (blue solid curve) for the indicated $p_T$ ranges. All plots are for MB events.

Figure 4

Simulated response of the HBD to different sources of electrons compared to the measured distribution for two different $p_T$ ranges, (a) $1.0<p_T<1.5 \mathrm{GeV}/c$ and (c) $p_T>2.5 \mathrm{GeV}/c$. (Black squares) total simulation, (red triangles) single electrons, (blue inverted triangles) ${\pi }^0$ Dalitz decays, (open magenta circles) conversions, (open cyan squares) $\eta$ Dalitz decays, and (green circles) data. For visual comparison, in (b) and (d) the distributions are normalized to 1 for the same $p_T$ ranges as in (a) and (c).

Figure 5

The efficiency of the HBD cut, $10<hbdq<35$, for a single electron as a function of (a) centrality and (b) $p_T$. The efficiency was determined by embedding a simulated single-electron response into the real data.

Figure 6

Invariant yield of candidate electrons measured in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}$ = 62.4 GeV for different centrality bins. The yields are scaled by powers of 10 for clarity. The systematic uncertainty is shown as boxes and is, in many cases, comparable to the symbol size.

Figure 7

Candidate electron yield with respect to the RP for different $p_T$ bins for events with centrality 20%–40% and fitted with the function $\frac{dN}{d\varphi }=N_0[1+2v_{2}cos2(\varphi -{\Phi }_{\mathrm{RP}})]$. The $p_T$ bins are as indicated.

Figure 8

Candidate electron $v_2$ as a function of $p_T$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}$ = 62.4 GeV for three different centrality bins. The systematic uncertainty is shown as boxes.

Figure 9

Invariant yield of (black dots) candidate electrons and (solid lines) electrons calculated from different photonic sources in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}} =$ 62.4 GeV for MB events.

Figure 10

$v_2$ of photonic electrons calculated as the sum of different photonic sources in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}} =$ 62.4 GeV for three different centrality bins. Shaded boxes show the systematic uncertainties.

Figure 11

Invariant yield of heavy-flavor electrons measured in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=62.4$ GeV for different centrality bins. The yields are scaled by powers of 10 for clarity. The uncertainty bars (boxes) show the statistical (systematic) uncertainties.

Figure 12

Ratio of the heavy-flavor electrons (signal) to photonic electrons (background) in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=62.4$ GeV for MB events and the three indicated centrality classes that are used in this analysis.

Figure 13

Invariant cross section of heavy-flavor electrons in $p+p$ collisions at $\sqrt{s_{NN}}=62.2$ GeV [39, 40, 41]. The curve is a combined power-law fit (see Table 3).

Figure 14

Invariant yield of heavy-flavor electrons per binary collisions in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=62.2$ GeV for (a) MB, (b) 0%–20%, (c) 20%–40%, (d) 40%–60%, and (e) $p+p$ collisions at $\sqrt{s_{NN}}=62.4$ GeV measured in ISR experiments. The curves are (red solid) FONLL calculations and (red dash) upper and lower limits.

Figure 15

Integrated invariant yield per binary collision vs $N_{\mathrm{coll}}$ for heavy-flavor electrons in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=62.4$ GeV for the indicated ${p_T}^e$ ranges. The data point at $N_{\mathrm{coll}} =1$ is for $p+p$ collisions.

Figure 16

The $R_{AA}$ for electrons from heavy-flavor decays in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=62.4$ GeV for the indicated centralities. The error bars (boxes) represent the statistical (systematic) uncertainties. The global uncertainty due to the uncertainty in $N_{\mathrm{coll}}$ for each centrality is given by the box on the right side of each plot.

Figure 17

The $R_{AA}$ values for electrons from heavy-flavor decay in Au + Au collisions at 62.4 GeV with the $R_{AA}$ results from $d$ + Au, Cu + Cu, and Au + Au collisions at $\sqrt{s_{NN}}=200$ GeV (data from Refs. [9, 21], as shown earlier in [44]). The error bars (boxes) represent the statistical (systematic) uncertainties. The $p_T$ ranges are as indicated: (a) $1<p_T<3 \mathrm{GeV}/c$ and (b) $3<p_T<5 \mathrm{GeV}/c$.

Figure 18

The $R_{AA}$ values from heavy-flavor decay for electrons and ${\pi }^0$ [19] in Au + Au collisions at 62.4 GeV. The error bars (boxes) show the statistical (systematic) uncertainties.

Figure 19

The nuclear modification factor $R_{AA}$ for electrons from heavy-flavor decays in 0%–20% central Au + Au collisions at $\sqrt{s_{NN}}=62.4$ GeV compared to predictions (dark-blue band) from Vitev et al. [13, 46].

Figure 20

Heavy-flavor electron $R_{\mathrm{CP}}$ between centrality 0%–20% and 40%–60% in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=62.4$ GeV. The curves are calculated using a model based on energy loss [47, 48].

Figure 21

Candidate (inclusive), photonic, and heavy-flavor electron $v_2$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=62.4$ GeV for 20%–40% centrality.

Figure 22

Heavy-flavor electron $v_2$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=62.4$ GeV for (a) 0%–20%, (b) 20%–40%, and (c) 40%–60% centrality bins.

Figure 23

The $v_2$ of heavy-flavor electrons and ${\pi }^0$ in $\mathrm{Au}+\mathrm{Au}$ collisions as a function of collision energy in the indicated $p_T$ range of $1.3<p_T<2.5 \mathrm{GeV}/c$ for (a) 0%–20% and (b) 20%–40% centrality.

Figure 24

Heavy-flavor electron $v_2$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=62.4$ GeV compared with multiple theory curves [47, 49].