Single electron yields from semileptonic charm and bottom hadron decays in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV

The PHENIX Collaboration at the Relativistic Heavy Ion Collider has measured open heavy flavor production in minimum bias $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV via the yields of electrons from semileptonic decays of charm and bottom hadrons. Previous heavy flavor electron measurements indicated substantial modification in the momentum distribution of the parent heavy quarks owing to the quark-gluon plasma created in these collisions. For the first time, using the PHENIX silicon vertex detector to measure precision displaced tracking, the relative contributions from charm and bottom hadrons to these electrons as a function of transverse momentum are measured in $\mathrm{Au}+\mathrm{Au}$ collisions. We compare the fraction of electrons from bottom hadrons to previously published results extracted from electron-hadron correlations in $p+p$ collisions at $\sqrt{s_{NN}}=200$ GeV and find the fractions to be similar within the large uncertainties on both measurements for $p_T>4\text{GeV}/c$. We use the bottom electron fractions in $\mathrm{Au}+\mathrm{Au}$ and $p+p$ along with the previously measured heavy flavor electron $R_{AA}$ to calculate the $R_{AA}$ for electrons from charm and bottom hadron decays separately. We find that electrons from bottom hadron decays are less suppressed than those from charm for the region $3<p_T<4\text{GeV}/c$.

Figure 1

(a) A schematic view of the PHENIX detector configuration for the 2011 run. (b) A schematic view of the VTX detector with the individual ladders shown.

Figure 2

Matching variable between the reconstructed track momentum ($p$) and the energy measured in the EMCal ($E$): $\text{dep}=(E/p-{\mu }_{E/p})/{\sigma }_{E/p}$. The black distribution is for identified electrons with $p_T=2.0–2.5\text{GeV}/c$, and the red distribution is the estimated contribution from misidentified electrons via the RICH swap method.

Figure 3

Illustration of the definition of ${\mathrm{DCA}}_T\equiv L-R$ in the transverse plane.

Figure 4

Distance-of-closest-approach distributions for (a) along the beam axis ${\mathrm{DCA}}_L$ and (b) transverse plane ${\mathrm{DCA}}_T$ for all VTX-associated tracks in $\text{Au}+\text{Au}$ at $\sqrt{s_{NN}}=200$ GeV in the range $2.0<p_T[\mathrm{GeV}/c]<2.5$. (c) The ${\mathrm{DCA}}_T$ resolution as a function of $p_T$ for all tracks.

Figure 5

${\mathrm{DCA}}_T$ distributions for electrons in MB $\mathrm{Au}+\mathrm{Au}$ at $\sqrt{s_{NN}}=200$ GeV that pass the reconstruction and conversion veto cut in the indicated five electron-$p_T$ selections. Also shown are the normalized contributions for the various background components detailed in Sec. 3e.

Figure 6

Simulated primary electron (a) ${\mathrm{DCA}}_T$ and (b) ${\mathrm{DCA}}_L$ distribution before and after embedding in real $\text{Au}+\text{Au}$ data.

Figure 7

(a) Distribution of correlated hits in B0 near electron tracks for $1<p_T<2\text{GeV}/c$. The red (circle) points are from $\text{Au}+\text{Au}$ data and the black (triangle) points are from Monte Carlo simulation. The inset in (a) illustrates the electron pairs from Dalitz decays. (b) The window of the conversion veto cut for B0 layer (hatched) and the hit distribution near electron track in 2D space of $\text{chrg}\mathrm{\Delta }\varphi$ vs $p_T$ of electrons in $\text{Au}+\text{Au}$ collisions. (See the text for details).

Figure 8

The survival rate as a function of electron $p_T\left(p_T^e\right)$ for electrons from photon conversion (black), Dalitz decay of ${\pi }^0$ (red), $\eta$ (green), electrons from direct photon (blue), and heavy flavor decay electrons (dark orange).

Figure 9

(a) The decay matrix, ${\mathbf{M}}^{\left(\mathbf{Y}\right)}$, encoding the probability for charmed hadrons decaying to electrons within $\left|\eta \right|<0.35$ as a function of both electron $p_T\left(p_T^e\right)$ and charm hadron $p_T\left(p_T^c\right)$. (b) An example decay matrix, ${\mathbf{M}}_j^{\left(\mathbf{D}\right)}$, encoding the probability for charmed hadrons decaying to electrons within $\left|\eta \right|<0.35$ and $1.5<p_T^e[\mathrm{GeV}/c]<2.0$ as a function of both electron ${\mathrm{DCA}}_T$ and charm hadron $p_T\left(p_T^c\right)$. In both cases the color intensity represents the probability of decay in the given bin.

Figure 10

The probability for (a) charm and (b) bottom hadrons in a given range of hadron $p_T$ ($p_T^c$ and $p_T^b$ for charm and bottom hadrons, respectively) to decay to electrons at midrapidity as a function of electron $p_T\left(p_T^e\right)$.

Figure 11

The joint probability distributions for the vector of hadron yields, $\mathbf{\theta }$, showing the 2D correlations between parameters. The diagonal plots show the marginalized probability distributions for each hadron $p_T$ bin (i.e., the 1D projection over all other parameters). Along the $Y$ axis the plots are organized from top to bottom as the 17 charm hadron $p_T\left(p_T^c\right)$ bins from low to high $p_T^c$ followed by the 17 bottom hadron $p_T\left(p_T^b\right)$ bins from low to high $p_T^b$. The $X$ axis is organized similarly from left to right. The $p_T^c$ and $p_T^b$ binning follows that shown in Fig. 15. The region of green plots (top-left quadrant) shows the charm hadron yields and the correlations between charm hadron yields. The region of blue plots (bottom-right quadrant) shows the bottom hadron yields and correlations between bottom hadron yields. The region of orange plots (bottom-left quadrant) shows the correlations between charm and bottom hadron yields. Panels (b)–(d) show a set of example distributions. (b) The 1D probability distribution of charm hadron yield in $3.5<p_T^c\text{GeV}/c<4.0$. (d) The 1D probability distribution of bottom hadron yield in $2.5<p_T^b\text{GeV}/c<3.0$. (c) The correlation between (b) and (d).

Figure 12

The heavy flavor electron-invariant yield as a function of $p_T$ from measured data [12] compared to electrons from the refolded charm and bottom hadron yields. The boxes represent the point-to-point correlated uncertainties on the measured heavy flavor electron invariant yield, while the error bars on the points represent the point-to-point uncorrelated uncertainties. The label “PHENIX Run 4 + Run 11” on this and all subsequent plots indicates that the unfolding result uses the heavy flavor electron-invariant yield as a function of $p_T$ from data taken in 2004 (Run 4) combined with ${\mathrm{DCA}}_T$ measurements from data taken in 2011 (Run 11).

Figure 13

The ${\mathrm{DCA}}_T$ distribution for measured electrons compared to the decomposed ${\mathrm{DCA}}_T$ distributions for background components, electrons from charm decays, and electrons from bottom decays. The sum of the background components, electrons from charm and bottom decays, is shown as the red (upper) curve for direct comparison to the data. The gray band indicates the region in ${\mathrm{DCA}}_T$ considered in the unfolding procedure. Also quoted in the figure is the bottom electron fraction for $|{\mathrm{DCA}}_T|<0.1$ cm integrated over the given $p_T$ range. The legend follows the same order from top to bottom as panel (b) at ${\mathrm{DCA}}_T=-0.1$ cm.

Figure 14

The relative contributions from the different components to the uncertainty on the fraction of electrons from bottom hadron decays as a function of $p_T$. The shaded red band in each panel is the total uncertainty.

Figure 15

Unfolded (a) charm and (b) bottom hadron-invariant yield as a function of $p_T$, integrated over all rapidities, as constrained by electron yield vs ${\mathrm{DCA}}_T$ in 5 $p_T^e$ bins and previously published heavy flavor electron-invariant yield vs $p_T^e$ [12].

Figure 16

The invariant yield of $D^0$ mesons as a function of $p_T$ for $\left|y\right|<1$ inferred from the unfolded yield of charm hadrons integrated over all rapidity compared to measurements from STAR [14]. See the text for details on the calculation of the $D^0$ yield inferred from the unfolded result. To match the centrality intervals, the STAR result has been scaled by the ratio of $N_{\mathrm{coll}}$ values. The bottom panel shows the ratio of the data to a fit of the STAR $D^0$ yield.

Figure 17

The fraction of heavy flavor electrons from bottom hadron decays as a function of $p_T$ from this work and from fonll $p+p$ calculations [33].

Figure 18

Bottom electron fraction as a function of $p_T$ compared to measurements in $p+p$ collisions at $\sqrt{s}=200$ GeV from PHENIX [34] and STAR [35]. Also shown are the central values for fonll [33] for $p+p$ collisions at $\sqrt{s_{NN}}=200$ GeV.

Figure 19

(a) The $R_{AA}$ for $c\to e$, $b\to e$ and combined heavy flavor [12] as a function of $p_T^e$. The $c\to e$ and $b\to e{R}_{AA}$ are calculated using Eqs. (11) and (12), where $F_{\mathrm{AuAu}}$ uses the unfolded result determined in this work and $F_{pp}$ determined from STAR $e-h$ correlations [35]. (b) The ratio $R_{AA}^{b\to e}/R_{AA}^{c\to e}$ as a function of $p_T^e$.

Figure 20

Bottom electron fraction as a function of $p_T$ compared to a series of model predictions detailed in the text.

Figure 21

The fraction of ${\pi }^0$, $\eta$, and direct photon Dalitz decay electrons in all Dalitz electrons as a function of electron $p_T\left(p_T^e\right)$.

Figure 22

The fraction of nonphotonic electrons to inclusive electrons as a function of electron $p_T\left(p_T^e\right)$.

Figure 23

The fraction of ${\pi }^0$, $\eta$, and direct photon electrons in all photonic electrons as a function of electron $p_T\left(p_T^e\right)$.