Heavy-quark production in $p$ + $p$ and energy loss and flow of heavy quarks in Au + Au collisions at $\sqrt{s_{NN}}=200$ GeV

Transverse momentum spectra of electrons ($p_T^e$) from semileptonic weak decays of heavy-flavor mesons in the range of $0.3<p_T^e<9.0$ GeV/$c$ have been measured at midrapidity ($\left|y\right|<0.35$) by the PHENIX experiment at the Relativistic Heavy Ion Collider in $p+p$ and $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV. In addition, the azimuthal anisotropy parameter $v_2$ has been measured for $0.3<p_T^e<5.0$ GeV/$c$ in $\mathrm{Au}+\mathrm{Au}$ collisions. The substantial modification in the $p_T^e$ spectra in $\mathrm{Au}+\mathrm{Au}$ compared with $p+p$ collisions as well as the nonzero $v_2$ indicate substantial interactions and flow of heavy quarks in traversing the produced medium. Comparisons of these observables with detailed theoretical calculations can be used to identify the nature of these interactions and to quantify their extent.

Figure 1

Beam view (at $z=0$) of the PHENIX central arm detector in 2004 ($\mathrm{Au}+\mathrm{Au}$) and 2005 ($p+p$). The detectors used in the present analysis are the drift chamber (DC) and the multiwire proportional pad chambers (PC1, PC2, PC3) for charged particle tracking, the ring-imaging $\check{\mathrm{C}}$erenkov detector (RICH) for electron identification, and the electromagnetic calorimeters, which are lead glass (PbGl) and lead scintillator (PbSc), for energy measurement.

Figure 2

Top view (at $y=0$) of the RICH in the PHENIX east arm.

Figure 3

The correlation between fractional BBC charge $Q/Q_{\max }$ and fractional ZDC energy $E/E_{\max }$. The selections from right to left correspond to centrality classes 0$\%$–10$\%$, 10$\%$–20$\%$, 20$\%$–40$\%$, 40$\%$–60$\%$, and 60$\%$–92$\%$.

Figure 4

A charged particle trajectory and the kinematic parameters are shown in (a) beam view, (b) side view, and (c) top view of the PHENIX central region. In (b) the $Z_{\mathrm{V}}$ is the same as $z_{\mathrm{vtx}}$ in the text.

Figure 5

$E/p$ distributions for (a) $0.3<p_T<0.4$ GeV/$c$ and (b) $3.5<p_T<4.0$ GeV/$c$ in $\mathrm{Au}+\mathrm{Au}$ collisions. See text for more details.

Figure 6

$E/p$ distributions in $p+p$ collisions for $0.8<p_T<1.0$ GeV/$c$ compared with the geant simulation. The black stars are the data points and the solid circles show the geant [49] simulation. The triangles and squares show the contributions from simulation of ${\pi }^0$ and $K_{e3}$, respectively. See text for more details.

Figure 7

${\epsilon }_{\Delta y}^{\mathrm{acc}}$ for $(N_{e^{+}}+N_{e^{-}})/2$ as a function of $p_T$ in $\mathrm{Au}+\mathrm{Au}$. The top, middle, and bottom curves are calculated with eID cuts applied for $0.3<p_T<5.0$, $5.0<p_T<7.0$, and $7.0<p_T<9.0$ GeV/$c$, respectively. The bands span the systematic error assigned for each correction.

Figure 8

Efficiency of the PH trigger in $p+p$ determined from the MB data set.

Figure 9

Invariant mass distribution of $e^{\pm }$ pairs from MB $\mathrm{Au}+\mathrm{Au}$ data with the minimum eID cuts used for the multiplicity-dependent efficiency loss estimate.

Figure 10

(Top) Invariant differential cross section of charged pions (blue squares) [50] and neutral pions (red circles) [51] for $p+p$ collisions at $\sqrt{s}$ = 200 GeV, together with a fit to Eq. (6). The uncertainties shown are the quadrature sum of the statistical and systematic uncertainties. (Bottom) Ratio of the data to the fit.

Figure 11

(Top) Invariant multiplicity of charged pions (blue squares) and neutral pions for minimum bias $\mathrm{Au}+\mathrm{Au}$ collisions from 2002 (green triangles) and 2004 (red circles) together with a fit according to Eq. (6). The uncertainties shown are the quadrature sum of the statistical and systematic uncertainties. (Bottom) Ratio of the data to the fit to the 2004 data. There is also a point-to-point correlated systematic uncertainty of 7$\%$ which is not shown in the figure.

Figure 12

Systematic error assigned to each cocktail ingredient for MB $\mathrm{Au}+\mathrm{Au}$ collisions. The points show the total systematic error for each $p_T$.

Figure 13

Measured direct photon spectrum (red squares) compared with the cocktail parametrization (histogram) for (upper) $p+p$ and (lower) MB $\mathrm{Au}+\mathrm{Au}$ collisions. The uncertainties shown are the quadrature sum of the statistical and systematic uncertainties. There is also a point-to-point correlated systematic uncertainty of 7$\%$ which is not shown in the figure.

Figure 14

Invariant differential cross sections and multiplicities of cocktail electrons in $p+p$ and $\mathrm{Au}+\mathrm{Au}$ collisions at 200 GeV for the indicated centrality ranges.

Figure 15

Electron background cocktail with quarkonium and Drell-Yan contributions for $p+p$ collisions. The shaded band (top panel) and dashed lines (bottom panel), respectively, reflect the uncertainty of the $J/\psi$ contribution.

Figure 16

Electron background cocktail with quarkonium and Drell-Yan contributions for 0$\%$–20$\%$ centrality $\mathrm{Au}+\mathrm{Au}$ collisions. The shaded band (top panel) and dashed lines (bottom panel), respectively, reflect the uncertainty of the $J/\psi$ contribution.

Figure 17

Invariant yields of inclusive electrons with (open circles) and without (solid circles) the photon converter for $\mathrm{Au}+\mathrm{Au}$ MB events.

Figure 18

(Top) Ratio of inclusive electrons with/without the converter ($R_{\mathrm{CN}}$, points with systematic uncertainty boxes) and ratio of photonic electrons with/without the converter ($R_{\gamma }$, solid line with a systematic uncertainty band). (Bottom) The ratio of nonphotonic yield to photonic electron yield ($R_{\mathrm{NP}}$, solid circles) and the ratio of electron yield from kaon decays to photonic electron yield ($R_{\mathrm{KP}}$, solid squares) as a function of $p_T^e$ for MB. Filled circles with statistical uncertainty bars indicate $R_{\mathrm{NP}}$ produced by both the converter and cocktail methods.

Figure 19

The ratio of photonic electrons measured by the converter method to the cocktail calculation in $\mathrm{Au}+\mathrm{Au}$ collisions (after renormalizing the cocktail yields up by 18$\%$) for the indicated centralities. The upper and lower curves show the systematic uncertainty of the cocktail. Uncertainty bars are statistical only.

Figure 20

The ratio of photonic electrons measured by the converter method to the cocktail calculation in $p+p$ collisions [29]. The data from the MB (PH) data set are shown below (above) 1.8 GeV/$c$. The upper and lower curves show the systematic uncertainty of the cocktail. Uncertainty bars are statistical only.

Figure 21

Ratio of nonphotonic electrons to photonic background in $p+p$ collisions [29]. Uncertainty bars are statistical uncertainties and the uncertainty band shows the cocktail systematic uncertainties. The solid, dashed, dot-dashed, and dotted curves are the remaining nonphotonic background from $K_{e3}$, $\rho \to e^{+}{e}^{-}$, $\omega \to e^{+}{e}^{-}$, and hadron contamination, respectively.

Figure 22

Azimuthal distributions relative to the reaction plane for various centrality and transverse momenta. The distributions have been normalized to their average value and centered around 0.

Figure 23

Reaction plane resolution as a function of centrality.

Figure 24

$p_T$ dependence of inclusive electron $v_2$, for different centrality bins. A 5$\%$ systematic scale uncertainty is not shown.

Figure 25

Inclusive electron $v_2$ for MB events as a function of $p_T$ measured in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV.

Figure 26

Relative contributions of electrons from ${\pi }^0$, $\eta$, and direct $\gamma$ to the background.

Figure 27

Electron $v_2$ from ${\pi }^0$ decay as a function of $p_T$, from a simulation.

Figure 28

Electron $v_2$ from $\eta$ decay as a function of $p_T$, from a simulation.

Figure 29

Electron $v_2$ from photonic sources as a function of $p_T$ and centrality.

Figure 30

Inclusive electron $v_2$ with and without the converter installed.

Figure 31

Photonic electron $v_2$ from MB $\mathrm{Au}+\mathrm{Au}$ collisions determined by two independent methods, the cocktail and the converter method. The lines are determined by the cocktail method and the data points shown with square symbols are obtained by the converter method.

Figure 32

(a) Invariant differential cross sections of single electrons as a function of $p_T$ in $p+p$ collisions at $\sqrt{s}=200$ GeV [29]. The uncertainty bars (bands) represent the statistical (systematic) uncertainties. The curves are the FONLL calculations [77]. (b) The ratio of Data/FONLL as a function of $p_T$. The upper (lower) curve shows the theoretical upper (lower) limit of the FONLL calculation. In both panels, a 10$\%$ normalization uncertainty is not shown.

Figure 33

Invariant yields of (left) inclusive electrons and (right) open heavy-flavor electrons for different $\mathrm{Au}+\mathrm{Au}$ centrality classes, scaled by powers of 10 for clarity. Uncertainty bars (boxes) depict statistical (systematic) uncertainties. The insert shows the ratio of these electrons to those from background sources in MB events. The curves are scaled fits to the $p+p$ spectrum.

Figure 34

Open heavy-flavor electron $R_{\mathrm{AA}}$ for the indicated centralities. The boxes show the point-to-point correlated systematic uncertainty.

Figure 35

Nuclear modification factors $R_{\mathrm{AA}}$ for open heavy-flavor electrons vs centrality, integrated above the indicated $p_T^e$ ranges.

Figure 36

Comparison of electron $p_T$ distributions calculated by pythia and the data (solid circles). The five curves are electron $p_T$ distributions from charm decay calculated using pythia with different $\langle k_T\rangle$ values shown in the legend. All five curves are normalized to the data for $0.3<p_T<1.6$ GeV/$c$.

Figure 37

$N_{\mathrm{coll}}$ dependence of the charm cross section per binary collision in $\mathrm{Au}+\mathrm{Au}$ and $p+p$ collisions. The uncertainty bars show the statistical uncertainties only.

Figure 38

Heavy-flavor electron $v_2$ as a function of $p_T$ in minimum bias $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV.

Figure 39

$v_2^{\mathrm{HF}}$ for the indicated centralities.

Figure 40

$R_{\mathrm{AA}}$ and $v_2$ from a BDMPS-based calculation from Armesto et al. [83].

Figure 41

$R_{\mathrm{AA}}$ and $v_2$ from Moore and Teaney for two different values for the diffusion coefficient [84].

Figure 42

$R_{\mathrm{AA}}$ and $v_2$ from Refs. [85, 86] for two different values for the resonance widths used in the calculation.

Figure 43

$R_{\mathrm{AA}}$ and $v_2$ from Gossiaux and Aichelin [87, 88, 89].

Figure 44

$R_{\mathrm{AA}}$ in the 0$\%$–10$\%$ centrality class compared with various models. The upper two bands are DGLV [90] calculations for electrons from $D$ and $B$ decays. While the uppermost band considers radiative energy loss only, the middle band takes into account collisional energy loss in addition. The thin dashed curves are DGLV calculations for electrons from $D$ decays only. The lower band is from a collisional dissociation model [91].

Figure 45

Theory comparison of experimental $v_2$ data with the models of Greco et al. [99] and Zhang et al. [100].