High-$p_T$ charged hadron suppression in $\text{Au}+\text{Au}$ collisions at $\sqrt{s_{NN}}=200\text{GeV}$

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured charged hadron yields at midrapidity over a wide range of transverse momenta $\left(0.5<p_T<10\text{GeV}∕c\right)$ in $\text{Au}+\text{Au}$ collisions at $\sqrt{s_{NN}}=200\text{GeV}$. The data are compared to ${\pi }^0$ measurements from the same experiment. For both charged hadrons and neutral pions, the yields per nucleon-nucleon collision are significantly suppressed in central compared to peripheral and nucleon-nucleon collisions. The suppression sets in gradually and increases with increasing centrality of the collisions. Above $4–5\text{GeV}∕c$ in $p_T$, a constant and almost identical suppression of charged hadrons and ${\pi }^0$’s is observed. The $p_T$ spectra are compared to published spectra from $\text{Au}+\text{Au}$ at $\sqrt{s_{NN}}=130$ in terms of $x_T$ scaling. Central and peripheral ${\pi }^0$ as well as peripheral charged spectra exhibit the same $x_T$ scaling as observed in $p+p$ data.

Figure 1

(Color online) PHENIX experimental layout for the $\text{Au}+\text{Au}$ run in 2001. The top panel shows the PHENIX central arm spectrometers viewed along the beam axis. The bottom panel shows a side view of the PHENIX muon arm spectrometers.

Figure 2

$D_{\varphi }^{pc2}$ (the difference between projection and hit location in $r\text{−}\varphi$ direction at PC2) vs $D_{\varphi }^{pc3}$ in centimeters for tracks with reconstructed $p_T>4\text{GeV}∕\mathrm{c}$. PC2, PC3 matching differences are correlated, with signal tracks peaked around 0 and background tracks extend along the $D_{\varphi }^{+}$ direction. The double-peak structure along $D_{\varphi }^{-}$ is related to the finite granularity of PC2 and PC3 pads. The positive directions of $D_{\varphi }^{+}$ and $D_{\varphi }^{-}$ are indicated by the arrow. $\mathrm{A}\pm 2\sigma$ cut on these variables is illustrated by the box region inside the dashed lines.

Figure 3

(Color online) Background contamination due to electrons, illustrated by the track match in $D_{\varphi }^{+}$ for tracks with associated RICH PMTs and $6<p_T<7\text{GeV}∕c$. The matching distributions are shown for minimum bias events and separately for positive (left) and negative (right) charged tracks. The first three distributions represent the raw counts for all tracks with RICH association (thick solid line), estimated conversion backgrounds (dashed line), and charged pions (dot-dashed line) that were obtained by subtracting the dashed line from the solid line. The thin solid line represents the matching distribution of background electrons from Monte Carlo simulation, arbitrarily scaled to match the data. The $\pm 2\sigma$ matching windows are illustrated by the vertical dashed line. Since $e^{+}$ and $e^{-}$ are deflected in opposite directions by the fringe field, they are shifted to positive and negative directions, respectively.

Figure 4

(Color online) Background contamination due to decays, illustrated by the track match in $D_{\varphi }^{+}$ for tracks without an associated RICH PMT and with $6<p_T<7\text{GeV}∕c$, shown for minimum bias events and separately for positive (left) and negative (right) charged tracks. The first three distributions represent the raw counts for all tracks without RICH association (thick solid line), estimated decay backgrounds (dashed line), and signal tracks (dot-dashed line) that were calculated as the difference of the two. The thin solid line represents the matching distribution of decay background from Monte Carlo simulation, arbitrarily scaled to match the data. The two $\pm 2\sigma$ matching windows are illustrated by the vertical dashed line. Outside the signal window, the shape of the dashed line matches the solid line rather well, the difference of $10\%$ level is taken into account in the error estimation of $R_{decay}$.

Figure 5

(Color online) Amount of background estimated as a function of $p_T$ for minimum bias collision. The left part shows the background subtracted charged hadron spectra (filled square), the background from $\gamma$ conversions (open square), and decays (open triangle). The right part shows the signal to background ratio. Only statistical errors are shown.

Figure 6

(Color online) Averaged correction functions for ${\pi }^{+}$ and ${\pi }^{-}$, $p$ and $\overline{p}$, and $K^{+}$ and $K^{-}$.

Figure 7

(Color online) Functions used to correct the charged particle $p_T$ spectra. The upper left panel shows the $p_T$-dependent correction $c\left(p_T\right)$. The upper right panel shows the centrality dependent correction $c\left(N_{part}\right)$. Systematic uncertainties are indicated by the dashed lines. The two corrections factorize at $p_T>1.5\text{GeV}∕c$, so that for given centrality the full correction function is given by $c\left(p_T\right)\times c\left(N_{part}\right)$. The accuracy of this factorization is demonstrated in the lower panel. The ratio of the full correction for central collisions ($5\%$ most central) to the correction for single particle events varies by less than $3\%$ above $1.5\text{GeV}∕c$ (the error bar is the statistical error from the Monte Carlo calculation).

Figure 8

(Color online) $p_T$ spectra of charged hadrons for minimum bias collisions along with spectra for nine centrality classes derived from the pseudorapidity region $\mid \eta \mid <0.18$. The minimum bias spectrum has been multiplied by 5 for visibility. Only statistical errors are shown in the spectra. Most of the $p_T$-dependent systematic errors are independent of centrality and are tabulated in Table 3.

Figure 9

(Color online) Ratios of centrality selected $p_T$ spectra to the minimum bias spectrum. Ratios for peripheral classes are scaled up for clarity. For the $p_T$ range shown, most of the systematic errors cancel in the ratio. The remaining systematic errors that can change the shape are less than $10\%$ (see Table 4) and are correlated bin-to-bin in $p_T$.

Figure 10

(Color online) Centrality dependence of $⟨p_T^{trunc}⟩$, the average $p_T$ of charged particles above a $p_T$ threshold as defined in Eq. (9). Shown are $⟨p_T^{trunc}⟩$ values for three $p_T^{min}$ cuts, with $p_T^{min}=0.5$, 2, and $4.5\text{GeV}∕c$, respectively. The errors shown are statistical only. The systematical errors for all data points are less than $3\%$.

Figure 11

(Color online) Ratio of charged hadron yields per nucleon-nucleon collision between central $\left(0–10\%\right)$ and peripheral $\left(60–92\%\right)$ $\text{Au}+\text{Au}$ collisions. The solid error bars on each data point are statistical. The error bar on the left hand side of the figure is the overall scale error relative to 0.5, which is the quadrature sum of (i) the uncertainty of $⟨N_{coll}⟩$ (see Table 1) and (ii) the uncertainty on the occupancy correction $\left({\delta }_{occupancy}\right)$. The shaded error band on each data point is the $p_T$-dependent systematic error from ${\delta }_{R_e\oplus R_{decay}}$ and centrality dependent feed down correction $\left({\delta }_{feeddown}\right)$ as given in Table 4.

Figure 12

(Color online) $R_{AA}$ for $\left(h^{+}+h^{-}\right)∕2$ and ${\pi }^0$ as a function of $p_T$ for minimum bias and nine centrality classes according to the “Fine” type of centrality classes defined in Table 1. The error bars on the ${\pi }^0$ data points include statistical and systematical errors on the $\text{Au}+\text{Au}$ data and the $N+N$ reference. The error bars on $\left(h^{+}+h^{-}\right)∕2$ data points are statistical errors only. The common normalization errors (${\delta }_{norm}^{{\pi }^0}$ from Table 5) on the references for charged hadrons and ${\pi }^0$’s are added in quadrature with the uncertainly on $⟨N_{coll}⟩$ and are indicated by the black bar on the left side of each panel. This error ranges from $15\%$ to $36\%$ from central to peripheral collisions and can shift all points in the charged and neutral pion $R_{AA}$ up and down together. The shaded band on charged $R_{AA}$ includes the remaining systematic errors on the charged $N+N$ reference summed in quadrature with the systematic errors from the $\text{Au}+\text{Au}$ spectra. This error amounts to $-12.5\%+18\%$ at low $p_T$ and changes to $\pm 12.5\%$ at $p_T=4.5\text{GeV}∕c$ and $\pm 18.5\%$ at $p_T=8\text{GeV}∕c$.

Figure 13

(Color online) Charged hadron to ${\pi }^0$ ratios for minimum bias events and nine centrality classes according to the “Fine” type of centrality classes defined in Table 1. The error bars represent the quadratic sum of statistical and point-by-point systematic errors from $\left(h^{+}+h^{-}\right)∕2$ and ${\pi }^0$. The shaded band shows the percent normalization error [dominantly from $\left(h^{+}+h^{-}\right)∕2$ data] common to all centrality classes. The dashed line at 1.6 is the $h∕\pi$ ratio measured in $p+p$ [31] and $e^{+}{e}^{-}$ [32] collisions.

Figure 14

(Color online) $\text{Au}+\text{Au}$ yield integrated for $p_T>4.5\text{GeV}∕c$ over the $N+N$ yield, normalized using either $N_{coll}$ ($R_{AA}$ in the top panel) or $N_{part}$ ($R_{AA}^{N_{part}}$ in the bottom panel), plotted as a function of $⟨N_{part}⟩$. The bands represent the expectation of binary collisions (solid) and participant pair (dashed) scaling. The width of the bands gives the systematic errors on $N_{coll}\left(N_{part}\right)$ added in quadrature with the common normalization errors on the $N+N$ references for charged hadrons and neutral pions. For charged hadrons, the statistical errors are given by the bars. The systematic errors, which are not common with the errors for neutral pions and which are correlated in $p_T$, are shown as brackets. The shaded bars around each neutral pion point represent the systematic and statistical errors; these errors are not correlated with the errors shown for the charged hadron data.

Figure 15

(Color online) (a) Transverse momentum dependence of the invariant cross section at seven center-of-mass energies from different experiments [31, 50, 63, 64]. (b) The same data multiplied by ${\sqrt{s}}^{6.3}$, plotted as a function of $x_T=2p_T∕\sqrt{s}$.

Figure 16

(Color online) (a) Transverse momentum dependence of the invariant cross section for ${\pi }^0$ at five center-of-mass energies from different experiments [16, 65, 66, 67, 68]. (b) The same data multiplied by ${\sqrt{s}}^{6.3}$, plotted vs $x_T=2p_T∕\sqrt{s}$.

Figure 17

(Color online) $x_T$ scaled spectra for central collisions and peripheral collisions at $\sqrt{s_{NN}}=130$ and $200\text{GeV}$. The left figure shows the ${\pi }^0$ $x_T$ spectra, and the right figure shows the $\left(h^{+}+h^{-}\right)∕2$ $x_T$ spectra. The central $\left(0–10\%\right)$ $x_T$ spectra are represented by triangular symbols, and the peripheral $\left(60–80\%\right)$ $x_T$ spectra are represented by square symbols. The open symbols represent $x_T$ spectra from $\sqrt{s_{NN}}=130\text{GeV}$ scaled by a factor of ${\left(130∕200\right)}^{6.3}$. The solid symbols represent $x_T$ spectra from $\sqrt{s_{NN}}=200\text{GeV}$ The error bars are statistical only.

Figure 18

(Color online) The $x_T$ scaling power $n$ [according to Eq. (21)] plotted as a function of $x_T$ calculated for ${\pi }^0$ (left) and $\left(h^{+}+h^{-}\right)∕2$ (right) in central $\left(0–10\%\right)$ and peripheral $\left(60–80\%\right)$ collisions. The solid (and dashed) lines indicate a constant fit along with the fitting ranges to the central (and peripheral) $n\left(x_T\right)$ functions. The error bars at each data point include statistical and point-to-point systematic errors from $\sqrt{s_{NN}}=130$ and $200\text{GeV}$. The scale errors on $x_T$ spectra are $20.7\%\left(15.9\%\right)$ for ${\pi }^0{x}_T$ spectra ratio in central (peripheral) collisions, and $18.6\%\left(15.7\%\right)$ for $\left(h^{+}+h^{-}\right)∕2x_T$ spectra ratio in central (peripheral) collisions. These type of errors propagate into the systematic errors on $x_T$ scaling power $n$ listed in Table 6.