Neutral pion production with respect to centrality and reaction plane in Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV

The PHENIX experiment has measured the production of ${\pi }^0$s in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}$ $=$ 200 GeV. The new data offer a fourfold increase in recorded luminosity, providing higher precision and a larger reach in transverse momentum, $p_T$, to 20 GeV/$c$. The production ratio of $\eta /{\pi }^0$ is $0.46\pm 0.01\left(\mathrm{stat}\right)\pm 0.05\left(\mathrm{syst}\right)$, constant with $p_T$ and collision centrality. The observed ratio is consistent with earlier measurements, as well as with the $p+p$ and $d+\mathrm{Au}$ values. ${\pi }^0$ are suppressed by a factor of 5, as in earlier findings. However, with the improved statistical precision a small but significant rise of the nuclear modification factor $R_{\mathrm{AA}}$ vs $p_T$, with a slope of 0.0106${\pm }_{0.0029}^{0.0034}$ (Gev/$c$)${}^{-1}$, is discernible in central collisions. A phenomenological extraction of the average fractional parton energy loss shows a decrease with increasing $p_T$. To study the path-length dependence of suppression, the ${\pi }^0$ yield is measured at different angles with respect to the event plane; a strong azimuthal dependence of the ${\pi }^0$ $R_{\mathrm{AA}}$ is observed. The data are compared to theoretical models of parton energy loss as a function of the path length $L$ in the medium. Models based on perturbative quantum chromodynamics are insufficient to describe the data, while a hybrid model utilizing pQCD for the hard interactions and anti-de-Sitter space/conformal field theory (AdS/CFT) for the soft interactions is consistent with the data.

Figure 1

PHENIX experimental setup in the 2007 data-taking period.

Figure 2

Event plane resolution as a function of collision centrality expressed in terms of $N_{\mathrm{part}}$, using only the BBC and using the combined MPC and RxNPin detectors.

Figure 3

Invariant mass spectrum of two photons (black) and the corresponding mixed events (red) at $7<p_T<7.5$ GeV/$c$ in minimum bias collisions. Vertical lines indicate a $\pm$2.5$\sigma$ integration window.

Figure 4

The corrected ratio $F(\Delta \varphi ,p_T)$ as a function of azimuthal angle at centrality 20–30$\%$.

Figure 5

Invariant yield of ${\pi }^0$ as a function of $p_T$ for each 10$\%$ centrality class, 0–5$\%$ centrality, and minimum bias. The $p_T$ scale starts at 4 GeV/$c$. Error bars are the sum of statistical and type A systematic uncertainties; boxes are the sum of type B and type C systematic uncertainties.

Figure 6

Power-law fit parameters (as tabulated in Table 3) to the ${\pi }^0$ spectra in the 7–20 GeV/$c$ $p_T$ range as a function of centrality, expressed in terms of $N_{\mathrm{part}}$ and for $p+p$ (first point). Shown are (a) amplitudes and (b) powers. Note that the open points ($N_{\mathrm{part}}=352$) correspond to 0–5$\%$ centrality and partially overlap with the adjacent points ($N_{\mathrm{part}}=325$, 0–10$\%$).

Figure 7

The $\eta$ to ${\pi }^0$ ratio as a function of $p_T$ for minimum bias $\mathrm{Au}+\mathrm{Au}$ collisions in 2004 and 2007 (this analysis) data sets, $d$Au collisions (2003 [32]), and pythia 6.131 [33]. Boxes are $p_T$-correlated systematic uncertainties (type B); the shaded box at 1 is the global uncertainty (type C).

Figure 8

The centrality dependence for the ratio of $\eta$ to ${\pi }^0$ as a function of $p_T$ and the expectation from pythia 6.131 [33]. Boxes are $p_T$-correlated systematic uncertainties (type B); the shaded box at 1 is the global uncertainty (type C).

Figure 9

The 1$\sigma$ and 2$\sigma$ standard deviation ${\chi }^2$ contours of the linear fit to the minimum bias $\eta /{\pi }^0$ ratio.

Figure 10

Statistical analysis of the constant fit to the minimum bias $\eta /{\pi }^0$ ratio following the method in Ref. [29].

Figure 11

The nuclear modification factor $R_{\mathrm{AA}}$ of ${\pi }^0$ as a function of $p_T$ for various 10$\%$-wide centrality classes. Solid (red) circles are the results from the current analysis, while open (black) circles are the data published in Ref. [17]. Shaded (gray) boxes around 1 indicate global systematic uncertainties and are of type C. The $p+p$ reference is from the 2005 PHENIX data [31].

Figure 12

Comparison of the ${\pi }^0$ $R_{\mathrm{AA}}$ from this measurement and the charged hadron $R_{\mathrm{AA}}$ in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathit{NN}}}$ $=$ 2.76 TeV from the ALICE experiment [38] at LHC. The central and peripheral classes are (a) 0–5$\%$ and (b) 70–80$\%$.

Figure 13

Linear fit to the $p_T$ dependence of $R_{\mathrm{AA}}$ in the 7–20 GeV/$c$ $p_T$ range in the most central (0–5$\%$) $\mathrm{Au}+\mathrm{Au}$ collisions. Both statistical (bars) and systematic (boxes) uncertainties are considered in the fit.

Figure 14

The 1$\sigma$ and 2$\sigma$ standard deviation ${\chi }^2$ contours of the linear fit (cf. Fig. 13) to the $p_T$ dependence of $R_{\mathrm{AA}}$ for three different centralities.

Figure 15

(a) Slopes of the linear fits to ${\pi }^0$ $R_{\mathrm{AA}}$ vs $p_T$ in $\sqrt{s_{\mathit{NN}}}$ $=$ 200 GeV $\mathrm{Au}+\mathrm{Au}$ collisions (as shown in Fig. 13) and the fitting uncertainties. The fits are in the 7–20 GeV/$c$ $p_T$ range. The horizontal axis is centrality, expressed in terms of $N_{\mathrm{part}}$. (b) Values of $R_{\mathrm{AA}}$ calculated from the fits at $p_T$ $=$ 7 GeV/$c$ and $p_T$ $=$ 20 GeV/$c$, also as a function of centrality. Note that the open points ($N_{\mathrm{part}}$ $=$ 352) correspond to 0–5$\%$ centrality and partially overlap with the adjacent points ($N_{\mathrm{part}}$ $=$ 325, 0–10$\%$).

Figure 16

Method of calculating average fractional momentum loss ($S_{\mathrm{loss}}\equiv \delta p_T/p_T$). This plot is for illustration only; errors are not shown. In the order of procedure: (1) Scale the $p+p$ data by $T_{\mathrm{AA}}$ corresponding to centrality selection of $\mathrm{Au}+\mathrm{Au}$ data, (2) shift the $p+p$ points closest to $\mathrm{Au}+\mathrm{Au}$ in yield, and (3) calculate momentum difference of $p+p$ and $\mathrm{Au}+\mathrm{Au}$ points.

Figure 17

Average fractional momentum loss, as defined in the text, between various centrality $\mathrm{Au}+\mathrm{Au}$ and $T_{\mathrm{AA}}$-scaled $p+p$ collisions. The horizontal axis is the $p_T$ in the $p+p$ collision. Note that for clarity the minimum bias data are shifted up by 0.15. $\delta$(global) stands for the uncertainty coming from the uncertainties of $T_{\mathrm{AA}}$. The overall normalization error from the $p+p$ measurement is 1.3$\%$ and is not shown here.

Figure 18

Comparison of average fractional momentum loss, as defined in the text, between the $\sqrt{s_{\mathit{NN}}}$ $=$ 200 GeV $\mathrm{Au}+\mathrm{Au}$ collisions (${\pi }^0$, current paper) and $\sqrt{s_{\mathit{NN}}}$ $=$ 2.76 TeV $\mathrm{Pb}+\mathrm{Pb}$ collisions (ALICE, charged hadrons [38]). The centrality selections are the same. $\delta$(global) stands for the uncertainty coming from the uncertainties of $T_{\mathrm{AA}}$. The overall normalization error from the $p+p$ measurement is 1.3$\%$ for $\mathrm{Au}+\mathrm{Au}$ data and is not shown here.

Figure 19

(a) The ${\pi }^0$ $R_{\mathrm{AA}}$ as a function of $p_T$ at centrality 0–5$\%$. The solid (red), dashed (green), and dotted (blue) curves are the expectations of the AMY [9, 43], HT [10], and ASW [11] models, respectively. (b) The ${\pi }^0$ $R_{\mathrm{AA}}$ as a function of $p_T$ at centrality 20–30$\%$. The theoretical curves in both panels are obtained from Ref. [37]. The gray boxes around 1 show global uncertainties and are of type C.

Figure 20

$R_{\mathrm{AA}}\left(\Delta \varphi \right)$ as a function of $p_T$ for the first six, 10$\%$-wide centrality classes. Each of the six curves represent a 15${}^{\circ }$-wide bin in azimuth, starting from $\varphi =0^{\circ }$ (in-plane) up to $\varphi ={90}^{\circ }$ (out of plane). The shaded (gray) band around 1 is the systematic uncertainty of the normalizing $\varphi$-integrated $R_{\mathrm{AA}}$. The shaded (blue) boxes around 1 show global uncertainties and are of type C.

Figure 21

Centrality dependence (expressed in terms of $N_{\mathrm{part}}$) of the ${\pi }^0$ $R_{\mathrm{AA}}\left(\Delta \varphi \right)$ in-plane solid (red) circles and out-of-plane solid (blue) triangles, averaged (a) in the 6–10 GeV/$c$ transverse momentum region and (b) above 10 GeV/$c$. Open boxes are systematic uncertainties on $R_{\mathrm{AA}}\left(\Delta \varphi \right)$.

Figure 22

The data points are $R_{\mathrm{AA}}\left(\Delta \varphi \right)$ in 20–30$\%$ centrality as a function of $p_T$ for in-plane solid (red) circles and out-of-plane solid (blue) triangles, compared to four model calculations (see text for description and references). (a) pQCD-based AMY [9, 43], (b) HT [10], (c) pQCD-based ASW [11], and (d) ASW using AdS/CFT correspondence [12]. The curves in panels (a)–(c) are taken from Ref. [37]. The dashed and solid lines are the in-plane and out-of-plane predictions, respectively. The definitions of the bands and boxes are the same as those in Fig. 20.