Identified particle production, azimuthal anisotropy, and interferometry measurements in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV

We present the first measurements of identified hadron production, azimuthal anisotropy, and pion interferometry from $\mathrm{Au}+\mathrm{Au}$ collisions below the nominal injection energy at the BNL Relativistic Heavy-Ion Collider (RHIC) facility. The data were collected using the large acceptance solenoidal tracker at RHIC (STAR) detector at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV from a test run of the collider in the year 2008. Midrapidity results on multiplicity density $\mathit{dN}/\mathit{dy}$ in rapidity $y$, average transverse momentum $\langle p_T\rangle$, particle ratios, elliptic flow, and Hanbury-Brown–Twiss (HBT) radii are consistent with the corresponding results at similar $\sqrt{s_{\mathit{NN}}}$ from fixed-target experiments. Directed flow measurements are presented for both midrapidity and forward-rapidity regions. Furthermore the collision centrality dependence of identified particle $\mathit{dN}/\mathit{dy}$, $\langle p_T\rangle$, and particle ratios are discussed. These results also demonstrate that the capabilities of the STAR detector, although optimized for $\sqrt{s_{\mathit{NN}}}=200$ GeV, are suitable for the proposed QCD critical-point search and exploration of the QCD phase diagram at RHIC.

Figure 1

Event-by-event distribution of the $z$ position of the primary vertex $V_z$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV. The vertical solid lines show the condition of $\left|V_z\right|<75$ cm for selected events.

Figure 2

Event-by-event distribution of $V_x$ vs $V_y$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV. The circle with dotted lines corresponds to a radius $(=\sqrt{V_x^2+V_y^2})$ of 2 cm.

Figure 3

Uncorrected charged-particle multiplicity distribution (open circles) measured in the TPC within $\left|\eta \right|<0.5$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV. The dashed histogram represents the simulated multiplicity distribution. The vertical dashed lines reflect the centrality selection criteria used in the paper. Errors are statistical only.

Figure 4

$\mathit{dE}/\mathit{dx}$ distribution for positively charged hadrons in the TPC, normalized by the expected pion $\mathit{dE}/\mathit{dx}$ at $0.3<p_T<0.4\hspace{0.5em}\mathrm{GeV}/c$ and $|y|<0.5$ in Au $+$ Au collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV. The curves are Gaussian fits representing contributions from pions (dot-dashed, red), electrons (dashed, green), kaons (dot-dashed, blue), and protons (dotted, magenta). See text for details. Errors are statistical only.

Figure 5

Second-order event plane resolution measured in the TPC as a function of collision centrality for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV. Errors are statistical only.

Figure 6

(a) Distribution of distance of closest approach of proton tracks to the primary vertex. The embedded tracks are compared with the ones in real data at 0.4 $<p_T<0.7$ GeV/$c$ at midrapidity in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV. The DCA distribution of antiprotons in a similar kinematic range is also shown for comparison. (b) Comparison between the distributions of number of fit points for pions from embedding and from real data for 0.4 $<p_T<0.7\hspace{0.5em}\mathrm{GeV}/c$ at midrapidity in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV.

Figure 7

(a) Efficiency $\times$ acceptance for reconstructed pions, kaons, and protons in the TPC as a function of $p_T$ at midrapidity in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV. (b) Percentage of pion background contribution estimated from HIJING $+$ GEANT as a function of $p_T$ at midrapidity in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV. The contributions from different sources and the total background are shown separately.

Figure 8

Transverse momentum spectra for (a) charged pions and (b) protons at midrapidity ($\left|y\right|<0.5$) in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV for various centralities. The distributions for antiprotons were measured in this limited statistics data only for 0–60% centrality. The antiproton yield shown in the figure is multiplied by a factor of 10. The errors shown are statistical and systematic errors (discussed in Sec. 2h) added in quadrature.

Figure 9

Transverse momentum spectra for (a) positive kaons and (b) negative kaons at midrapidity ($\left|y\right|<0.5$) in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV for various centralities. The errors shown are statistical and systematic errors (discussed in Sec. 2h) added in quadrature.

Figure 10

$\mathit{dN}/\mathit{dy}$ of (a) ${\pi }^{+}$ and (b) $p$, normalized by $\langle N_{\mathrm{part}}\rangle /2$, for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV, plotted as a function of $\langle N_{\mathrm{part}}\rangle$. The lower energy results are compared with corresponding results for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=62.4$ and 200 GeV [23, 37]. The errors shown are the quadrature sum of statistical and systematic uncertainties. The systematic errors on pion and proton yields for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV data are $~$12% and $~$20%, respectively, for all the collision centralities studied.

Figure 11

$\mathit{dN}/\mathit{dy}$ of (a) $K^{+}$ and (b) $K^{-}$, normalized by $\langle N_{\mathrm{part}}\rangle /2$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV, plotted as a function of $\langle N_{\mathrm{part}}\rangle$. The lower energy results are compared with corresponding results for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=62.4$ and 200 GeV [4, 23, 37]. The errors shown are the quadrature sum of statistical and systematic uncertainties. The systematic errors on $K^{+}$ and $K^{-}$ yields for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV data are similar, about 18% for all the collision centralities studied.

Figure 12

$\langle p_T\rangle$ for ${\pi }^{+}$, $K^{+}$, and $p$ plotted as a function of $\langle N_{\mathrm{part}}\rangle$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV and compared with corresponding results at $\sqrt{s_{\mathit{NN}}}=$ 62.4 GeV [4, 23, 37]. The errors shown are the quadrature sum of statistical and systematic uncertainties. The systematic errors for pions, kaons, and protons for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV are $~$12%, 18%, and 21%, respectively, and similar for all the collision centralities studied.

Figure 13

$\langle p_T\rangle$ for ${\pi }^{+}$, $K^{+}$ and $p$ plotted as a function of $\langle N_{\mathrm{part}}\rangle$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV and compared with corresponding results at $\sqrt{s_{\mathit{NN}}}=200$ GeV [4, 23, 37]. The errors shown are the quadrature sum of statistical and systematic uncertainties. The systematic errors for pions, kaons, and protons for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV are $~$12%, 18%, and 21%, respectively, and similar for all the collision centralities studied.

Figure 14

Variation of (a) $K^{-}/K^{+}$ and (b) $K^{-}/{\pi }^{-}$ ratios as a function of $\langle N_{\mathrm{part}}\rangle$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV. For comparison we also show the corresponding results from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=62.4$ and 200 GeV [23, 37]. The errors shown are the quadrature sum of statistical and systematic uncertainties. The systematic errors for $K^{-}/K^{+}$ and $K^{-}/{\pi }^{-}$ for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV data are $~$25% and 22%, respectively, and similar for all the collision centralities studied.

Figure 15

Variation of (a) $p/{\pi }^{+}$ and (b) $K^{+}/{\pi }^{+}$ ratios as a function of $\langle N_{\mathrm{part}}\rangle$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV. For comparison, we also show the corresponding results from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=62.4$ and 200 GeV [4, 23, 37]. The errors shown are the quadrature sum of statistical and systematic uncertainties. The systematic errors for $p/{\pi }^{+}$ and $K^{+}/{\pi }^{+}$ for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV data are $~$25% and 22%, respectively, and similar for all the collision centralities studied.

Figure 16

Midrapidity ${\mathit{dN}}_{\mathrm{ch}}/\mathit{d}\eta$ normalized by $\langle N_{\mathrm{part}}\rangle /2$ as a function of $\sqrt{s_{\mathit{NN}}}$. $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV are compared with previous results from AGS [38], SPS [39], and RHIC [23, 40]. The errors shown are the quadrature sum of statistical and systematic uncertainties. The systematic error for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV data is 39%.

Figure 17

(a) $\mathit{dN}/\mathit{dy}$ normalized by $\langle N_{\mathrm{part}}\rangle /2$ and (b) $\langle m_T\rangle -m$ of ${\pi }^{\pm }$, in 0–10% central $\mathrm{Au}+\mathrm{Au}$ collisions for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV compared with previous results from AGS [38], SPS [39], and RHIC [23]. The errors shown are the quadrature sum of statistical and systematic uncertainties.

Figure 18

(a) $\mathit{dN}/\mathit{dy}$ normalized by $\langle N_{\mathrm{part}}\rangle /2$ and (b) $\langle m_T\rangle -m$ of $K^{\pm }$, in 0–10% central $\mathrm{Au}+\mathrm{Au}$ collisions for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV compared with previous results from AGS [38], SPS [39], and RHIC [23]. The errors shown are the quadrature sum of statistical and systematic uncertainties.

Figure 19

(a) ${\pi }^{-}/{\pi }^{+}$ and (b) $\mathrm{p̄}/p$ ratios at midrapidity ($|y|<0.5$) for central 0–10% $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV compared with previous results from AGS [38], SPS [39], and RHIC [23]. The errors shown are the quadrature sum of statistical and systematic uncertainties. The systematic errors on ${\pi }^{-}/{\pi }^{+}$ and $\mathrm{p̄}/p$ for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV data are 15% and 27%, respectively.

Figure 20

(a) $K^{-}/K^{+}$ and (b) $K/\pi$ ratios at midrapidity ($|y|<0.5$) for central 0–10% $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV compared with previous results from AGS [38], SPS [39], and RHIC [23]. The errors shown are the quadrature sum of statistical and systematic uncertainties. The systematic errors on $K^{-}/K^{+}$ and $K/\pi$ for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV data are 23% and 19%, respectively.

Figure 21

Charged-hadron $v_1$ vs $\eta$ from the 0–60% collision centrality $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV. The errors shown are statistical. Systematic errors are discussed in Sec. 2h. The solid star symbols are the results obtained from the mixed harmonic method, while the open star and open plus symbols represent results from the standard methods (see text for details). The results are compared to $v_1$ from 30–60% collision centrality $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=62.4$ and 200 GeV [53]. For comparison, $v_1$ for charged pions for the 0–60% collision centrality from $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathit{NN}}}=8.8$ GeV are also shown [54].

Figure 22

Same as Fig. 21, but plotted as a function of $\eta /y_{\mathrm{beam}}$.

Figure 23

$v_2$ as a function of $p_T$ for charged hadrons (solid triangles), $\pi$ (solid circles), and $p$ (solid squares) in 0–60% $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV. The error bars include only statistical uncertainties for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV data. The corresponding systematic error is discussed in Sec. 2h. For comparison, $v_2$($p_T$) results for $\pi$ (open circles) from NA49 [54] in 0$–43.5\%$ Pb $+$ Pb collisions at $\sqrt{s_{\mathit{NN}}}=8.8$ GeV are also shown.

Figure 24

Energy dependence of $v_2$ near midrapidity ($-1<\eta <1$) for $\sqrt{s_{\mathit{NN}}}=9.2$ GeV 0–60% central $\mathrm{Au}+\mathrm{Au}$ collisions. Only statistical errors are shown. The results of STAR charged-hadron $v_2$ [55] are compared with those measured by E877 [56], NA49 [54], PHENIX [57], and PHOBOS [46, 50, 58] collaborations.

Figure 25

Projections of the three-dimensional correlation function and corresponding Bowler-Sinyukov [34] fits (lines) for negative pions from the 0–60$\%$ central $\mathrm{Au}+\mathrm{Au}$ events and $k_T$ $=$ [150, 250] MeV/$c$.

Figure 26

Midrapidity transverse momentum distributions of pions, kaons, and protons (no feed-down correction) for 0–10% most central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV, fitted to blast-wave model calculations [60]. The extracted kinetic freeze-out parameters are $T_{\mathrm{kin}}=105\pm 10$ (stat.) $\pm$ 16 (sys.) MeV and $\langle {\beta }_T\rangle =0.46c\pm 0.01c$ (stat.) $\pm$ 0.04$c$ (sys.).

Figure 27

Midrapidity particle ratios for 0–10% most central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV, fitted to thermal model calculations. See text for details. The extracted chemical freeze-out temperature is $T_{\mathrm{ch}}=151\pm 2$ (stat.) $\pm$ 7 (sys.) MeV and baryon chemical potential is ${\mu }_B=354\pm 7$ (stat.) $\pm$ 30 (sys.) MeV.

Figure 28

Temperature vs baryon chemical potential (${\mu }_B$) from heavy-ion collisions at various $\sqrt{s_{\mathit{NN}}}$ [23]. The ${\mu }_B$ values were estimated at chemical freeze-out. The kinetic and chemical freeze-out parameters, extracted using models assuming thermal and chemical equilibrium from midrapidity measurement in central 0–10% $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=9.2$ GeV, are shown as star symbols. The range of critical temperatures ($T_{\mathrm{c}}$) [66] of the crossover quark-hadron phase transition at ${\mu }_B=0$ [6] and the QCD critical point from two different calculations [9] from lattice QCD are also indicated. Model-based estimates of the range of initial temperature ($T_{\mathrm{initial}}$) achieved in heavy-ion collisions based in part on direct photon data at top RHIC [64] and SPS [65] energies are also shown. The range of ${\mu }_B$ to be scanned in the upcoming RHIC critical-point search and beam energy scan program corresponding to $\sqrt{s_{\mathit{NN}}}=5.5$–39 GeV is indicated by horizontal arrows near the ${\mu }_B$ axis [12].