Bulk properties of the medium produced in relativistic heavy-ion collisions from the beam energy scan program

We present measurements of bulk properties of the matter produced in Au+Au collisions at $\sqrt{s_{NN}}=7.7,11.5,19.6,27$, and 39 GeV using identified hadrons (${\pi }^{\pm }$, $K^{\pm }$, $p$, and $\overline{p}$) from the STAR experiment in the Beam Energy Scan (BES) Program at the Relativistic Heavy Ion Collider (RHIC). Midrapidity ($\left|y\right|<0.1$) results for multiplicity densities $dN/dy$, average transverse momenta $\langle p_T\rangle$, and particle ratios are presented. The chemical and kinetic freeze-out dynamics at these energies are discussed and presented as a function of collision centrality and energy. These results constitute the systematic measurements of bulk properties of matter formed in heavy-ion collisions over a broad range of energy (or baryon chemical potential) at RHIC.

Figure 1

The $x$ and $y$ positions of the reconstructed event vertices in Au+Au collisions at (a) $\sqrt{s_{NN}}=7.7\mathrm{GeV}$ and (b) $\sqrt{s_{NN}}=39\mathrm{GeV}$. The events involving beam-pipe interactions are rejected by applying a cut of less than 2 cm on the transverse radial position of the event vertex. See text for more details.

Figure 2

Distributions of the $z$ position of the reconstructed primary vertex ($V_z$) in Au+Au collisions at (a) $\sqrt{s_{NN}}=7.7$ and (b) $\sqrt{s_{NN}}=39\mathrm{GeV}$.

Figure 3

(a) The $\langle dE/dx\rangle$ of charged tracks at midrapidity ($\left|y\right|<0.1$) plotted as function of rigidity $(p/q)$ in Au+Au collisions at $\sqrt{s_{NN}}=39\mathrm{GeV}$. The various bands correspond to different particles such as ${\pi }^{\pm }$, $K^{\pm }$, $p$, and $\overline{p}$. The curves represent the Bichsel [44] expectation values of the corresponding particles. (b) $1/\beta$ from TOF vs rigidity at same energy. The curves, from bottom to top, show the expected mean values of pions, kaons, and (anti)protons, respectively.

Figure 4

The $z_{\pi }$, $z_K$, and $z_p$ distributions for positively charged hadrons ($\pi$, $K$, and $p$) at midrapidity ($\left|y\right|<0.1$) in the TPC for various $p_T$ ranges in Au+Au collisions at $\sqrt{s_{NN}}=7.7\mathrm{GeV}$. The curves are Gaussian fits representing contributions from pions (dash-dotted, red), electrons (dotted, green), kaons (dashed, blue), and protons (long-dash-dotted, magenta). Uncertainties are statistical only.

Figure 5

The $m^2$ distributions for positively charged hadrons used to extract raw yields for pions, kaons, and protons in $\left|y\right|<0.1$ for Au+Au collisions at 7.7 GeV at three different $p_T$ ranges. The curves are predicted $m^2$ fits representing contributions from pions (dash-dotted, red), kaons (dashed, green), and protons (dotted, blue).

Figure 6

(a) Distribution of distance of closest approach of pion tracks to the primary vertex. The embedded tracks are compared to the ones in real data at 0.2 $<p_T<0.5\mathrm{GeV}/c$ at midrapidity ($\left|y\right|<0.1$) in Au+Au collisions at $\sqrt{s_{NN}}=7.7\mathrm{GeV}$. (b) Comparison between the distributions of number of fit points for pions from embedding and from real data for 0.2 $<p_T<0.5\mathrm{GeV}/c$ at midrapidity in Au+Au collisions at $\sqrt{s_{NN}}=7.7\mathrm{GeV}$.

Figure 7

Efficiency $\times$ acceptance obtained from Monte Carlo embedding for reconstructed (a) pions, (b) kaons, and (c) protons in the TPC as a function of $p_T$ at midrapidity ($\left|y\right|<0.1$) for 0–5% Au+Au collisions at $\sqrt{s_{NN}}=7.7\mathrm{GeV}$. The curves represent the functional fit of the form $p_{0}exp[-{(p_1/p_T)}^{p_2}]$.

Figure 8

TOF matching efficiency for (a) pions, (b) kaons, and (c) protons as a function of $p_T$ at midrapidity ($\left|y\right|<0.1$) for 0–5% Au+Au collisions at $\sqrt{s_{NN}}=7.7\mathrm{GeV}$.

Figure 9

The $p_T$ difference between reconstructed and embedded tracks plotted as a function of the $p_T$ of the reconstructed track for (a) pions, (b) kaons, and (c) protons at midrapidity ($\left|y\right|<0.1$) in Au+Au collisions at $\sqrt{s_{NN}}=39\mathrm{GeV}$. This difference is due to particle energy loss in the detector material, which is already corrected in the tracking algorithm for pions, but only partially for kaons and protons.

Figure 10

Percentage of pion background contribution estimated from hijing+geant simulation as a function of $p_T$ at midrapidity ($\left|y\right|<0.1$) in 0–5% Au+Au collisions at $\sqrt{s_{NN}}=7.7\mathrm{GeV}$. The contributions from different sources are shown separately, as well as the total background.

Figure 11

The DCA distributions of protons and antiprotons for 0.40 $<p_T<$ 0.45 GeV/$c$ at midrapidity ($\left|y\right|<0.1$) in 0–5% Au+Au collisions at $\sqrt{s_{NN}}=39\mathrm{GeV}$. The dashed curve is the fitted proton background; the dotted histogram is the $\overline{p}$ distribution scaled by the $p/\overline{p}$ ratio; and the solid histogram is the fit given by Eq. (6).

Figure 12

Midrapidity ($\left|y\right|<0.1$) transverse momentum spectra for (a) ${\pi }^{+}$, (b) ${\pi }^{-}$, (c) $K^{+}$, (d) $K^{-}$, (e) $p$, and (f) $\overline{p}$ in Au+Au collisions at $\sqrt{s_{NN}}=7.7\mathrm{GeV}$ for different centralities. The spectra for centralities other than 0–5% are scaled for clarity as shown in the figure. The curves represent the Bose-Einstein, $m_T$-exponential, and double-exponential function fits to 0–5% central data for pions, kaons, and (anti)protons, respectively. The uncertainties are statistical and systematic added in quadrature.

Figure 13

Same as Fig. 12 but for Au+Au collisions at $\sqrt{s_{NN}}=11.5\mathrm{GeV}$.

Figure 14

Same as Fig. 12 but for Au+Au collisions at $\sqrt{s_{NN}}=19.6\mathrm{GeV}$.

Figure 15

Same as Fig. 12 but for Au+Au collisions at $\sqrt{s_{NN}}=27\mathrm{GeV}$.

Figure 16

Same as Fig. 12 but for Au+Au collisions at $\sqrt{s_{NN}}=39\mathrm{GeV}$.

Figure 17

Centrality dependence of $dN/dy$ normalized by $\langle N_{\mathrm{part}}\rangle /2$ for (a) ${\pi }^{+}$, (b) ${\pi }^{-}$, (c) $K^{+}$, (d) $K^{-}$, (e) $p$, and (f) $\overline{p}$ at midrapidity ($\left|y\right|<0.1$) in Au+Au collisions at $\sqrt{s_{NN}}=7.7,11.5,19.6,27$, and 39 GeV. Results are compared with published results in Au+Au collisions at $\sqrt{s_{NN}}=62.4$ and 200 GeV [43, 48]. Errors shown are the quadrature sum of statistical and systematic uncertainties. For clarity, $\langle N_{\mathrm{part}}\rangle$ uncertainties are not added in quadrature.

Figure 18

Centrality dependences of $\langle p_T\rangle$ for (a) ${\pi }^{+}$, (b) ${\pi }^{-}$, (c) $K^{+}$, (d) $K^{-}$, (e) $p$, and (f) $\overline{p}$ at midrapidity ($\left|y\right|<0.1$) in Au+Au collisions at $\sqrt{s_{NN}}=7.7,11.5,19.6,27$, and 39 GeV. Results are compared with published results in Au+Au collisions at $\sqrt{s_{NN}}=62.4$ and 200 GeV [43, 48]. Errors shown are quadrature sum of statistical and systematic uncertainties where the latter dominates.

Figure 19

Variation of (a) ${\pi }^{-}/{\pi }^{+}$, (b) $K^{-}/K^{+}$, and (c) $\overline{p}/p$ ratios as a function of $\langle N_{\mathrm{part}}\rangle$ at midrapidity ($\left|y\right|<0.1$) in Au+Au collisions at all BES energies. Also shown for comparison are the corresponding results in Au+Au collisions at $\sqrt{s_{NN}}=62.4$ and 200 GeV [11, 12, 13, 14, 43]. Errors shown are the quadrature sum of statistical and systematic uncertainties where the latter dominates.

Figure 20

Variation of (a) $K^{-}/{\pi }^{-}$, (b) $\overline{p}/{\pi }^{-}$, (c) $K^{+}/{\pi }^{+}$, and (d) $p/{\pi }^{+}$ ratios as a function of $\langle N_{\mathrm{part}}\rangle$ at midrapidity ($\left|y\right|<0.1$) in Au+Au collisions at all BES energies. Also shown for comparison are the corresponding results in Au+Au collisions at $\sqrt{s_{NN}}=62.4$ and 200 GeV [11, 12, 13, 14, 43]. Errors shown are the quadrature sum of statistical and systematic uncertainties where the latter dominates.

Figure 21

The midrapidity ($\left|y\right|<0.1$) $dN/dy$ normalized by $\langle N_{\mathrm{part}}\rangle$/2 as a function of $\sqrt{s_{NN}}$ for (a) ${\pi }^{\pm }$, (b) $K^{\pm }$, and (c) $p$ and $\overline{p}$. Results in 0–5% Au+Au collisions at BES energies are compared to previous results from AGS [53, 54, 55, 56, 57, 58, 59, 60], SPS [61, 62, 63, 64], RHIC [27, 43, 65], and LHC [66]. AGS results correspond to 0–5%, SPS to 0–7%, top RHIC to 0–5% (62.4 and 200 GeV) and 0–6% (130 GeV), and LHC to 0–5% central collisions. Errors shown are the quadrature sum of statistical and systematic uncertainties where the latter dominates.

Figure 22

$\langle m_T\rangle -m$ of (a) ${\pi }^{\pm }$, (b) $K^{\pm }$, and (c) $p$ and $\overline{p}$ as a function of $\sqrt{s_{NN}}$. Midrapidity ($\left|y\right|<0.1$) results are shown for 0–5% central Au+Au collisions at BES energies and are compared to previous results from AGS [53, 54, 55, 56, 57, 58, 59, 60], SPS [61, 62, 63, 64], RHIC [43], and LHC [66]. AGS results correspond to 0–5%, SPS to 0–7%, top RHIC to 0–5% (62.4 and 200 GeV), and 0–6% (130 GeV), and LHC to 0–5% central collisions. The errors shown are the quadrature sum of statistical and systematic uncertainties where the latter dominates.

Figure 23

(a) ${\pi }^{-}/{\pi }^{+}$, (b) $K^{-}/K^{+}$, and (c) $\overline{p}/p$ ratios at midrapidity ($\left|y\right|<0.1$) in central 0–5% Au+Au collisions at $\sqrt{s_{NN}}=7.7,11.5,19.6,27$, and 39 GeV, compared to previous results from AGS [53, 54, 55, 56, 57, 58, 59, 60], SPS [61, 62, 63, 64], RHIC [27, 43], and LHC [66]. AGS results correspond to 0–5%, SPS to 0–7%, top RHIC to 0–5% (62.4 and 200 GeV) and 0–6% (130 GeV), and LHC to 0–5% central collisions. Errors shown are the quadrature sum of statistical and systematic uncertainties where the latter dominates.

Figure 24

$K/\pi$ ratio at midrapidity ($\mid y\mid <0.1$) for central 0–5% Au+Au collisions at $\sqrt{s_{NN}}=7.7,11.5,19.6,27$, and 39 GeV, compared to previous results from AGS [53, 54, 55, 56, 57, 58, 59, 60], SPS [61, 62, 63, 64], RHIC [27, 43], and LHC [66]. AGS results correspond to 0–5%, SPS to 0–7%, top RHIC to 0–5% (62.4 and 200 GeV) and 0–6% (130 GeV), and LHC to 0–5% central collisions. Errors shown are the quadrature sum of statistical and systematic uncertainties where the latter dominates.

Figure 25

The GCE model fits shown along with standard deviations for (a) Au+Au 7.7 and (b) Au+Au 39 GeV in 0–5% central collisions. Top panels are for the particle yields fit and lower panels are for the particle ratios fit. Uncertainties on experimental data represent statistical and systematic uncertainties added in quadrature. Here, the uncertainties are smaller than the symbol size.

Figure 26

The SCE model fits shown along with standard deviations for (a) Au+Au 7.7 and (b) Au+Au 39 GeV in 0–5% central collisions. Top panels are for the particle yields fit and lower panels are for particle ratios fit. Uncertainties on experimental data represent statistical and systematic uncertainties added in quadrature. Here, the uncertainties are smaller than the symbol size.

Figure 27

Chemical freeze-out parameters (a) $T_{\mathrm{ch}}$, (b) ${\mu }_B$, (c) ${\mu }_S$, (d) ${\gamma }_S$, and (e) $R$ plotted vs $\langle N_{\mathrm{part}}\rangle$ in GCE for particle yields fit. Uncertainties represent systematic errors.

Figure 28

Ratio of chemical freeze-out parameters (a) $T_{\mathrm{ch}}$, (b) ${\mu }_B$, (c) ${\mu }_S$, and (d) ${\gamma }_S$ between results from particle yield fits to particle ratio fits in GCE plotted vs $\langle N_{\mathrm{part}}\rangle$. Uncertainties represent systematic errors.

Figure 29

Chemical freeze-out parameters (a) $T_{\mathrm{ch}}$, (b) ${\mu }_B$, (c) ${\gamma }_S$, and (d) $R$ plotted vs $\langle N_{\mathrm{part}}\rangle$ in SCE for particle yields fit. Uncertainties represent systematic errors.

Figure 30

Ratio of chemical freeze-out parameters (a) $T_{\mathrm{ch}}$, (b) ${\mu }_B$, and (c) ${\gamma }_S$ between yield and ratio fits in SCE plotted vs $\langle N_{\mathrm{part}}\rangle$. Uncertainties represent systematic errors.

Figure 31

Ratio of chemical freeze-out parameters (a) $T_{\mathrm{ch}}$, (b) ${\mu }_B$, and (c) ${\gamma }_S$ between GCE and SCE results using particle ratios in fits plotted vs $\langle N_{\mathrm{part}}\rangle$. Uncertainties represent systematic errors.

Figure 32

Ratio of chemical freeze-out parameters (a) $T_{\mathrm{ch}}$, (b) ${\mu }_B$, (c) ${\gamma }_S$, and (d) $R$ between GCE and SCE results using particle yields in fits plotted vs $\langle N_{\mathrm{part}}\rangle$. Uncertainties represent systematic errors.

Figure 33

Extracted chemical freeze-out temperature vs baryon chemical potential for (a) GCE and (b) SCE cases using particle yields as input for fitting. Curves represent two model predictions [81, 82]. The gray bands represent the theoretical prediction ranges of the Cleymans et al. model [81]. Uncertainties represent systematic errors.

Figure 34

Choice on constraints: Extracted chemical freeze-out temperatures shown in panels (a), (c), and (e) and baryon chemical potentials shown in panels (b), (d), and (f) for GCE using particle yields as input for fitting, respectively, for Au+Au collisions at $\sqrt{s_{NN}}=7.7,19.6$, and 39 GeV. Results are compared for three initial conditions: ${\mu }_Q=0,{\mu }_Q$ constrained to $B/2Q$ value, and ${\mu }_Q$ constrained to $B/2Q$ along with ${\mu }_S$ constrained to 0. Uncertainties represent systematic errors.

Figure 35

Choice on including more particles: Extracted chemical freeze-out parameters (a) $T_{\mathrm{ch}}$, (b) ${\mu }_B$, and (c) ${\gamma }_S$ along with (d) ${\chi }^2/\mathrm{ndf}$ for GCE using particle yields as input for fitting. Results are compared for Au+Au collisions at $\sqrt{s_{NN}}=39\mathrm{GeV}$ for four different sets of particle yields used in fitting. Uncertainties represent systematic errors.

Figure 36

Blast wave model fits of ${\pi }^{\pm }$, $K^{\pm }$, $p$ and $\overline{p}{p}_T$ spectra in 0–5% central Au+Au collisions at $\sqrt{s_{NN}}=$ (a) 7.7, (b) 11.5, (c) 19.6, (d) 27, and (e) 39 GeV. Uncertainties on experimental data represent statistical and systematic uncertainties added in quadrature. Here, the uncertainties are smaller than the symbol size.

Figure 37

Variation of $T_{\mathrm{kin}}$ with $\langle \beta \rangle$ for different energies and centralities. The centrality increases from left to right for a given energy. The data points other than BES energies are taken from Refs. [43, 66]. Uncertainties represent systematic uncertainties.

Figure 38

(a) Energy dependence of kinetic and chemical freeze-out temperatures for central heavy-ion collisions. The curves represent various theoretical predictions [81, 82]. (b) Energy dependence of average transverse radial flow velocity for central heavy-ion collisions. The data points other than BES energies are taken from Refs. [43, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66] and references therein. The BES data points are for 0–5% central collisions, AGS energies are mostly for 0–5%, SPS energies are for mostly 0–7%, and top RHIC and LHC energies are for 0–5% central collisions. Uncertainties represent systematic uncertainties.