Bulk properties of the system formed in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV at the BNL STAR detector

We report systematic measurements of bulk properties of the system created in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV recorded by the STAR detector at the Relativistic Heavy Ion Collider (RHIC). The transverse momentum spectra of ${\pi }^{\pm }, K^{\pm }$, and $p\left(\overline{p}\right)$ are studied at midrapidity ($\left|y\right|<0.1$) for nine centrality intervals. The centrality, transverse momentum ($p_T$), and pseudorapidity ($\eta$) dependence of inclusive charged particle elliptic flow ($v_2$), and rapidity-odd charged particles directed flow ($v_1$) results near midrapidity are also presented. These measurements are compared with the published results from $\mathrm{Au}+\mathrm{Au}$ collisions at other energies, and from $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76$ TeV. The results at $\sqrt{s_{NN}}=14.5$ GeV show similar behavior as established at other energies and fit well in the energy dependence trend. These results are important as the 14.5-GeV energy fills the gap in ${\mu }_B$, which is of the order of 100 MeV, between $\sqrt{s_{NN}}=11.5$ and 19.6 GeV. Comparisons of the data with UrQMD and AMPT models show poor agreement in general.

Figure 1

Uncorrected charged-particle multiplicity distribution (open circles) measured in the TPC within $\left|\eta \right|<0.5$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. The blue dashed line represents the charged particle multiplicity distribution from a MC Glauber model [50]. The vertical dashed lines represent the centrality selection criteria used.

Figure 2

(a) The $〈dE/dx〉$ distribution of charged particles from the TPC as a function of momentum/charge for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. The curves represent the expected mean values of $〈dE/dx〉$ for the corresponding particle species. (b) $1/\beta$ as a function of momentum/charge from TOF in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. The curves represent the expected values of $1/\beta$ for the indicated particle species.

Figure 3

(a) The $z_{\pi }$ distribution at midrapidity ($\left|y\right|<0.1$) for the $p_{\mathrm{T}}$ range $0.30–0.35\mathrm{GeV}/c$ in 0–5% central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. The curves are Gaussian fits representing contributions from pions (dashed red), electrons (dotted green), kaons (dash-dotted blue), and protons (dash-dot-dotted magenta). The uncertainties are statistical only. (b) The $m^2$ distributions used to obtain the raw yields from TOF for ${\pi }^{+}$ within $\left|y\right|<0.1$ in the $p_{\mathrm{T}}$ range $0.5–0.6\mathrm{GeV}/c$. These distributions are for $0–5\%$ centrality in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. The curves are fits to the $m^2$ distribution, representing contributions from pions (red), kaons (blue), and protons (magenta).

Figure 4

The $p_{\mathrm{T}}$ difference of reconstructed momentum $p_{\mathrm{T}}^{\mathrm{REC}}$ and MC momentum $p_{\mathrm{T}}^{\mathrm{MC}}$ as a function of $p_{\mathrm{T}}^{\mathrm{REC}}$ for (a) pions, (b) kaons, and (c) protons in 0–5% central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. The red curves represent the functional fit of the form $f\left(p_{\mathrm{T}}\right)=A+B{\left(1+\frac{C}{p_{\mathrm{T}}^2}\right)}^D$.

Figure 5

The combined tracking efficiency and acceptance as a function of $p_{\mathrm{T}}\mathrm{calculated}$ from the Monte Carlo embedding technique for reconstructed (a) pions, (b) kaons, and (c) protons at midrapidity ($\left|y\right|<0.1$) for 0–5% $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. The curves represent the functional fit of the form $p_{0}exp[-{(p_1/p_T)}^{p_2}]$.

Figure 6

TOF matching efficiency as a function of $p_{\mathrm{T}}\mathrm{for}$ (a) pions, (b) kaons, and (c) protons at midrapidity ($\left|y\right|<0.1$) in 0–5% $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV.

Figure 7

The $p_{\mathrm{T}}\mathrm{spectra}$ of ${\pi }^{\pm }, K^{\pm }, p$ ($\overline{p}$) measured at midrapidity ($\left|y\right|<0.1$) in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. Spectra are plotted for nine centrality classes, with some spectra multiplied by a scale factor to improve clarity, as indicated in the legend. The data points shown for $p_{\mathrm{T}}=0.4–2.0\mathrm{GeV}/c$ for pions and kaons, and for $0.5–2.0\mathrm{GeV}/c$ for protons, are obtained using both TPC and TOF. Data points measured using only the TPC are shown for $p_{\mathrm{T}}\mathrm{in}$ the range 0.2–0.8, 0.3–0.8, and $0.5–1.0\mathrm{GeV}/c$ for pions, kaons, and protons, respectively. The $p_{\mathrm{T}}\mathrm{range} 0.4–0.8\mathrm{GeV}/c, 0.4–0.8\mathrm{GeV}/c$, and $0.5–1.0\mathrm{GeV}/c$ for pions, kaons, and protons, respectively, is the overlap region containing data measurements in both categories, namely, TPC only, and $\mathrm{TPC}+\mathrm{TOF}$. The $p_{\mathrm{T}}$-spectra are fitted with a Bose-Einstein function for pions, an $m_T$ exponential for kaons, and a double exponential for (anti)protons. Statistical and systematic uncertainties are added in quadrature.

Figure 8

$〈p_{\mathrm{T}}〉$ of ${\pi }^{+}, K^{+}$, and $p\left(\overline{p}\right)$ as a function of $〈N_{\text{part}}〉$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. These averages are compared with the corresponding results from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, and 200 GeV measured by STAR in earlier runs [32, 60, 65]. Statistical and systematic uncertainties have been added in quadrature.

Figure 9

$dN/dy$ of ${\pi }^{+}, {\pi }^{-}, K^{+}, K^{-}, p$, and $\overline{p}$ scaled by ($0.5\times 〈N_{\text{part}}〉$) as a function of $〈N_{\text{part}}〉$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. These yields are compared with the corresponding results from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, and 200 GeV measured by STAR in earlier runs [32, 60, 65]. Statistical and systematic uncertainties have been added in quadrature.

Figure 10

${\pi }^{-}/{\pi }^{+}, K^{-}/K^{+}$, and $\overline{p}/p$ ratios as a function of $〈N_{\text{part}}〉$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. These ratios are compared with the corresponding results from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, and 200 GeV measured by STAR in earlier runs [32, 60, 65]. Statistical and systematic uncertainties have been added in quadrature.

Figure 11

$K^{+}/{\pi }^{+}, K^{-}/{\pi }^{-}, p/{\pi }^{+}$, and $\overline{p}/{\pi }^{-}$ ratios as a function of $〈N_{\text{part}}〉$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. These ratios are compared with the corresponding results from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, and 200 GeV measured by STAR in earlier runs [32, 60, 65]. Statistical and systematic uncertainties have been added in quadrature.

Figure 12

Simultaneous blast-wave model fits to the $p_{\mathrm{T}}\mathrm{spectra}$ of ${\pi }^{\pm }, K^{\pm }, p(\overline{p}$) from 0–5% central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. Uncertainties on experimental data represent statistical and systematic uncertainties added in quadrature, mostly smaller than the symbol size.

Figure 13

(a) $T_k$ as a function of $〈N_{\mathrm{part}}〉$. (b) $\beta$ as a function of $〈N_{\mathrm{part}}〉$. (c) Variation of $T_k$ with $\beta$. In all three panels, present results for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV are shown in comparison with the same quantities for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, and 200 GeV measured by STAR in earlier runs [32]. Systematic uncertainties are shown. Statistical uncertainties are much smaller than systematic ones.

Figure 14

The event plane resolution calculated for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV (solid star) as a function of centrality. The current results are compared with those for 7.7, 11.5, 14.5, 19.6, 27, and 39 GeV. Panel (a) shows the second-order event plane resolution reconstructed by using the TPC tracks ($\left|\eta \right|<1$). Panel (b) shows the second-order event plane resolution for 39 GeV from the FTPC ($2.5<\left|\eta \right|<4.0$) and the first-order event plane resolution from the inner tiles of the BBC ($3.8<\left|\eta \right|<5.2$).

Figure 15

Inclusive charged particle $v_2$ at midpseudorapidity ($\left|\eta \right|<1.0$) as a function of $p_{\mathrm{T}}\mathrm{for}$ (a) 10–20%, (b) 20–30%, and (c) 30–40% centralities in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. Results are shown for the $\eta$-subevent plane method (circles), BBC event plane (open triangles), two-particle (solid squares), and four-particle (open squares) cumulants. The bottom panels (d)–(f) show the ratio of $v_2$ measured using the various methods with respect to the two-particle cumulant result, $v_2\left\{2\right\}$. Errors are statistical. Systematic uncertainties are small ($\sim 2\%$).

Figure 16

Inclusive charged particle elliptic flow $v_2$ at midpseudorapidity ($\left|\eta \right|<1.0$) as a function of transverse momentum $p_{\mathrm{T}}\mathrm{and}$ the $p_{\text{T}}$-integrated $v_2\left(\eta \right)$ for six centrality classes, obtained using the $\eta$-subevent plane method in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. Statistical uncertainties are shown by error bars, while systematic uncertainties are smaller and are plotted as caps.

Figure 17

The ratio $v_2/{\epsilon }_{\mathrm{part}}\left\{2\right\}$ for inclusive charged particle elliptic flow $v_2$ at midpseudorapidity as a function of $p_{\mathrm{T}}\mathrm{for}$ 10–20%, 30–40%, and 50–60% collision centralities in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV.

The $v_2$ data are from the $\eta$-subevent plane method, and the spatial eccentricity ${\epsilon }_{\mathrm{part}}\left\{2\right\}$ is based on a Glauber calculation. The error bars and shaded boxes present the statistical and systematic uncertainties, respectively.

Figure 18

The upper panels (a)–(c) show inclusive charged particle elliptic flow $v_2\left\{4\right\}$ versus $p_{\mathrm{T}}\mathrm{for}$ various collision energies ($\sqrt{s_{NN}}=7.7$ GeV to 2.76 TeV) at three centralities: 10–20%, 20–30%, and 30–40%. The present results at 14.5 GeV (and also for other energies except 2.76 TeV) are for midpseudorapidity ($\left|\eta \right|<1.0$). The measurement of $v_2$ at 2.76 TeV was done at midpseudorapidity ($\left|\eta \right|<0.8$). Furthermore, all results for $\sqrt{s_{NN}}=7.7$–200 GeV are for $\mathrm{Au}+\mathrm{Au}$ collisions and those for 2.76 TeV are for $\mathrm{Pb}+\mathrm{Pb}$ collisions. The dashed red curves show fifth-order polynomial function fits to the results from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV. The lower panels (d)–(f) show the ratio of $v_2\left\{4\right\}$ versus $p_{\mathrm{T}}\mathrm{for}$ all $\sqrt{s_{NN}}$ with respect to the fit curve. Error bars are shown only for statistical uncertainties. Systematic uncertainties are small ($\sim 2\%$).

Figure 19

Panel (a) shows inclusive charged particle elliptic flow $v_2(\eta$-sub) versus $\eta$ at mid-pseudorapidity for various collision energies ($\sqrt{s_{NN}}=7.7$–200 GeV). The dashed red curve shows an empirical fit to the result from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7$ GeV. Panel (b) shows the ratio of $v_2\left\{4\right\}$ versus $\eta$ for all $\sqrt{s_{NN}}$ with respect to the fit curve. The results are shown for 10–40% collision centrality. Error bars are shown only for statistical uncertainties.

Figure 20

Charged particle $v_1$ as a function of $p_{\mathrm{T}}\mathrm{in} \mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7$–39 GeV for 0–10%, 10–40%, and 40–80% centrality intervals. Error bars are shown only for statistical uncertainties. Systematic uncertainties are small ($\sim 2\%$).

Figure 21

Charged particle $v_1$ as a function of $\eta$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7$–39 GeV for 0–10%, 10–40%, and 40–80% centrality intervals. Error bars are shown only for statistical uncertainties. Systematic uncertainties are small ($\sim 2\%$).

Figure 22

(a) Charged particle $v_1$ as a function of $\eta$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7$–39 GeV for 30–60% centrality interval. Results are compared to 62.4- and 200-GeV $\mathrm{Au}+\mathrm{Au}$ collisions at RHIC and to 2.76-TeV $\mathrm{Pb}+\mathrm{Pb}$ collisions at the LHC. (b) Charged particle $v_1$ slope, $d{v}_1/dy$, at midpseudorapidity as a function of $\sqrt{s_{NN}}$ for different centralities. Error bars are shown only for statistical uncertainties. Systematic uncertainties are small ($\sim 2\%$).

Figure 23

$〈p_{\mathrm{T}}〉$ of ${\pi }^{+}, K^{+}$, and $p$ as a function of $〈N_{\text{part}}〉$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV in STAR. These measurements are compared with UrQMD, AMPT 1.5 mb, and AMPT 10 mb.

Figure 24

$(dN/dy)/(0.5\times 〈N_{\text{part}}〉)$ for ${\pi }^{+}, K^{+}$ and $p$ as a function of $〈N_{\text{part}}〉$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV in STAR. These measurements are compared with UrQMD, AMPT 1.5 mb, and AMPT 10 mb.

Figure 25

${\pi }^{-}/{\pi }^{+}, K^{-}/K^{+}$, and $\overline{p}/p$ ratios as a function of $〈N_{\text{part}}〉$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV in STAR. These experimental ratios are compared with UrQMD, AMPT 1.5 mb, and AMPT 10 mb.

Figure 26

$K^{+}/{\pi }^{+}, K^{-}/{\pi }^{-}, p/{\pi }^{+}$, and $\overline{p}/{\pi }^{-}$ ratios as a function of $〈N_{\text{part}}〉$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV in STAR. These experimental ratios are compared with UrQMD, AMPT 1.5 mb, and AMPT 10 mb.

Figure 27

(a)–(c) $p_T$ dependence of $v_2\left\{\eta -\mathrm{sub}\right\}$ for 14.5-GeV $\mathrm{Au}+\mathrm{Au}$ collisions at 10–20%, 20–30%, and 30–40% centralities, as measured by STAR. Calculations from UrQMD, AMPT 1.5 mb, and AMPT 10 mb are also plotted. (d)–(f) Ratios of the experimental data to each model calculation.

Figure 28

(a)–(c) Pseudorapidity ($\eta$) dependence of $v_2\left\{\eta -\mathrm{sub}\right\}$ for 14.5-GeV $\mathrm{Au}+\mathrm{Au}$ collisions at 10–20%, 20–30%, and 30–40% centralities, as measured by STAR. Calculations from UrQMD, AMPT 1.5 mb, and AMPT 10 mb are also plotted. (d)–(f) Ratios of the experimental data to each model calculation.

Figure 29

Charged particle $v_1\left(p_T\right)$ (a) and $v_1\left(\eta \right)$ (b) for 10–40% centrality $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=14.5$ GeV. The measured directed flow is compared to UrQMD, AMPT, AMPT 1.5-mb, and AMPT 10-mb model calculations.