Strange hadron production in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, and 39 GeV

We present STAR measurements of strange hadron (${\mathrm{K}}_S^0, \mathrm{\Lambda }, \overline{\mathrm{\Lambda }}, {\mathrm{\Xi }}^{-}, {\overline{\mathrm{\Xi }}}^{+}, {\mathrm{\Omega }}^{-}, {\overline{\mathrm{\Omega }}}^{+}$, and $\varphi$) production at midrapidity ($\left|y\right|<0.5$) in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV from the Beam Energy Scan Program at the Relativistic Heavy Ion Collider (RHIC). Transverse-momentum spectra, averaged transverse mass, and the overall integrated yields of these strange hadrons are presented versus the centrality and collision energy. Antibaryon-to-baryon ratios ($\overline{\mathrm{\Lambda }}/\mathrm{\Lambda }, {\overline{\mathrm{\Xi }}}^{+}/{\mathrm{\Xi }}^{-}, {\overline{\mathrm{\Omega }}}^{+}/{\mathrm{\Omega }}^{-}$) are presented as well and used to test a thermal statistical model and to extract the temperature normalized strangeness and baryon chemical potentials at hadronic freeze-out (${\mu }_B/T_{\mathrm{ch}}$ and ${\mu }_S/T_{\mathrm{ch}}$) in central collisions. Strange baryon-to-pion ratios are compared to various model predictions in central collisions for all energies. The nuclear modification factors ($R_{\text{CP}}$) and antibaryon-to-meson ratios as a function of transverse momentum are presented for all collision energies. The ${\mathrm{K}}_S^0 R_{\text{CP}}$ shows no suppression for $p_T$ up to 3.5 $\mathrm{GeV}/c$ at energies of 7.7 and 11.5 GeV. The $\overline{\mathrm{\Lambda }}/{\mathrm{K}}_S^0$ ratio also shows baryon-to-meson enhancement at intermediate $p_T$ ($\approx 2.5 \mathrm{GeV}/c$) in central collisions at energies above 19.6 GeV. Both observations suggest that there is likely a change of the underlying strange quark dynamics at collision energies below 19.6 GeV.

Figure 1

${\mathrm{K}}_S^0, \mathrm{\Lambda }, {\mathrm{\Xi }}^{-}$, and ${\mathrm{\Omega }}^{-}$ invariant mass distributions in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7 GeV. The red solid lines represent the function fit results (double Gaussian plus polynomial for ${\mathrm{K}}_S^0, \mathrm{\Lambda }$, and ${\mathrm{\Xi }}^{-}$; single Gaussian plus polynomial for ${\mathrm{\Omega }}^{-}$), and the blue dashed lines are the fitted background contributions. The orange area shows the corresponding rotational background distribution.

Figure 2

$\varphi$ invariant mass distributions in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7 GeV. The upper panel shows the unlike-charge invariant mass distribution (full points) and the mixed-event background (orange area). The lower panel shows the invariant mass distribution after subtracting the background. The red solid line represents the function fit result (Breit-Wigner plus polynomial), and the blue dashed line is the fitted residual background contributions.

Figure 3

Geometrical acceptance and reconstruction efficiency of various strange hadrons at midrapidity ($\left|y\right|<0.5$) in central (left) and peripheral (right) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 39 GeV. The branching ratios of measured decay channels are not taken into account here.

Figure 4

MC and data comparison on ${\mathrm{K}}_S^0$ topological variable distributions in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 27 GeV. A same set of loose selection cuts have been applied to both MC and data. The distributions of combinatorial backgrounds in data were estimated with the rotation method and subtracted, and then the resulting data distributions were scaled down to match with the MC statistics.

Figure 5

The transverse-momentum spectra of ${\mathrm{K}}_S^0$ at midrapidity ($\left|y\right|<$ 0.5) from $\mathrm{Au}+\mathrm{Au}$ collisions at different centralities and energies ($\sqrt{s_{{}_{NN}}}$= 7.7–39 GeV). The data points are scaled by factors of 10 from central to peripheral collisions for clarity. The vertical gray bands represent the systematic errors, which are small hence the bands look like horizontal bars. The blast-wave model (or Levy function) fit results are shown in the fit range and the low-$p_T$ extrapolation range as solid (dashed) lines for the centrality bins within 0–30% (30–80%).

Figure 6

The transverse-momentum spectra of $\mathrm{\Lambda }$ at midrapidity ($\left|y\right|<$ 0.5) from $\mathrm{Au}+\mathrm{Au}$ collisions at different centralities and energies ($\sqrt{s_{{}_{NN}}}$= 7.7–39 GeV). The spectra are corrected for the feed-down of ${\mathrm{\Xi }}^{-}$ and ${\mathrm{\Xi }}^0$ decays. The data points are scaled by factors of 10 from central to peripheral collisions for clarity. The vertical gray bands represent the systematic errors, which are small hence the bands look like horizontal bars. The blast-wave model fit results are shown in the fit range and the low-$p_T$ extrapolation range as solid lines for all centrality bins.

Figure 7

The transverse-momentum spectra of $\overline{\mathrm{\Lambda }}$ at midrapidity ($\left|y\right|<$ 0.5) from $\mathrm{Au}+\mathrm{Au}$ collisions at different centralities and energies ($\sqrt{s_{{}_{NN}}}$= 7.7–39 GeV). The spectra are corrected for the feed-down of ${\overline{\mathrm{\Xi }}}^{+}, {\overline{\mathrm{\Xi }}}^0$, and ${\overline{\mathrm{\Omega }}}^{+}$ decays. The data points are scaled by factors of 10 from central to peripheral collisions for clarity. The vertical gray bands represent the systematic errors, which are small hence the bands look like horizontal bars. The blast-wave model fit results are shown in the fit range and the low-$p_T$ extrapolation range as solid lines for all centrality bins.

Figure 8

The transverse-momentum spectra of ${\mathrm{\Xi }}^{-}$ at midrapidity ($\left|y\right|<$ 0.5) from $\mathrm{Au}+\mathrm{Au}$ collisions at different centralities and energies ($\sqrt{s_{{}_{NN}}}$= 7.7–39 GeV). The data points are scaled by factors of 10 from central to peripheral collisions for clarity. The vertical gray bands represent the systematic errors, which are small hence the bands look like horizontal bars. The blast-wave model fit results are shown in the fit range and the low-$p_T$ extrapolation range as solid lines for all centrality bins.

Figure 9

The transverse-momentum spectra of ${\overline{\mathrm{\Xi }}}^{+}$ at midrapidity ($\left|y\right|<$ 0.5) from $\mathrm{Au}+\mathrm{Au}$ collisions at different centralities and energies ($\sqrt{s_{{}_{NN}}}$= 7.7–39 GeV). The data points are scaled by factors of 10 from central to peripheral collisions for clarity. The vertical gray bands represent the systematic errors, which are small hence the bands look like horizontal bars. The blast-wave model fit results are shown in the fit range and the low-$p_T$ extrapolation range as solid lines for all centrality bins.

Figure 10

The transverse-momentum spectra of ${\mathrm{\Omega }}^{-}$ at midrapidity ($\left|y\right|<$ 0.5) from $\mathrm{Au}+\mathrm{Au}$ collisions at different centralities and energies ($\sqrt{s_{{}_{NN}}}$= 7.7–39 GeV). The data points are scaled by factors of 10 from central to peripheral collisions for clarity. The vertical gray bands represent the systematic errors, which are small hence the bands look like horizontal bars. The exponential function fit results are shown in the fit range and the low-$p_T$ extrapolation range as solid lines for all centrality bins.

Figure 11

The transverse-momentum spectra of ${\overline{\mathrm{\Omega }}}^{+}$ at midrapidity ($\left|y\right|<$ 0.5) from $\mathrm{Au}+\mathrm{Au}$ collisions at different centralities and energies ($\sqrt{s_{{}_{NN}}}$= 7.7–39 GeV). The data points are scaled by factors of 10 from central to peripheral collisions for clarity. The vertical gray bands represent the systematic errors, which are small hence the bands look like horizontal bars. The exponential function fit results are shown in the fit range and the low-$p_T$ extrapolation range as solid lines for all centrality bins.

Figure 12

The transverse-momentum spectra of $\varphi$ at midrapidity ($\left|y\right|<$ 0.5) from $\mathrm{Au}+\mathrm{Au}$ collisions at different centralities and energies ($\sqrt{s_{{}_{NN}}}$= 7.7–39 GeV). The data points are scaled by factors of 10 from central to peripheral collisions for clarity. The vertical gray bands represent the systematic errors, which are small hence the bands look like horizontal bars. The Boltzmann function fit results are shown in the fit range and the low-$p_T$ extrapolation range as solid lines for all centrality bins.

Figure 13

The averaged transverse mass, $〈m_T〉-m_0$, at midrapidity ($\left|y\right|<$ 0.5) for ${\mathrm{K}}_S^0, \mathrm{\Lambda }$, and $\overline{\mathrm{\Lambda }}$ as a function of $\langle N_{\mathrm{part}}\rangle$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV. The box on each data point denotes the systematic error.

Figure 14

The averaged transverse mass, $〈m_T〉-m_0$, at midrapidity ($\left|y\right|<$ 0.5) for ${\mathrm{\Xi }}^{-}$ and ${\overline{\mathrm{\Xi }}}^{+}$ as a function of $\langle N_{\mathrm{part}}\rangle$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV. The box on each data point denotes the systematic error.

Figure 15

The averaged transverse mass, $〈m_T〉-m_0$, at midrapidity ($\left|y\right|<$ 0.5) for $\varphi , \mathrm{\Omega }$, and $\overline{\mathrm{\Omega }}$ as a function of $\langle N_{\mathrm{part}}\rangle$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV. The box on each data point denotes the systematic error.

Figure 16

The averaged transverse mass, $〈m_T〉-m_0$, at midrapidity ($\left|y\right|<$ 0.5) for ${\mathrm{K}}_S^0, \mathrm{\Lambda }, \overline{\mathrm{\Lambda }}, {\mathrm{\Xi }}^{-}$, and ${\overline{\mathrm{\Xi }}}^{+}$ as a function of energy from 0–5% central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV. For comparison, previous results from central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 6.3–17.3 GeV at SPS [24] and from central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 130 GeV at RHIC are shown as open markers [29, 31]. The NA49 and STAR 130 GeV $\overline{\mathrm{\Lambda }}$ and ${\overline{\mathrm{\Xi }}}^{+}$ data points are slightly shifted to the left for clarity. The orange shaded bands on the STAR BES data points represent the systematic errors.

Figure 17

The integrated yield, $dN/dy$, per average number of participating nucleon pairs ($〈N_{\mathrm{part}}〉/2$), of various strange hadrons (${\mathrm{K}}_S^0, \varphi , \mathrm{\Lambda }, \overline{\mathrm{\Lambda }}, {\mathrm{\Xi }}^{-}, {\overline{\mathrm{\Xi }}}^{+}, {\mathrm{\Omega }}^{-}, {\overline{\mathrm{\Omega }}}^{+}$) at midrapidity ($\left|y\right|<0.5$) as a function of number of participating nucleons, $\langle N_{\mathrm{part}}\rangle$, from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV. The box on each data point denotes the systematic error. For clarity, uncertainties in $\langle N_{\mathrm{part}}\rangle$ are not included.

Figure 18

The ${\mathrm{K}}_S^0$ integrated yield, $dN/dy$, at midrapidity ($\left|y\right|<0.5$) as a function of collision energy from 0–5% central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV. The orange shaded bands on the STAR BES data points represent the systematic errors. Also shown are the previous midrapidity results from 0–5% central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 130 and 200 GeV ($\left|y\right|<0.5$) from STAR [30, 37], from 0–5% central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 8.7 GeV ($\left|y\right|<0.5$) from NA57 [26, 27], and from 0–7% central $\mathrm{Pb}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 17.3 GeV from CERES [28]. CERES midrapidity data are the extrapolated values based on the measurements at backward rapidity.

Figure 19

Collision energy dependence of the $\mathrm{\Lambda }, \overline{\mathrm{\Lambda }}, {\mathrm{\Xi }}^{-}$, and ${\overline{\mathrm{\Xi }}}^{+}$ integrated yields, $dN/dy$, at midrapidity ($\left|y\right|<0.5$) in 0–5% central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV. $\mathrm{\Lambda }\left(\overline{\mathrm{\Lambda }}\right)$ yields are corrected for weak decay feed-down. The orange shaded bands on the STAR BES data points represent the systematic errors. Also shown are the results from central $\mathrm{Au}+\mathrm{Au}$ collisions at AGS [14, 15, 17, 18], PHENIX [38] and STAR [29, 31, 32, 37] and central $\mathrm{Pb}+\mathrm{Pb}$ collisions at NA57 [26, 27] and NA49 [24]. The rapidity ranges are $\left|y\right|<0.5$ for NA57, PHENIX, NA49 ${\mathrm{\Xi }}^{-}$(${\overline{\mathrm{\Xi }}}^{+}$), and STAR $\mathrm{\Lambda }$ at 130 and 200 GeV, $\left|y\right|<0.75$ for STAR $\mathrm{\Xi }$ at 130 and 200 GeV, $\left|y\right|<0.4$ for AGS and NA49 $\mathrm{\Lambda }$($\overline{\mathrm{\Lambda }}$). The $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$ results from AGS and PHENIX are inclusive, and those from NA49 and from STAR at higher energies are corrected for weak decay feed-down, while those from NA57 are not significantly affected by weak decay feed-down ($<5\%$ for $\mathrm{\Lambda }$ and $<10\%$ for $\overline{\mathrm{\Lambda }}$). The E896, PHENIX, and NA57 8.7 GeV ${\overline{\mathrm{\Xi }}}^{+}$ data points are slightly shifted to the right for clarity.

Figure 20

The antibaryon-to-baryon ratios, $\overline{\mathrm{\Lambda }}/\mathrm{\Lambda }, {\overline{\mathrm{\Xi }}}^{+}/{\mathrm{\Xi }}^{-}$, and ${\overline{\mathrm{\Omega }}}^{+}/{\mathrm{\Omega }}^{-}$, as functions of $\langle N_{\mathrm{part}}\rangle$ from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV. The box on each data point denotes the systematic error.

Figure 21

$\overline{\mathrm{\Lambda }}/\mathrm{\Lambda }$ ratio as a function of $p_T$ from different centralities of $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7 GeV. The errors are statistical only.

Figure 22

Normalized $\overline{\mathrm{\Lambda }}/\mathrm{\Lambda }$ ratio as a function of $p_T$ from 0–5% central $\mathrm{Au}+\mathrm{Au}$ collisions at different energies. The STAR results at $\sqrt{s_{{}_{NN}}}$ = 200 GeV [32] are shown as open circles for comparison. The errors are statistical only. All the ratios are normalized according to the average values inside the $p_T$ range of $[1.4,2.0] \mathrm{GeV}/c$.

Figure 23

The collision energy dependence of $\overline{\mathrm{\Lambda }}/\mathrm{\Lambda }, {\overline{\mathrm{\Xi }}}^{+}/{\mathrm{\Xi }}^{-}$, and ${\overline{\mathrm{\Omega }}}^{+}/{\mathrm{\Omega }}^{-}$ ratios at midrapidity ($\left|y\right|<0.5$) in central (0–5% for $\overline{\mathrm{\Lambda }}/\mathrm{\Lambda }$ and ${\overline{\mathrm{\Xi }}}^{+}/{\mathrm{\Xi }}^{-}$; 0–10% for ${\overline{\mathrm{\Omega }}}^{+}/{\mathrm{\Omega }}^{-}$ for $\sqrt{s_{{}_{NN}}}\ge 11.5$ GeV; and 0–60% for ${\overline{\mathrm{\Omega }}}^{+}/{\mathrm{\Omega }}^{-}$ for $\sqrt{s_{{}_{NN}}}=7.7$ GeV) $\mathrm{Au}+\mathrm{Au}$ collisions from the STAR Beam Energy Scan (solid symbols). The orange shaded bands represent the systematic errors. The ratios in central $\mathrm{Pb}+\mathrm{Pb}$ collisions from NA49 [22, 24] and in central $\mathrm{Au}+\mathrm{Au}$ collisions at higher energies ($\ge 130$ GeV) from STAR [29, 31, 32, 37] are also shown as open symbols for comparison. The previous STAR ${\overline{\mathrm{\Xi }}}^{+}/{\mathrm{\Xi }}^{-}$ and ${\overline{\mathrm{\Omega }}}^{+}/{\mathrm{\Omega }}^{-}$ data points are slightly shifted to the left and to the right, respectively, for clarity.

Figure 24

Testing result of the thermal model in ${\mu }_B/T_{\mathrm{ch}}$ and ${\mu }_S/T_{\mathrm{ch}}$ parameter space with three strange antibaryon-to-baryon ratios in central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV. Errors are propagated from the corresponding $\overline{\mathrm{B}}/\mathrm{B}$ ratios, whose errors are the quadratic sum of statistical and systematic errors.

Figure 25

Thermal model fitting to $ln(\overline{\mathrm{B}}/\mathrm{B})$ vs $\mathrm{\Delta }S$ with a linear function to determine ${\mu }_B/T_{\mathrm{ch}}$ and ${\mu }_S/T_{\mathrm{ch}}$ for central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV. The ${\overline{\mathrm{\Omega }}}^{+}/{\mathrm{\Omega }}^{-}$ data points at 11.5 and 27 GeV are slightly shifted to the left for clarity.

Figure 26

The ${\mu }_B/T_{\mathrm{ch}}$ and ${\mu }_S/T_{\mathrm{ch}}$ parameters (red symbols) in central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV obtained from the fits shown in Fig. 25. The blue symbols are the corresponding results from the thermal model fit to the yields of $\pi$, K, $p, \mathrm{\Lambda }, \mathrm{\Xi }, {\mathrm{K}}_S^0$, and $\mathrm{\Omega }$ at $\sqrt{s_{{}_{NN}}}$ = 39 GeV [7].

Figure 27

Energy dependence of $\mathrm{\Lambda }, \overline{\mathrm{\Lambda }}, {\mathrm{\Xi }}^{-}$, and ${\overline{\mathrm{\Xi }}}^{+}$ to pions ($1.5({\pi }^{+}+{\pi }^{-})$) ratios at midrapidity in central $\mathrm{Au}+\mathrm{Au}$ collisions from STAR Beam Energy Scan (solid symbols). The STAR BES midrapidity pion yields are taken from [7]. Errors are the quadratic sum of statistical and systematic errors. Also shown are existing AGS [14, 15, 17, 18, 78], NA49 [20, 23, 24, 79], PHENIX [38, 80], and STAR [29, 31, 32, 37, 81, 82] data as open symbols, as well as calculations from hadronic transport models (UrQMD 1.3 and HSD) [83, 84, 85, 86] and a statistical hadron gas model (SHM) [44] as dashed or solid lines. The E896, PHENIX, and NA57 8.7 GeV ${\overline{\mathrm{\Xi }}}^{+}/\pi$ data points are slightly shifted to the right for clarity.

Figure 28

${\mathrm{K}}_S^0, \mathrm{\Lambda }+\overline{\mathrm{\Lambda }}$, and ${\mathrm{\Xi }}^{-}+{\overline{\mathrm{\Xi }}}^{+} R_{\text{CP}}$(0–5%)/(40–60%), $\varphi$ and ${\mathrm{\Omega }}^{-}+{\overline{\mathrm{\Omega }}}^{+} R_{\text{CP}}$(0–10%)/(40–60%), at midrapidity ($\left|y\right|<0.5$) in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV. The vertical bars denote the statistical errors. The box on each data point of ${\mathrm{K}}_S^0, \mathrm{\Lambda }$, and $\mathrm{\Xi }$ denotes the systematic error. There are only statistical errors for $\mathrm{\Omega }$ and $\varphi$. For $\sqrt{s_{{}_{NN}}} \le$ 19.6 GeV, the $\mathrm{\Lambda }+\overline{\mathrm{\Lambda }} R_{\text{CP}}$ excludes the minor contribution from $\overline{\mathrm{\Lambda }}$. The gray and blue bands on the right side of each panel represent the normalization errors from $N_{\text{coll}}$ for $R_{\text{CP}}$(0–5%)/(40–60%) and $R_{\text{CP}}$(0–10%)/(40–60%), respectively.

Figure 29

$\overline{\mathrm{\Lambda }}/{\mathrm{K}}_S^0$ ratio as a function of $p_T$ at midrapidity ($\left|y\right|<0.5$) in different centralities from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}$ = 7.7–39 GeV. Errors are statistical only.