Energy dependence of Λ and Ξ production in central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A,30A,40A,80A$, and 158$A$ GeV measured at the CERN Super Proton Synchrotron

Results on $\Lambda ,\overline{\Lambda },{\Xi }^{-}$, and ${\overline{\Xi }}^{+}$ production in central $\mathrm{Pb}+\mathrm{Pb}$ reactions at $20A,30A,40A,80A$, and 158$A$ GeV are presented. The energy dependence of transverse mass spectra, rapidity spectra, and multiplicities is discussed. Comparisons to string hadronic models (UrQMD and HSD) and statistical hadron gas models are shown. Although the latter provide a reasonable description of all particle yields, the first class of models fails to match the ${\Xi }^{-}$ and ${\overline{\Xi }}^{+}$ multiplicities.

Figure 1

The invariant mass distributions of all $\Lambda$ and $\overline{\Lambda }(\mathrm{a}\text{−}\mathrm{d})$ and ${\Xi }^{-}$ and ${\overline{\Xi }}^{+}(\mathrm{e}\text{−}\mathrm{h})$ candidates in central $\mathrm{Pb}+\mathrm{Pb}$ collisions at the lowest and highest analyzed beam energies. The full curves represent a fit to signal and background as described in the text; the dashed curves show the background contribution only. The gray vertical lines denote the PDG masses [27].

Figure 2

The total reconstruction efficiency of $\Lambda (\overline{\Lambda })$ (a and b) and ${\Xi }^{-}({\overline{\Xi }}^{+})$ (c and d) as a function of $p_t$ (a and c) and as a function of rapidity (b and d) for central $\mathrm{Pb}+\mathrm{Pb}$ collisions at 158$A$ GeV. The symbols denote the efficiency for the standard analysis procedure (STD). In addition, the $\Lambda ({\Xi }^{-})$ efficiencies for two other selection criteria are shown (dashed: CUT A, dotted: CUT B; see text).

Figure 3

The feed-down contribution to $\Lambda (\overline{\Lambda })$ around mid-rapidity as a function of (a) $p_t$ and (b) rapidity for central $\mathrm{Pb}+\mathrm{Pb}$ at 158$A$ GeV. The symbols denote the feed-down for the standard analysis procedure (STD). In addition, the feed-down to $\Lambda$ for two other selection criteria are shown (dashed: CUT A, dotted: CUT B; see text).

Figure 4

The differences between the fully corrected results of the standard procedure and of the two alternative analysis strategies (see Sec. 2e) for $\Lambda$ (a and b) and ${\Xi }^{-}$ (c and d) in central $\mathrm{Pb}+\mathrm{Pb}$ collisions at 158$A$ GeV. Shown are the $p_t$ dependence at mid-rapidity (a and c) and the rapidity dependence (b and d). The gray boxes illustrate the systematic error estimate.

Figure 5

The transverse mass spectra of (a) $\Lambda$ and (b) $\overline{\Lambda }$ at mid-rapidity ($\left|y\right|<0.4$) for five different beam energies. The data points are scaled for clarity. Only statistical errors are shown. The solid/dashed lines represent a fit with an exponential, where the solid part denotes the $m_t$ range in which the fit was performed. The dotted lines are the results of a fit with a blast wave model [33] (see text for details).

Figure 6

The transverse mass spectra of (a) ${\Xi }^{-}$ and (b) ${\overline{\Xi }}^{+}$ at mid-rapidity ($\left|y\right|<0.5$) for different beam energies. The data points are scaled for clarity. Only statistical errors are shown. The solid/dashed lines represent a fit with an exponential, where the solid part denotes the $m_t$ range in which the fit was performed. The dotted lines are the results of a fit with a blast wave model [33] (see text for details).

Figure 7

The $\langle m_t\rangle -m_0$ values for central $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{Au}+\mathrm{Au}$ reactions as a function of $\sqrt{s_{{}_{\mathit{NN}}}}$. The systematic errors are represented by the gray boxes. Filled symbols correspond to $\Lambda$ and ${\Xi }^{-}$; open symbols denote $\overline{\Lambda }$ and ${\overline{\Xi }}^{+}$. Also shown are data from the NA57 Collaboration [6, 34], from AGS [35, 36] and RHIC experiments [37, 38, 39], as well as $p+p$ data on $\Lambda$ [40]. The lines are calculations with the UrQMD1.3 model [41, 42].

Figure 8

The transverse mass spectra of $\Lambda ,{\Xi }^{-},\overline{\Lambda }$, and ${\overline{\Xi }}^{+}$ for central $\mathrm{Pb}+\mathrm{Pb}$ collisions in different rapidity bins at $20A,30A,40A,80A$, and 158$A$ GeV. Every rapidity bin has a width of 0.4. Bin $y0$ starts at $-2.0$. The data points are scaled for clarity. Only statistical errors are shown.

Figure 9

The rapidity spectra of $\Lambda ,{\Xi }^{-},\overline{\Lambda }$, and ${\overline{\Xi }}^{+}$ for five different beam energies. The open symbols show data points reflected around mid-rapidity. The systematic errors are represented by the gray boxes. Solid lines are fits to the data points, used to extract the total yields; dashed lines are the fits to ${\Xi }^{-}$ and ${\overline{\Xi }}^{+}$ from Ref. [23]. The gray area in the $\Lambda$ spectrum at 158$A$ GeV depicts the uncertainty from the different extrapolations (see text).

Figure 10

The rms widths of the rapidity distributions ${\mathit{RMS}}_y$, normalized by the projectile rapidity $y_{\mathrm{proj}}$, as a function of $y_{\mathrm{proj}}$. The systematic errors are represented by the gray boxes.

Figure 11

The rapidity densities $\mathrm{d}N/\mathrm{d}y$ at mid-rapidity ($\Lambda /\overline{\Lambda }:\left|y\right|<0.4,{\Xi }^{-}/{\overline{\Xi }}^{+}:\left|y\right|<0.5$) in central $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{Au}+\mathrm{Au}$ collisions as a function of $\sqrt{s_{{}_{\mathit{NN}}}}$. The systematic errors are represented by gray areas, mostly hidden by the symbols. Also shown are data from the NA57 Collaboration [6, 34], as well as from AGS [35, 36, 45] and RHIC experiments [37, 38, 39, 46].

Figure 12

The $\overline{p}/p$ [47], $\overline{\Lambda }/\Lambda ,{\overline{\Xi }}^{+}/{\Xi }^{-}$, and ${\overline{\Omega }}^{+}/{\Omega }^{-}$ [11] ratios around mid-rapidity ($\Lambda :\left|y\right|<0.4,\Xi$ and $\Omega :\left|y\right|<0.5$) in central $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{Au}+\mathrm{Au}$ collisions as a function of $\sqrt{s_{{}_{\mathit{NN}}}}$. Also shown as open symbols are data from the SPS experiments NA44 [48] and NA57 [6, 34] and from AGS [35, 36, 45, 49] and RHIC experiments [37, 38, 39, 46, 50, 51, 52]. The symbols are slightly displaced for clarity.

Figure 13

The total multiplicities of (a) $\Lambda$, (b) $\overline{\Lambda }$, (c) ${\Xi }^{-}$, and (d) ${\overline{\Xi }}^{+}$ in central $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{Au}+\mathrm{Au}$ collisions as a function of $\sqrt{s_{{}_{\mathit{NN}}}}$. The systematic errors are represented by the gray boxes. Also shown are AGS data [9, 35, 45], as well as calculations with string hadronic models (HSD, UrQMD1.3 [41, 42, 53]) and with a statistical hadron gas model (SHM(A) [29]).

Figure 14

The total multiplicities of (a) $\Lambda$, (b) $\overline{\Lambda }$, (c) ${\Xi }^{-}$, and (d) ${\overline{\Xi }}^{+}$ divided by the total pion multiplicities [$\langle \pi \rangle =1.5\hspace{1em}(\langle {\pi }^{+}\rangle +\langle {\pi }^{-}\rangle )$] in central $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{Au}+\mathrm{Au}$ collisions as a function of $\sqrt{s_{{}_{\mathit{NN}}}}$. The systematic errors are represented by the gray boxes. Also shown are AGS data [9, 35, 45, 54, 55], as well as calculations with string hadronic models (HSD, UrQMD1.3 [41, 42, 53]) and a statistical hadron gas model (SHM(A) [29]).

Figure 15

The rapidity densities $\mathrm{d}N/\mathrm{d}y$ at mid-rapidity of (a) $\Lambda$, (b) $\overline{\Lambda }$, (c) ${\Xi }^{-}$, and (d) ${\overline{\Xi }}^{+}$ divided by the pion rapidity densities [$\pi =1.5\hspace{1em}({\pi }^{+}+{\pi }^{-})$] in central $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{Au}+\mathrm{Au}$ collisions as a function of $\sqrt{s_{{}_{\mathit{NN}}}}$. The systematic errors are represented by the gray boxes. Also shown are NA57 [6, 34], AGS [35, 36, 45, 55], and RHIC [37, 38, 39, 46, 56, 57, 58] data, as well as calculations with string hadronic models (HSD, UrQMD1.3 [41, 42, 53]) and a statistical hadron gas model (SHM(B) [59]).

Figure 16

The total multiplicities of (a) $\Lambda$ and (b) $\overline{\Lambda }$ divided by the total pion multiplicities [$\langle \pi \rangle =1.5\hspace{1em}(\langle {\pi }^{+}\rangle +\langle {\pi }^{-}\rangle )]$ for central $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{Au}+\mathrm{Au}$ collisions as a function of $\sqrt{s_{{}_{\mathit{NN}}}}$. The systematic errors are represented by the gray boxes. Also shown are AGS data [9, 35, 45, 54, 55], measurements for $p+p$ collisions by other experiments (open squares) [60, 61], as well as a calculation with the UrQMD1.3 model (dashed line: $\mathrm{Pb}+\mathrm{Pb}$, dotted line $p+p$). The solid line represents a parametrization of the $p+p$ data (see text). The enhancements relative to the $p+p$ parametrization are shown in panels (c) and (d). The gray boxes denote the uncertainty of the $p+p$ reference parametrization. The dashed line represents the values from the UrQMD1.3 model.