Beam energy dependence of net-$\mathrm{\Lambda }$ fluctuations measured by the STAR experiment at the BNL Relativistic Heavy Ion Collider

The measurements of particle multiplicity distributions have generated considerable interest in understanding the fluctuations of conserved quantum numbers in the quantum chromodynamics (QCD) hadronization regime, in particular near a possible critical point and near the chemical freeze-out. Net-protons and net-kaons have been used as proxies for the net-baryon number and net-strangeness, respectively. We report the measurement of efficiency- and centrality-bin width-corrected cumulant ratios ($C_2/C_1$, $C_3/C_2$) of net-$\mathrm{\Lambda }$ distributions, in the context of both strangeness and baryon number conservation, as a function of collision energy, centrality, and rapidity. The results are for $\text{Au}+\text{Au}$ collisions at five beam energies ($\sqrt{s_{NN}}=19.6$, 27, 39, 62.4, and 200 GeV) recorded with the Solenoidal Tracker at RHIC (STAR). We compare our results to the Poisson and negative binomial (NBD) expectations, as well as to ultrarelativistic quantum molecular dynamics (UrQMD) and hadron resonance gas (HRG) model predictions. Both NBD and Poisson baselines agree with data within the statistical and systematic uncertainties. UrQMD describes the measured net-$\mathrm{\Lambda }{C}_1$ and $C_3$ at 200 GeV reasonably well but deviates from $C_2$, and the deviation increases as a function of collision energy. The ratios of the measured cumulants show no features of critical fluctuations. The chemical freeze-out temperatures extracted from a recent HRG calculation, which was successfully used to describe the net-proton, net-kaon, and net-charge data, indicate $\mathrm{\Lambda }$ freeze-out conditions similar to those of kaons. However, large deviations are found when comparing with temperatures obtained from net-proton fluctuations. The net-$\mathrm{\Lambda }$ cumulants show a weak but finite dependence on the rapidity coverage in the acceptance of the detector, which can be attributed to quantum number conservation.

Figure 1

Reconstructed invariant-mass distribution of (a) $\mathrm{\Lambda }$ and (b) $\overline{\mathrm{\Lambda }}$ for 62.4 GeV $\text{Au}+\text{Au}$ collisions. Topological cuts shown in Table 1 are applied.

Figure 2

Centrality dependence of first three single cumulants $C_1$, $C_2$, and $C_3$ of net-$\mathrm{\Lambda }$ multiplicity distributions at $\text{Au}+\text{Au}$ collision energies $\sqrt{s_{NN}}=19.6$, 27, 39, 62.4, and 200 GeV. NBD and Poisson baselines are presented by dashed lines. UrQMD predictions are shown in solid lines. Black vertical lines represent the statistical uncertainties and caps represent systematic uncertainties. Results are corrected for the reconstruction efficiency and the CBWC is applied.

Figure 3

Centrality dependence of net-$\mathrm{\Lambda }$ cumulant ratio, $C_2/C_1$ at $\text{Au}+\text{Au}$ collision energies $\sqrt{s_{NN}}=19.6$, 27, 39, 62.4, and 200 GeV. NBD and Poisson baselines are presented by dashed lines. UrQMD predictions are shown in solid lines. Black vertical lines represent the statistical uncertainties and caps represent systematic uncertainties. Results are corrected for the reconstruction efficiency, and the CBWC is applied.

Figure 4

Centrality dependence of net-$\mathrm{\Lambda }$ cumulant ratio, $C_3/C_2$ at $\text{Au}+\text{Au}$ collision energies $\sqrt{s_{NN}}=19.6$, 27, 39, 62.4, and 200 GeV. NBD and Poisson baselines are presented by dashed lines. UrQMD predictions are shown in solid lines. Black vertical lines represent the statistical uncertainties and caps represent systematic uncertainties. Results are corrected for the reconstruction efficiency, and the CBWC is applied.

Figure 5

Beam-energy dependence of net-$\mathrm{\Lambda }$ cumulant ratios $C_2/C_1$ and $C_3/C_2$ in most-central (0%–5%) and peripheral (50%–60%) $\text{Au}+\text{Au}$ collisions. NBD and Poisson baselines are presented by dashed lines. UrQMD predictions are shown in solid lines. Black vertical lines represent the statistical uncertainties and caps represent systematic uncertainties. Results are corrected for the reconstruction efficiency and the CBWC is applied. The red data points are shifted left for clarity.

Figure 6

Beam-energy dependence of net-$\mathrm{\Lambda }$ (in black), net-proton (in red) and net-kaon (in blue) cumulant ratios, (a) $C_2/C_1$ and (b) $C_3/C_2$ in most-central (0%–5%) $\text{Au}+\text{Au}$ collisions. The vertical lines represent the statistical uncertainties and caps represent systematic uncertainties. Results are corrected for the reconstruction efficiency and the CBWC is applied. The black data points are shifted left for clarity.

Figure 7

Black markers show the beam-energy dependence of the measured net-$\mathrm{\Lambda }$ cumulant ratios, (a) $C_2/C_1$ and (b) $C_3/C_2$ in most-central (0%–5%) $\text{Au}+\text{Au}$ collisions. Magenta bands show the net-$\mathrm{\Lambda }$ cumulant ratios from a HRG calculation [22] assuming $\mathrm{\Lambda }$s freeze-out under the same FO conditions as the kaons. Blue bands show the net-$\mathrm{\Lambda }$ cumulant ratios from the same HRG calculation assuming $\mathrm{\Lambda }$s freeze-out under the same FO conditions as the charged particles and protons. Results are corrected for the reconstruction efficiency, and the CBWC is applied. The vertical bars and the caps represent the statistical and systematic uncertainties, respectively. Uncertainties in the HRG calculations are shown by the width of the bands.

Figure 8

Rapidity dependence of net-$\mathrm{\Lambda }$ cumulant ratios (a) $C_2/C_1$ and (b) $C_3/C_2$ in $\sqrt{s_{NN}}=200$ GeV $\text{Au}+\text{Au}$ collisions at 0%–5% centrality. Dashed lines show the NBD expectations. Vertical error bars represent the statistical uncertainties and caps represent the systematic uncertainties. Results are corrected for the reconstruction efficiency and the CBWC is applied.

Figure 9

Rapidity dependence of the normalized $C_2(\mathrm{\Lambda }$-$\overline{\mathrm{\Lambda }}$) in most-central (0%–5%) collisions for 19.6 and 200 GeV collision energies. The solid lines show the expected effects from baryon number $B$ and strangeness $s$ conservation.