Energy dependence of particle ratio fluctuations in central $\mathrm{Pb}+\mathrm{Pb}$ collisions from $\sqrt{s_{{}_{\mathit{NN}}}}=6.3$ to 17.3 GeV

We present measurements of the energy dependence of event-by-event fluctuations in the $K/\pi$ and $(p+\overline{p})/\pi$ multiplicity ratios in heavy-ion collisions at the CERN SPS. The particle ratio fluctuations were obtained for central $\mathrm{Pb}+\mathrm{Pb}$ collisions at five collision energies, $\sqrt{s_{\mathit{NN}}}$, between 6.3 and 17.3 GeV. After accounting for the effects of finite-number statistics and detector resolution, we extract the strength of nonstatistical fluctuations at each energy. For the $K/\pi$ ratio, larger fluctuations than expected for independent particle production are found at all collision energies. The fluctuations in the $(p+\overline{p})/\pi$ ratio are smaller than expectations from independent particle production, indicating correlated pion and proton production from resonance decays. For both ratios, the deviation from purely statistical fluctuations shows an increase toward lower collision energies. The results are compared to transport model calculations, which fail to describe the energy dependence of the $K/\pi$ ratio fluctuations.

Figure 1

The experimental set-up of the NA49 experiment [14] and target arrangement (a) for $\mathrm{Pb}+\mathrm{Pb}$ collisions.

Figure 2

Phase-space distributions of charged particles used for the fluctuation analysis at all collision energies, from $\sqrt{s_{\mathit{NN}}}=6.3$ to 17.3 GeV. Data are shown using pion, kaon, and proton mass. The solid line indicates the 3 GeV/$c$ cutoff in total laboratory momentum. The dashed line indicates cutoffs at each energy that were used for the study of acceptance effects (see text).

Figure 3

(Top) Event-averaged $\mathit{dE}/\mathit{dx}$ distributions (symbols) compared to the extracted $\mathit{dE}/\mathit{dx}$ probability density functions (solid lines) for protons, kaons, pions and the sum of all particles. For all energies, data distributions and projected PDFs are shown for a narrow momentum range ($\Delta p_{\mathrm{tot}}\approx 1$ GeV/$c$) for 200MeV/$c<p_T<400$ MeV/$c$, close to $y=0$ assuming kaon mass. (Bottom) Fit residuals for the sum of $\mathit{dE}/\mathit{dx}$ probability density functions shown in the upper panels.

Figure 4

(Left) Distributions of the event-by-event $K/\pi$ ratio for data (points) and mixed events (histogram) for all five collision energies. (Right) Distributions of the event-by-event $(p+\overline{p})/\pi$ ratio for data (points) and mixed events (histogram) for all five collision energies. No acceptance corrections were applied to the particle ratios shown.

Figure 5

Difference between measured and input $K/\pi$ ratio versus average input $K/\pi$ ratio for mixed events, showing that the event-by-event fit is linear with respect to the input ratio.

Figure 6

Relative deviation of extracted $K/\pi$ nonstatistical fluctuations from the input value, ${\sigma }_{\mathrm{dyn}}^{\mathrm{in}}$, as a function of ${\sigma }_{\mathrm{dyn}}^{\mathrm{in}}$ for modified mixed events (see text). The shaded band indicates the assigned estimate of systematic uncertainty from the fitting procedure as a function of amplitude.

Figure 7

Expanded view of the low $K/\pi$ ratio region of the event-by-event $K/\pi$ ratio distribution of the $\sqrt{s_{\mathit{NN}}}=6.3$ GeV data set for data (points) and mixed events (histogram).

Figure 8

Ratio of the event-by-event $K/\pi$ ratio distribution for data and mixed events of the $\sqrt{s_{\mathit{NN}}}=6.3$ GeV data set.

Figure 9

Results of various studies on systematic uncertainties in the determination of ${\sigma }_{\mathrm{dyn}}(K/\pi )$: (a) extraction of ${\sigma }_{\mathrm{dyn}}$ using Eq. (2), (b) $\mathit{dE}/\mathit{dx}$ fit versus particle counting in UrQMD, (c) removal of tails of event-by-event distributions, (d) variation of $\mathit{dE}/\mathit{dx}$ width scaling, (e) variation of track quality cuts, and (f) variation of $p_{\mathrm{tot}}$ cutoff. Shaded bands indicate the contribution to the systematic error for $K/\pi$ fluctuations. Where applicable, dashed lines indicate corresponding contribution to systematic error for $(p+\overline{p})/\pi$ fluctuations. See text for details.

Figure 10

Energy dependence of the event-by-event nonstatistical fluctuations of the $K/\pi$ ratio (top panel) and the $(p+\overline{p})/\pi$ ratio (bottom panel). Filled symbols show data; open symbols show calculations with the UrQMD transport code, using NA49 acceptance tables. Systematic uncertainties are shown as brackets. Data of the STAR Collaboration are taken from Ref. [24].