Energy dependence of kaon-to-proton ratio fluctuations in central $\text{Pb}+\text{Pb}$ collisions from $\sqrt{s_{\mathrm{NN}}}=6.3$ to 17.3 GeV

Kaons and protons carry large parts of two conserved quantities: strangeness and baryon number. It is argued that their correlation and thus also fluctuations are sensitive to conditions prevailing at the anticipated parton-hadron phase boundary. Fluctuations of the $({\mathrm{K}}^{+}+{\mathrm{K}}^{-})/(\mathrm{p}+\overline{\mathrm{p}})$ and ${\mathrm{K}}^{+}/\mathrm{p}$ ratios have been measured for the first time by NA49 in central $\mathrm{Pb}+\mathrm{Pb}$ collisions at five CERN Super Proton Synchrotron energies between $\sqrt{s_{{}_{\mathrm{NN}}}}=6.3$ and $\sqrt{s_{{}_{\mathrm{NN}}}}=17.3$ GeV. Both ratios exhibit a change of sign in ${\sigma }_{\mathrm{dyn}}$, a measure of nonstatistical fluctuations, around $\sqrt{s_{{}_{\mathrm{NN}}}}=8$ GeV. Below this energy, ${\sigma }_{\mathrm{dyn}}$ is positive, indicating higher fluctuation compared to a mixed event background sample, while for higher energies, ${\sigma }_{\mathrm{dyn}}$ is negative, indicating correlated emission of kaons and protons. The results are compared to hadronic transport model calculations which fail to reproduce the energy dependence.

Figure 1

The acceptance for kaons and protons, as used in the present analysis, as a function of transverse momentum and the center-of-mass rapidity, normalized by the corresponding beam rapidity, for all analyzed energies. Lines delimit the regions in which particles can be identified. Limits are attributable to geometric acceptance and available statistics, the latter predominantly at large momenta $p$ and transverse momenta $p_{\mathrm{T}}$.

Figure 2

(Top) Event-by-event distribution of the $({\mathrm{K}}^{+}+{\mathrm{K}}^{-})/(\mathrm{p}+\overline{\mathrm{p}})$ ratio at $\sqrt{s_{{}_{\mathrm{NN}}}}=17.3$ GeV for real data events compared to the mixed event reference. (Bottom) The ratio data/mixed, where the convex shape indicates negative dynamical fluctuations. Only in the ratio plot, for better readability, statistically insignificant bins are not shown.

Figure 3

(Top) Event-by-event distribution of the $({\mathrm{K}}^{+}+{\mathrm{K}}^{-})/(\mathrm{p}+\overline{\mathrm{p}})$ ratio at $\sqrt{s_{{}_{\mathrm{NN}}}}=6.3$ GeV for real data events compared to the mixed event reference. (Bottom) The ratio data/mixed, where the concave shape indicates positive dynamical fluctuations.

Figure 4

Energy dependence of the event-by-event dynamical fluctuations of the $({\mathrm{K}}^{+}+{\mathrm{K}}^{-})/(\mathrm{p}+\overline{\mathrm{p}})$ and the ${\mathrm{K}}^{+}/\mathrm{p}$ ratios. Symbols represent the NA49 measurements with statistical and systematic (brackets) uncertainties. Calculations within the UrQMD and Hadron-String Dynamics transport models, processed through an NA49 acceptance filter, are represented by lines. The statistical errors on the model results decrease from approximately 1.5% at 6.3 GeV to 0.5% at 17.3 GeV.