System-size dependence of particle-ratio fluctuations in Pb + Pb collisions at 158$A$ GeV

New measurements by the NA49 experiment of the centrality dependence of event-by-event fluctuations of the particle yield ratios $(K^{+}+K^{-})/({\pi }^{+}+{\pi }^{-})$, $(p+\overline{p})/({\pi }^{+}+{\pi }^{-})$, and $(K^{+}+K^{-})/(p+\overline{p})$ are presented for Pb+Pb collisions at 158$A$ GeV. The absolute values of the dynamical fluctuations of these ratios, quantified by the measure ${\sigma }_{\text{dyn}}$, increase by about a factor of two from central to semiperipheral collisions. Multiplicity scaling scenarios are tested and found to apply for both the centrality and the previously published energy dependence of the $(K^{+}+K^{-})/({\pi }^{+}+{\pi }^{-})$ and $(p+\overline{p})/({\pi }^{+}+{\pi }^{-})$ ratio fluctuations. A description of the centrality and energy dependence of $(K^{+}+K^{-})/(p+\overline{p})$ ratio fluctuations by a common scaling prescription is not possible since there is a sign change in the energy dependence.

Figure 1

Acceptance in center-of-mass rapidity $y$ and transverse momentum $p_T$ for the most central Pb+Pb collisions at 158$A$ GeV.

Figure 2

Distribution of the total energy $E_{\text{VETO}}$ of the projectile spectators deposited in the VCAL of NA49 in Pb+Pb collisions at 158$A$ GeV  beam energy. An event vertex cut (see text) was applied to remove background triggers. Vertical lines separate bins of 5$\%$ of the total inelastic cross section.

Figure 3

Dependence of the ${\sigma }_{\text{dyn}}$ measure of $K/\pi$ ratio fluctuations for the most central collisions on the width of the centrality bin in Pb+Pb collisions at 158$A$ GeV.

Figure 4

Distribution of specific energy loss $dE/dx$ in the MTPCs of negatively (a) and positively (b) charged particles for the momentum interval $p=10.3$–12.6 GeV$/c$, $p_T=0.6$–0.8 GeV$/c$. Curves show the fit results for the total distribution (solid) and the individual particle distributions (broken). The lower panels depict the fit residuals.

Figure 5

Event-by-event particle-ratio distributions for central (left) and semiperipheral (right) Pb+Pb collisions at 158$A$ GeV. The data points show real event and the histogram mixed event distributions. Loose track cuts (see Table 1) were applied.

Figure 6

Centrality dependence of the measure ${\sigma }_{dyn}$ for $K/\pi$ (a), $p/\pi$ (b), and $K/p$ (c) ratio fluctuations evaluated for events simulated by the UrQMD model [11] using either true identity or the event-by-event fit results based on the simulated particle $dE/dx$.

Figure 7

Centrality dependence of the measure ${\sigma }_{\text{dyn}}$ of $K/\pi$ (a), $p/\pi$ (b), and $K/p$ (c) ratio fluctuations. Dots show results from this analysis, squares show previously published measurements [9, 10]. The curves depict predictions of the UrQMD model [11] for the NA49 acceptance. The shaded bands show the systematic errors.

Figure 8

Dynamical fluctuations of the $K/\pi$ (a), $p/\pi$ (b), and $K/p$ (c) ratio as a function of $\sqrt{1/\langle K\rangle +1/\langle \pi \rangle }$, $\sqrt{1/\langle p\rangle +1/\langle \pi \rangle }$, and $\sqrt{1/\langle K\rangle +1/\langle p\rangle }$, respectively. $\langle \pi \rangle$, $\langle K\rangle$, and $\langle p\rangle$ are the average number of pions, kaons, and protons in the acceptance. The solid lines show fits to Poisson multiplicity scaling ${\sigma }_{\text{dyn}}\propto \sqrt{1/\langle A\rangle +1/\langle B\rangle }$ (see text). Shaded bands indicate systematic uncertainties.

Figure 9

Dynamical fluctuations of the $p/\pi$ ratio as a function of the product of average numbers of protons and pions in the detector acceptance.

Figure 10

Dynamical fluctuations of the $K/\pi$ ratio as a function of average number of kaons in the detector acceptance. Open square symbols show the results for the acceptance of the most peripheral set of events. The solid line shows the fit of the centrality dependence with the function of Eq. (10).