Hadron yields and fluctuations at energies available at the CERN Super Proton Synchrotron: System-size dependence from Pb + Pb to $p+p$ collisions

The kaon-to-pion ratio $K^{+}/{\pi }^{+}$ and the scaled variance ${\omega }^{-}$ for fluctuations of negatively charged particles are studied within the statistical hadron resonance gas (HRG) model and the ultrarelativistic quantum molecular dynamics (urqmd) transport model. The calculations are done for $p+p,\text{Be}+\text{Be},\text{Ar}+\text{Sc}$, and $\text{Pb}+\text{Pb}$ collisions at the CERN Super Proton Synchrotron energy range to reveal the system-size dependence of hadron production. For the HRG calculations the canonical ensemble is imposed for all conserved charges. In the urqmd simulations the centrality selection in nucleus-nucleus collisions is done by calculating the forward energy $E_{\mathrm{F}}$ deposited in the Projectile Spectator Detector, and the acceptance maps of the NA61/SHINE detectors are used. The HRG and urqmd results are compared with the data of the NA61/SHINE Collaboration. To understand the difference in the event-by-event fluctuations in $p+p$ and heavy-ion collisions, the centrality-selection procedure in the sample of all inelastic $p+p$ events is proposed and analyzed within the urqmd simulations.

Figure 1

(a) The baryon density ${\rho }_B$ and (b) the radius $R$ of the statistical system at the chemical freeze-out as functions of collision energy.

Figure 2

(a) The results of the CE HRG calculations for the $K^{+}/{\pi }^{+}$ ratio and (b) the scaled variance ${\omega }^{-}$ of negatively charged particles as functions of collision energy.

Figure 3

The CE HRG results for (a), (b) $K^{+}/{\pi }^{+}$ and (c), (d) ${\omega }^{-}$ as functions of $W\equiv A_1+A_2$ which equals the total number of nucleons in the colliding nuclei. See text for details. The data are shown by red squares for $K^{+}/{\pi }^{+}$ [7, 38, 39] and for ${\omega }^{-}$ [20, 40].

Figure 4

Number of events as a function of the forward energy $E_{\mathrm{F}}$ calculated in the minimum bias urqmd simulations. The colored regions correspond to different centrality classes that are indicated with respective numbers.

Figure 5

The urqmd results for the scaled variance ${\omega }^{-}$ (full symbols) and strongly intensive quantity $\mathrm{\Omega }[N_{-},E_{\mathrm{P}}]$ (open symbols) as functions of the centrality for $\text{Be}+\text{Be}$ (top) and $\text{Ar}+\text{Sc}$ (bottom) collisions at $p_{\mathrm{lab}}=30A\mathrm{GeV}/c$ (left) and $p_{\mathrm{lab}}=150A\mathrm{GeV}/c$ (right).

Figure 6

The number of events as functions of the forward energy $E_{\mathrm{F}}$ calculated within urqmd for inelastic $p+p$ collisions at (a) $p_{\mathrm{lab}}=30A\mathrm{GeV}/c$ and (b) $p_{\mathrm{lab}}=150A\mathrm{GeV}/c$. The scaled variance ${\omega }^{-}$ (full symbols) and strongly intensive measure $\mathrm{\Omega }[N_{-},E_{\mathrm{P}}]$ (open symbols) as functions of the centrality for inelastic $p+p$ collisions at (c) $p_{\mathrm{lab}}=30A\mathrm{GeV}/c$ and (d) $p_{\mathrm{lab}}=150A\mathrm{GeV}/c$.

Figure 7

The data are the same as in Fig. 3. The urqmd results are shown by open circles. See text for details. Crosses denote the urqmd results for the most central $p+p$ inelastic collisions.