Statistical hadron-gas treatment of systems created in proton-proton interactions at energies available at the CERN Super Proton Synchrotron

We analyze the newest data from the NA61/SHINE Collaboration which, in addition to previous results on pions and kaons, include mean multiplicities of $p$, $\mathrm{\Lambda }$, and $\varphi$ mesons produced in inelastic proton-proton ($p+p$) interactions at $\sqrt{s_{NN}}=6.3\text{–}17.3\mathrm{GeV}$. The canonical ensemble formulation of the ideal hadron resonance gas (HRG) model is used with exact conservation of net baryon number $B=2$, electric charge $Q=2$, and strangeness $S=0$. The chemical freeze-out parameters in $p+p$ interactions are obtained and compared to those in central nucleus-nucleus collisions. Several features of $p+p$ interactions at the CERN Super Proton Synchrotron within a statistical model are studied: (1) the inclusion of the $\varphi$-meson yields in thermal fits worsens significantly the fit quality; (2) the data show large event-by-event multiplicity fluctuations in inelastic $p+p$ interactions which cannot be explained by a single fireball described by a statistical model; and (3) the fits within the canonical ensemble formulation of HRG do not give any improvement over the fits within the grand canonical ensemble formulation, i.e., there are no indications of the existence of a single statistical system in $p+p$ inelastic interactions in the considered energy range.

Figure 1

The ratios of mean hadron multiplicities measured by the NA61/SHINE Collaboration in $p+p$ interactions at $\sqrt{s_{NN}}=7.7\text{–}17.3\mathrm{GeV}$ (Data) to the mean multiplicities calculated from the best fit to the data in the HRG model (Model).

Figure 2

Temperature $T$ (a), strangeness saturation factor ${\gamma }_S$ (b), radius of the system $R$ (c), and ${\chi }^2/N_{\mathrm{dof}}$ (d) in inelastic $p+p$ reactions as functions of the collision energy. Solid lines in (a) and (b) show the corresponding results in central Pb+Pb collisions from Ref. [17].

Figure 3

The data-to-model ratios for the CE HRG model fit to the NA49 data on the $4\pi$ hadron multiplicities in inelastic $p+p$ interactions at $\sqrt{s_{NN}}=17.3\mathrm{GeV}$. For ${\mathrm{\Omega }}^{-}$ the data-to-model ratios are $5.9\pm 2.9$ in the “no $\varphi$” fit and $6.7\pm 3.3$ “with $\varphi$.” The corresponding values for ${\overline{\mathrm{\Omega }}}^{+}$ are, respectively, $6.0\pm 3.4$ and $7.2\pm 4.0$.

Figure 4

The average energy of the statistical system calculated with the parameters of the CE and GCE HRG models presented in Table 3.

Figure 5

The data-to-model ratios for the CE HRG and GCE HRG model fits to the NA49 data on the $4\pi$ hadron multiplicities in inelastic $p+p$ interactions at $\sqrt{s_{NN}}=17.3\mathrm{GeV}$. For the CE the results are the same as in Fig. 3. The parameters of the CE and GCE fits are presented in Table 4.