Freeze-out conditions in proton-proton collisions at the highest energies available at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider

The freeze-out conditions in proton-proton collisions at $\sqrt{s_{\mathrm{NN}}}=200$, 900, and 7000 GeV have been extracted by fits to the mean hadron yields at midrapidity within the framework of the statistical model of an ideal gas of hadrons and resonances in the grand canonical ensemble. The variation of the extracted freeze-out thermal parameters and the goodness of the fits with $\sqrt{s_{NN}}$ are discussed. We find the extracted temperature and baryon chemical potential of the freeze-out surface to be similar in $p+p$ and heavy-ion collisions. On the other hand, the thermal behavior of the strange hadrons is qualitatively different in $p+p$ as compared to $A+A$ collisions. We find an additional parameter accounting for nonequilibrium strangeness production is essential for describing the $p+p$ data. This is in contrast to $A+A$ where the nonequilibrium framework could be successfully replaced by a sequential and complete equilibrium model with an early freeze-out of the strange hadrons.

Figure 1

Freeze-out parameters $T_{\mathrm{ch}}$, ${\mu }_B$, ${\gamma }_S$, $R$, and ${\chi }^2/ndf$ obtained from a statistical model fit [16] using midrapidity particle yields.

Figure 2

(a) The deviation between model and data for each species in the 1CFO scheme at $\sqrt{s_{NN}}=200$ GeV compared between $p+p$ and heavy-ion collisions. (b) The deviation between model and data in the 1CFO scheme at $\sqrt{s_{NN}}=7$ TeV.

Figure 3

A compilation of $T$ (a), ${\mu }_B$ (b), ${\gamma }_S$ (c), and $R$ (d) vs $\sqrt{s_{NN}}$ in $p+p$ collisions shown by blue squares for energies available at the CERN Super Proton Synchroton (SPS) taken from Ref. [14] and by blue circles for energies available at the RHIC and the LHC, which are the results of this paper. The results for $A+A$ are shown by red triangles for comparison [3]. The $T$ vs $\sqrt{s_{NN}}$ parametrizations shown by dashed lines are from Refs. [25] and [26].