Comparison of $p-p, p-\mathrm{Pb}$, and Pb-Pb collisions in the thermal model: Multiplicity dependence of thermal parameters

An analysis is made of the particle composition (hadrochemistry) of the final state in proton-proton ($p-p$), proton-lead ($p\text{-Pb}$) and lead-lead (Pb-Pb) collisions as a function of the charged particle multiplicity ($d{N}_{\mathrm{ch}}/d\eta$). The thermal model is used to determine the chemical freeze-out temperature as well as the radius and strangeness saturation factor ${\gamma }_s$. Three different ensembles are used in the analysis; namely, the grand canonical ensemble, the canonical ensemble with exact strangeness conservation, and the canonical ensemble with exact baryon number, strangeness, and electric charge conservation. It is shown that for high multiplicities (at least 20 charged hadrons in the midrapidity interval considered) the three ensembles lead to the same results.

Figure 1

The chemical freeze-out temperature $T_{\mathrm{ch}}$ obtained for three different ensembles. The black points are obtained by using the grand canonical ensemble, the blue points use exact strangeness conservation, while the red points have built-in exact baryon number, strangeness, and charge conservation. Circles are for $p-p$ collisions at 7 TeV [27], squares are for $p\text{-Pb}$ collisions at 5.02 TeV [28, 29], while triangles are for Pb-Pb collisions at 2.76 TeV [30, 31, 32].

Figure 2

The strangeness saturation factor ${\gamma }_s$ obtained for three different ensembles. The black points were obtained by using the grand canonical ensemble, the blue points use exact strangeness conservation, while the red points have built-in exact baryon number, strangeness, and charge conservation. Circles are for $p-p$ collisions at 7 TeV [27], squares are for $p\text{-Pb}$ collisions at 5.02 TeV [28, 29], while triangles are for Pb-Pb collisions at 2.76 TeV [30, 31, 32].

Figure 3

The chemical freeze-out radius obtained for three different ensembles. The black points were obtained by using the grand canonical ensemble, the blue points use exact strangeness conservation, while the red points have built-in exact baryon number, strangeness, and charge conservation. Circles are for $p-p$ collisions at 7 TeV [27], squares are for $p\text{-Pb}$ collisions at 5.02 TeV [28, 29], while triangles are for Pb-Pb collisions at 2.76 TeV [30, 31, 32].

Figure 4

Hadronic yields in $p-p$ collisions at 7 TeV in centrality bins 1, 2, and 3 corresponding to 0%–4.7% (left panel) and 4.7%–14% (middle panel), and 14%–28% (right panel), respectively. The lower panel shows the ratio of experimental data divided by the fit results. The black points were obtained by using the grand canonical ensemble, the blue points use exact strangeness conservation, while the red ones have built-in exact baryon number, strangeness, and charge conservation. In some cases the bars overlap. The data are taken from Ref. [27].

Figure 5

Hadronic yields in $p-p$ collisions at 7 TeV in centrality bins 4 and 5 corresponding to 28%–48% (left panel) and 48%–100% (right panel), respectively. The lower panel shows the ratio of experimental data divided by the fit results. The black bars were obtained by using the grand canonical ensemble, the blue ones use exact strangeness conservation, while the red ones have been obtained by using exact baryon number, strangeness, and charge conservation. The data are taken from Ref. [27].