Role of system size in freeze-out conditions extracted from transverse momentum spectra of hadrons

The data on hadron transverse momentum spectra in different centrality classes of p + Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV have been analyzed to extract the freeze-out hypersurface within a simultaneous chemical and kinetic freeze-out scenario. The freeze-out hypersurface has been extracted for three freeze-out schemes that differ in the way strangeness is treated: (i) unified freeze-out for all hadrons at complete thermal equilibrium (1FO), (ii) unified freeze-out for all hadrons with an additional parameter ${\gamma }_S$ which accounts for possible out-of-equilibrium production of strangeness ($1\mathrm{FO}+{\gamma }_S$), and (iii) separate freeze-out for hadrons with and without strangeness content (2FO). Unlike in heavy-ion collisions where 2FO performs best in describing the mean hadron yields as well as the transverse momentum spectra, with p + Pb we find that $1\mathrm{FO}+{\gamma }_S$ with one fewer parameter than 2FO performs better. This confirms expectations based on previous analysis of system size dependence in the freeze-out scheme with mean hadron yields: while heavy-ion collisions that are dominated by constituent interactions prefer 2FO, smaller collision systems like proton + nucleus and proton + proton collisions with lesser constituent interaction prefer a unified freeze-out scheme with varying degrees of strangeness equilibration.

Figure 1

Comparison of $p_T$ spectra in p + Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$ obtained from the THERMINATOR [21, 22] and data [35, 36, 37] shown for three centralities—$0\text{−}5\%$, $10–20\%$, and $60–80\%$—in three FO schemes at $0<y_{\mathrm{cm}}<0.5$. The gross features of the spectral comparison seem to be independent of the freeze-out scheme. The bottom panels (a–i) show the ratio of data to model calculation.

Figure 2

The ${\chi }^2$/ndf values are compared for the three freeze-out schemes across central to peripheral collisions in p + Pb. $1\mathrm{FO}+{\gamma }_S$ provides the best description across all centralities. The improvement over 1FO and 2FO gets better as one goes to more peripheral collisions.

Figure 3

The extracted freeze-out parameters with the best goodness of fit for different centralities in p + Pb and Pb + Pb collisions. There is a gradual preference for sequential freeze-out of the strange and nonstrange flavors as we go to higher multiplicity events. The ${\gamma }_S$ value is fixed at 1 for Pb + Pb collisions at ${\sqrt{s}}_{\mathrm{NN}}=2.76$ TeV.