With the experimental data collected by the ALICE collaboration in Pb-Pb collisions at a centerof-mass energy per nucleon pair 2.76 TeV for six different centralities (0-5%, 5-10%, 10-20%, 20-40%, 40-60% and 60-80%), we investigate the scaling property of the pion, kaon and proton transverse momentum (p T ) spectra at these centralities. We show that in the low p T region with p T ≤ 2.75 (3.10 and 2.35) GeV/c the pion (kaon and proton) spectra exhibit a scaling behaviour independent of the centrality of the collisions. This scaling behaviour arises when these spectra are presented in terms of a suitable variable, z = p T /K. The scaling parameter K is determined by the quality factor method and is parameterized by a N part b , where N part is the average value of the number of participating nucleons, a and b are free parameters, b characterizes the rate at which lnK changes with ln N part . The values of b for pions and kaons are consistent within uncertainties, while they are smaller than that for protons. In the high p T region, due to the suppression of the spectra, a violation of the proposed scaling is observed going from central to peripheral collisions. The more peripheral the collisions are, the more clearly violated the proposed scaling becomes. In the framework of the colour string percolation model, we argue that the pions, kaons and protons originate from the fragmentation of clusters which are formed by strings overlapping and the cluster's fragmentation functions are different for different hadrons. The scaling behaviour of the pion, kaon and proton spectra in the low p T region can be simultaneously explained by the colour string percolation model in a qualitative way.
As a complementary study to that performed on the transverse momentum (pT) spectra of charged pions, kaons and protons in proton-proton (pp) collisions at LHC energies 0.9, 2.76 and 7 TeV, we present a scaling behaviour in the pT spectra of strange particles (K 0 S , Λ, Ξ and φ) at these three energies. This scaling behaviour is exhibited when the spectra are expressed in a suitable scaling variable z = pT/K, where the scaling parameter K is determined by the quality factor method and increases with the center of mass energy ( √ s). The rates at which K increases with ln √ s for these strange particles are found to be identical within errors. In the framework of the colour string percolation model, we argue that these strange particles are produced through the decay of clusters that are formed by the colour strings overlapping. We observe that the strange mesons and baryons are produced from clusters with different size distributions, while the strange mesons (baryons) K 0 S and φ (Λ and Ξ) originate from clusters with the same size distributions. The cluster's size distributions for strange mesons are more dispersed than those for strange baryons. The scaling behaviour of the pT spectra for these strange particles can be explained by the colour string percolation model in a quantitative way.
We systematically investigate the scaling property of mesons (pions and kaons) and baryons (protons, Λ, Ξ and Ω) transverse momentum (p T ) spectra at different centrality classes (0-5%, 5-10%, 10-20%, 20-40%, 40-60%, 60-80% and 80-100%) in proton-lead collisions with center of mass energy per nucleon pair 5.02 TeV. In the low p T region with p T ≤ 3.9 (3.1, 2.5, 2.7, 2.4 and 2.8) GeV/c, a universal scaling independent of the centrality is observed in the pion (kaon, proton, Λ, Ξ and Ω) spectra when a dilatation, p T → p T /K, is applied. Here K is a scaling parameter depending on the centrality class. We find that the rates at which lnK changes with the logarithmic value of the average value of the number of participating nucleons, ln N part , are stronger for baryons than those for mesons. In the high p T region, there is a deviation from the scaling. The more peripheral the collisions are, the more obvious the violation of the scaling is. In the framework of the colour string percolation (CSP) model, we show that mesons and baryons are generated from the decay of clusters formed by strings overlapping in the transverse plane with the same size dispersion but with different mean size. The mean size of clusters for baryons is smaller than that of mesons. For the same hadrons at different centrality classes, the mean size of clusters decreases with the increase of centrality. The fragmentation functions for cluster decay are different for different hadrons, while they are universal for the same hadrons at different centrality classes. The universal scaling of the meson and baryon spectra in the low p T region can be quantitatively understood with the CSP model at the same time.1 Unless otherwise stated, in the later of the paper, we will follow the same definition of centrality classes.
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