Analysis of Transverse-Momentum Distributions of Charged Particles in Proton–Proton Collisions at Energies in the Range of $$\boldsymbol{(s_{nn})^{1/2}=2.76}$$–7 TeV at the LHC

Experimental transverse-momentum distributions measured by the ALICE Collaboration for charged pions and kaons, protons, and antiprotons at midrapidities in inelastic proton–proton ( $$p+p$$ ) collisions at energies in the range of $$(s)^{1/2}=2.76$$ –7 TeV in experiments at the Large Hadron Collider (LHC, CERN) are systematically analyzed by employing the thermodynamically consistent Tsallis distribution function and the Hagedorn formula with an embedded collective transverse flow. As approximate equality of the nonextensivity parameter $$q$$ of the Tsallis function for pions and kaons, $$q$$ (pions) $$\approx q$$ (kaons), and the relationship $$q$$ (mesons) $$>q$$ (baryons) are obtained from a fit to the transverse-momentum spectra of particle species under analysis on the basis of the thermodynamically consistent Tsallis function in optimum identical fitting ranges of $$p_{t}$$ in $$p+p$$ collisions at $$(s)^{1/2}=2.76$$ , 5.02, and 7 TeV. The parameter $$q$$ increases systematically for all particle species as the $$p+p$$ collision energy $$(s)^{1/2}$$ grows from 2.76 to 5.02 TeV but remains virtually unchanged within the fitting errors over the collision-energy range of $$(s)^{1/2}=5$$ –7 TeV, this being indicative of the saturation of $$q$$ in $$p+p$$ collisions at energies in the region of $$(s)^{1/2}>5$$ TeV. A nearly negligible radial flow velocity, which is compatible with zero value within the fitting errors, is obtained for $$p+p$$ collisions in the energy range of $$(s)^{1/2}=2.76$$ –7 TeV upon approximating the $$p_{t}$$ distributions of charged pions and kaons, protons, and antiprotons by the Hagedorn formula with an embedded transverse flow in the chosen optimum identical intervals of $$p_{t}$$ , as well as in the full measured ranges of $$p_{t}$$ .

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