Combined analysis of midrapidity transverse momentum spectra of the charged pions and kaons, protons and antiprotons in $p+p$ and Pb+Pb collisions at $(s_{nn})^{1/2}$ = 2.76 and 5.02 TeV at the LHC

The experimental transverse momentum spectra of the charged pions and kaons, protons and antiprotons, produced at midrapidity in p + p collisions at (s)1/2 = 2.76 and 5.02 TeV, central (0–5%) and peripheral (60–80%) Pb+Pb collisions at (snn)1/2 = 2.76 TeV, central (0–5%), semicentral (40–50%) and peripheral (80–90%) Pb+Pb collisions at (snn)1/2 = 5.02 TeV, measured by ALICE collaboration, were analyzed using the Tsallis distribution function as well as Hagedorn formula with the embedded transverse flow. To exclude the influence (on the results) of different available fitting pt ranges in the analyzed collisions, we compare the results obtained from combined (simultaneous) fits of midrapidity spectra of the charged pions and kaons, protons and antiprotons with the above theoretical model functions using the identical fitting pt ranges in p + p as well as Pb+Pb collisions at (snn)1/2 = 2.76 and 5.02 TeV. Using the combined fits with the thermodynamically consistent Tsallis distribution as well as the simple Tsallis distribution without thermodynamical description, it is obtained that the global temperature T and non-extensivity parameter q slightly increase (consistently for all the particle types) with an increase in center-of-mass (c.m.) energy (s)1/2 of p + p collisions from 2.76 TeV to 5.02 TeV, indicating that the more violent and faster p + p collisions at (s)1/2 = 5.02 TeV result in a smaller degree of thermalization (higher degree of non-equilibrium) compared to that in p + p collisions at (s)1/2 = 2.76 TeV. The q values for pions and kaons proved to be very close to each other, whereas q for protons and antiprotons proved to be significantly lower than that for pions and kaons, that is q(baryons) < q(mesons). The results of the combined fits using Hagedorn formula with the embedded transverse flow are consistent with practically no (zero) transverse (radial) flow in p + p collisions at (s)1/2 = 2.76 and 5.02 TeV. Using Hagedorn formula with the embedded transverse flow, it is obtained that the value of the (average) transverse flow velocity increases and the temperature T decreases with an increase in collision centrality in Pb+Pb collisions at (snn)1/2 = 2.76 and 5.02 TeV, which is in good agreement with the results of the combined Boltzmann–Gibbs blast-wave fits to the particle spectra in Pb+Pb collisions at (snn)1/2 = 2.76 and 5.02 TeV in recent works of ALICE collaboration. The temperature (T) parameter, which approximates the kinetic freeze-out temperature, was shown to coincide in central (0–5%) Pb+Pb collisions at (snn)1/2 = 2.76 and 5.02 TeV, which implies, taking into account the results of our previous analysis, that kinetic freeze-out temperature stays practically constant in central heavy-ion collisions in (snn)1/2 = 200–5020 GeV energy range.