https://doi.org/10.1140/epjp/s13360-026-07325-0
Regular Article
Analysis of midrapidity pT distributions of the charged pions and kaons, protons and antiprotons in Pb + Pb collisions at 
= 5.02 TeV using new combined Tsallis-Hagedorn function with transverse flow
1
Physical-Technical Institute of Uzbekistan Academy of Sciences, Chingiz Aytmatov Str. 2B, 100084, Tashkent, Uzbekistan
2
New Uzbekistan University, Tashkent, Uzbekistan
3
National University of Science and Technology MISIS (NUST MISIS), Almalyk Branch, Almalyk, Uzbekistan
4
Institute of Physics and Technology, Satbayev University, Almaty, Kazakhstan
5
Institute of Nuclear Physics, Almaty, Kazakhstan
6
Institute of Theoretical Physics, Shanxi University, 030006, Taiyuan, China
7
Samarkand State University Named After Sh. Rashidov, Samarkand, Uzbekistan
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Received:
2
January
2025
Accepted:
14
January
2026
Published online:
26
January
2026
Abstract
The transverse momentum spectra of particles coming from high-energy collisions can generally be divided into the lower and higher pT parts, where mostly the soft and hard processes contribute, respectively. In this paper, we have presented the new combined Tsallis-Hagedorn function with transverse flow in an attempt to describe better the longer range of pT spectra of hadrons. This new model function combines thermodynamically consistent Tsallis distribution with embedded transverse flow and QCD inspired Hagedorn function, assuming independence of the soft and hard processes, which contribute to the lower and higher parts of pT distribution. In order to study an influence of the pT fit range on the values of the parameters and quality of fits, the experimental midrapidity transverse momentum distributions of the charged pions and kaons, protons and antiprotons in ten centrality classes in Pb + Pb collisions at = 5.02 TeV, measured by the ALICE Collaboration, have been analyzed using simultaneous minimum χ2 fits by the introduced combined Tsallis-Hagedorn function with transverse flow in two pT fit ranges up to 5 and 8 GeV/c. The results obtained using combined Tsallis-Hagedorn function with transverse flow for kinetic freeze-out temperature and average transverse flow velocity as well as non-extensivity parameter q, and dependencies of these parameters on collision centrality, have been compared systematically with those obtained using thermodynamically consistent Tsallis function with embedded transverse flow. On the whole, both functions have resulted in comparably good fit qualities and similar trends of collision centrality dependencies of the extracted kinetic freeze-out parameters, confirming the important findings of the earlier work in both shorter and longer pT fit ranges.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
