Eur. Phys. J. Plus (2023) 138: 414
https://doi.org/10.1140/epjp/s13360-023-04037-7

Regular Article

Correlations among parameters of the Tsallis distribution and Hagedorn function with embedded transverse flow in proton–proton collisions at (s)^1/2 = 7 and 13 TeV

¹ Physical-Technical Institute of Uzbekistan Academy of Sciences, Chingiz Aytmatov Str. 2B, 100084, Tashkent, Uzbekistan
² Institute of Physics and Technology, Satbayev University, Almaty, Kazakhstan
³ National University of Science and Technology MISIS (NUST MISIS), Almalyk Branch, Almalyk, Uzbekistan
⁴ Institute of Nuclear Physics, Almaty, Kazakhstan
⁵ Institute of Theoretical Physics & Collaborative Innovation Center of Extreme Optics & State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, 030006, Taiyuan, China
⁶ Institute of Nuclear Physics of Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

^a khkolimov@gmail.com, kh.olimov@uzsci.net

Received: 14 March 2023
Accepted: 27 April 2023
Published online: 16 May 2023

Abstract

We have analyzed the correlations among parameters of the thermodynamically consistent Tsallis distribution and Hagedorn function with embedded transverse flow, obtained from combined analysis of the experimental midrapidity transverse momentum spectra of the charged pions and kaons, protons and antiprotons as a function of the average charged-particle multiplicity density, $⟨d{N}_{\mathit{ch}}/d\eta ⟩$, in p + p collisions at (s)^1/2 = 7 and 13 TeV, measured by ALICE Collaboration at the LHC. We have observed strong anticorrelation between non-extensivity parameter q for the charged pions and effective temperature, T, of the Tsallis distribution in both p + p collisions at (s)^1/2 = 7 and 13 TeV. The parameter q for protons and antiprotons has proved to be strongly positively correlated with T in both p + p collisions at (s)^1/2 = 7 and 13 TeV. Quite strong positive correlation between parameter q (n) for the charged pions and q (n) for the charged kaons has been obtained in both p + p collisions at (s)^1/2 = 7 and 13 TeV. This is likely due to similarity of mechanisms of production of pions and kaons, which have a similar quark structure, in high-energy proton–proton collisions. A strong negative correlation between parameter q for the charged pions and q for the protons and antiprotons has been found in both p + p collisions at (s)^1/2 = 7 and 13 TeV. The observed significant differences in the characters of parameter correlations for protons and antiprotons, on the one hand, and pions and kaons, on the other hand, could be due to significant differences in the quark structure and corresponding mechanisms of production of baryons and mesons in high-energy collisions. The significantly different behavior of the q (n) versus $⟨d{N}_{\mathit{ch}}/d\eta ⟩$ dependencies in regions $⟨d{N}_{\mathit{ch}}/d\eta ⟩$ < 6 − 7 and $⟨d{N}_{\mathit{ch}}/d\eta ⟩$ > 6 − 7 has been observed for all studied particle species in both collisions. The observed totally opposite correlations between parameter n (q) for pions and kaons and $⟨d{N}_{\mathit{ch}}/d\eta ⟩$ in regions $⟨d{N}_{\mathit{ch}}/d\eta ⟩$ < 6 ($⟨d{N}_{\mathit{ch}}/d\eta ⟩$ < 7) and $⟨d{N}_{\mathit{ch}}/d\eta ⟩$ > 6 ($⟨d{N}_{\mathit{ch}}/d\eta ⟩$ > 7) are consistent with and support the finding of the recent work suggesting a possible onset of deconfinement phase transition at $⟨d{N}_{\mathit{ch}}/d\eta ⟩$ ≈ 6.1 ± 0.3 ($⟨d{N}_{\mathit{ch}}/d\eta ⟩$ ≈ 7.1 ± 0.2) in p + p collisions at (s)^1/2 = 7 TeV ((s)^1/2 = 13 TeV).