Thermal freeze-out and collective signatures in $$pp$$ collisions with a non-extensive statistical study on energy and pseudorapidity systematics

Abstract This paper presents a comprehensive analysis of the double-differential $$p_T$$ distributions of charged particles across twelve pseudorapidity regions ( $$|\eta | < 2.4$$ , bin width $$\Delta \eta = 0.2$$ ) in $$pp$$ collisions at $$\sqrt{s} = 0.9$$ , 2.36, and 7 TeV. Using a modified T...

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Main Authors: Haifa I. Alrebdi, Muhammad Ajaz, Murad Badshah, Muhammad Waqas, Norah A. M. Alsaif, Mohammad Ayaz Ahmad, Jihane Ben Slimane
Format: Article
Language:English
Published: Nature Portfolio 2025-07-01
Series:Scientific Reports
Online Access:https://doi.org/10.1038/s41598-025-08380-w
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author Haifa I. Alrebdi
Muhammad Ajaz
Murad Badshah
Muhammad Waqas
Norah A. M. Alsaif
Mohammad Ayaz Ahmad
Jihane Ben Slimane
author_facet Haifa I. Alrebdi
Muhammad Ajaz
Murad Badshah
Muhammad Waqas
Norah A. M. Alsaif
Mohammad Ayaz Ahmad
Jihane Ben Slimane
author_sort Haifa I. Alrebdi
collection DOAJ
description Abstract This paper presents a comprehensive analysis of the double-differential $$p_T$$ distributions of charged particles across twelve pseudorapidity regions ( $$|\eta | < 2.4$$ , bin width $$\Delta \eta = 0.2$$ ) in $$pp$$ collisions at $$\sqrt{s} = 0.9$$ , 2.36, and 7 TeV. Using a modified Tsallis function incorporating an effective transverse flow velocity, we achieve excellent agreement between the model and experimental data, with consistent fit quality across all $$p_T$$ ranges (validated by Data/Fit panels). The extracted parameters including kinetic freeze-out temperature ( $$T_0$$ ), mean transverse flow velocity ( $$\langle \beta _T\rangle$$ ), non-extensivity parameter ( $$q$$ ), and mean transverse momentum ( $$\langle p_T \rangle$$ ) reveal systematic dependencies on $$\eta$$ and $$\sqrt{s}$$ . Both $$T_0$$ , $$\langle \beta _T\rangle$$ , and $$\langle p_T \rangle$$ decrease with $$|\eta |$$ , attributed to reduced energy deposition and weaker thermalization in fragmentation-dominated high- $$|\eta |$$ regions. These parameters also exhibit marked growth with $$\sqrt{s}$$ , reflecting collision-energy-driven dynamics. In contrast, $$q$$ increases with $$|\eta |$$ , signaling greater deviation from thermal equilibrium (Boltzmann limit $$q \rightarrow 1$$ ) at larger $$|\eta |$$ , while mid- $$\eta$$ particles ( $$|\eta | \approx 0$$ ) approach near-equilibrium behavior. Parameter correlations, particularly between $$T_0$$ , $$\langle \beta _T\rangle$$ , $$q$$ , and $$\langle p_T \rangle$$ , highlight interplay between thermal and collective-like dynamics. The results provide critical insights into the interplay of thermalization, effective flow, and non-equilibrium effects in small collision systems, advancing the understanding of bulk hadronic matter in high-energy $$pp$$ interactions.
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spelling doaj-art-a7d66b92f4a04bb983ad47e640252b8a2025-08-20T03:05:17ZengNature PortfolioScientific Reports2045-23222025-07-0115111110.1038/s41598-025-08380-wThermal freeze-out and collective signatures in $$pp$$ collisions with a non-extensive statistical study on energy and pseudorapidity systematicsHaifa I. Alrebdi0Muhammad Ajaz1Murad Badshah2Muhammad Waqas3Norah A. M. Alsaif4Mohammad Ayaz Ahmad5Jihane Ben Slimane6Department of Physics, College of Science, Princess Nourah bint Abdulrahman UniversityDepartment of Physics, Abdul Wali Khan University MardanDepartment of Physics, Abdul Wali Khan University MardanHubei Key Laboratory of Energy Storage and Power Battery, School of Optoelectronic Engineering, School of New Energy, Hubei University of Automotive TechnologyDepartment of Physics, College of Science, Princess Nourah bint Abdulrahman UniversityDepartment of Mathematics, Physics and Statistics, Faculty of Natural Sciences, University of GuyanaDepartment of Computer Sciences, Faculty of Computing and Information Technology, Northern Border UniversityAbstract This paper presents a comprehensive analysis of the double-differential $$p_T$$ distributions of charged particles across twelve pseudorapidity regions ( $$|\eta | < 2.4$$ , bin width $$\Delta \eta = 0.2$$ ) in $$pp$$ collisions at $$\sqrt{s} = 0.9$$ , 2.36, and 7 TeV. Using a modified Tsallis function incorporating an effective transverse flow velocity, we achieve excellent agreement between the model and experimental data, with consistent fit quality across all $$p_T$$ ranges (validated by Data/Fit panels). The extracted parameters including kinetic freeze-out temperature ( $$T_0$$ ), mean transverse flow velocity ( $$\langle \beta _T\rangle$$ ), non-extensivity parameter ( $$q$$ ), and mean transverse momentum ( $$\langle p_T \rangle$$ ) reveal systematic dependencies on $$\eta$$ and $$\sqrt{s}$$ . Both $$T_0$$ , $$\langle \beta _T\rangle$$ , and $$\langle p_T \rangle$$ decrease with $$|\eta |$$ , attributed to reduced energy deposition and weaker thermalization in fragmentation-dominated high- $$|\eta |$$ regions. These parameters also exhibit marked growth with $$\sqrt{s}$$ , reflecting collision-energy-driven dynamics. In contrast, $$q$$ increases with $$|\eta |$$ , signaling greater deviation from thermal equilibrium (Boltzmann limit $$q \rightarrow 1$$ ) at larger $$|\eta |$$ , while mid- $$\eta$$ particles ( $$|\eta | \approx 0$$ ) approach near-equilibrium behavior. Parameter correlations, particularly between $$T_0$$ , $$\langle \beta _T\rangle$$ , $$q$$ , and $$\langle p_T \rangle$$ , highlight interplay between thermal and collective-like dynamics. The results provide critical insights into the interplay of thermalization, effective flow, and non-equilibrium effects in small collision systems, advancing the understanding of bulk hadronic matter in high-energy $$pp$$ interactions.https://doi.org/10.1038/s41598-025-08380-w
spellingShingle Haifa I. Alrebdi
Muhammad Ajaz
Murad Badshah
Muhammad Waqas
Norah A. M. Alsaif
Mohammad Ayaz Ahmad
Jihane Ben Slimane
Thermal freeze-out and collective signatures in $$pp$$ collisions with a non-extensive statistical study on energy and pseudorapidity systematics
Scientific Reports
title Thermal freeze-out and collective signatures in $$pp$$ collisions with a non-extensive statistical study on energy and pseudorapidity systematics
title_full Thermal freeze-out and collective signatures in $$pp$$ collisions with a non-extensive statistical study on energy and pseudorapidity systematics
title_fullStr Thermal freeze-out and collective signatures in $$pp$$ collisions with a non-extensive statistical study on energy and pseudorapidity systematics
title_full_unstemmed Thermal freeze-out and collective signatures in $$pp$$ collisions with a non-extensive statistical study on energy and pseudorapidity systematics
title_short Thermal freeze-out and collective signatures in $$pp$$ collisions with a non-extensive statistical study on energy and pseudorapidity systematics
title_sort thermal freeze out and collective signatures in pp collisions with a non extensive statistical study on energy and pseudorapidity systematics
url https://doi.org/10.1038/s41598-025-08380-w
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