Thermal freeze-out and collective signatures in [Formula: see text] collisions with a non-extensive statistical study on energy and pseudorapidity systematics

Haifa I Alrebdi; Muhammad Ajaz; Murad Badshah; Muhammad Waqas; Norah A M Alsaif; Mohammad Ayaz Ahmad; Jihane Ben Slimane

doi:10.1038/s41598-025-08380-w

Thermal freeze-out and collective signatures in [Formula: see text] collisions with a non-extensive statistical study on energy and pseudorapidity systematics

Sci Rep. 2025 Jul 26;15(1):27194. doi: 10.1038/s41598-025-08380-w.

Authors

Haifa I Alrebdi¹, Muhammad Ajaz², Murad Badshah³, Muhammad Waqas⁴, Norah A M Alsaif⁵, Mohammad Ayaz Ahmad⁶, Jihane Ben Slimane⁷

Affiliations

¹ Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia. hialrebdi@pnu.edu.sa.
² Department of Physics, Abdul Wali Khan University Mardan, Mardan, 23200, Pakistan. ajaz@awkum.edu.pk.
³ Department of Physics, Abdul Wali Khan University Mardan, Mardan, 23200, Pakistan.
⁴ Hubei Key Laboratory of Energy Storage and Power Battery, School of Optoelectronic Engineering, School of New Energy, Hubei University of Automotive Technology, Shiyan, 442002, People's Republic of China. 20220073@huat.edu.cn.
⁵ Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia.
⁶ Department of Mathematics, Physics and Statistics, Faculty of Natural Sciences, University of Guyana, Georgetown, 101110, Guyana.
⁷ Department of Computer Sciences, Faculty of Computing and Information Technology, Northern Border University, Rafha, 91911, Saudi Arabia.

Abstract

This paper presents a comprehensive analysis of the double-differential [Formula: see text] distributions of charged particles across twelve pseudorapidity regions ([Formula: see text], bin width [Formula: see text]) in [Formula: see text] collisions at [Formula: see text], 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 [Formula: see text] ranges (validated by Data/Fit panels). The extracted parameters including kinetic freeze-out temperature ([Formula: see text]), mean transverse flow velocity ([Formula: see text]), non-extensivity parameter ([Formula: see text]), and mean transverse momentum ([Formula: see text]) reveal systematic dependencies on η and [Formula: see text]. Both [Formula: see text], [Formula: see text], and [Formula: see text] decrease with [Formula: see text], attributed to reduced energy deposition and weaker thermalization in fragmentation-dominated high-[Formula: see text] regions. These parameters also exhibit marked growth with [Formula: see text], reflecting collision-energy-driven dynamics. In contrast, [Formula: see text] increases with [Formula: see text], signaling greater deviation from thermal equilibrium (Boltzmann limit [Formula: see text]) at larger [Formula: see text], while mid-η particles ([Formula: see text]) approach near-equilibrium behavior. Parameter correlations, particularly between [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], 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 [Formula: see text] interactions.

Abstract

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