Thermal freeze-out and collective signatures in $$pp$$ 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 (Scientific Reports)
Abstract This paper presents a comprehensive analysis of the double-differential $$p_T$$ distributions of charged particles across twelve pseudorapidity regions ( $$|η | < 2.4$$ , bin width $$Δ η = 0.2$$ ) 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 ( $$\langle β _T\rangle$$ ), non-extensivity parameter ( $$q$$ ), and mean transverse momentum ( $$\langle p_T \rangle$$ ) reveal systematic dependencies on $$η$$ and $$\sqrt{s}$$ . Both $$T_0$$ , $$\langle β _T\rangle$$ , and $$\langle p_T \rangle$$ decrease with $$|η |$$ , attributed to reduced energy deposition and weaker thermalization in fragmentation-dominated high- $$|η |$$ regions. These parameters also exhibit marked growth with $$\sqrt{s}$$ , reflecting collision-energy-driven dynamics. In contrast, $$q$$ increases with $$|η |$$ , signaling greater deviation from thermal equilibrium (Boltzmann limit $$q → 1$$ ) at larger $$|η |$$ , while mid- $$η$$ particles ( $$|η | ≈ 0$$ ) approach near-equilibrium behavior. Parameter correlations, particularly between $$T_0$$ , $$\langle β _T\rangle$$ , $$q$$ , 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.