Multiplicity dependence of the freezeout parameters in high energy hadron-hadron collisions* *Supported by Princess Nourah bint Abdulrahman University, Researchers Supporting Project Number PNURSP2024R106, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. We would like to express our gratitude for the support received from Abdul Wali Khan University Mardan, Pakistan; Hubei University of Automotive Technology, Doctoral Research Fund number BK202313; University

Abstract

We examined the transverse momentum ( ) spectra of various identified particles, encompassing both light-flavored and strange hadrons ( , , , ϕ, , , , and ), across different multiplicity classes in proton-proton collisions (p-p) at a center-of-mass energy of TeV. Utilizing the Tsallis and Hagedorn models, parameters relevant to the bulk properties of nuclear matter were extracted. Both models exhibit good agreement with experimental data. In our analyses, we observed a consistent decrease in the effective temperature (T) for the Tsallis model and the kinetic or thermal freeze-out temperature ( ) for the Hagedorn model, as we transitioned from higher multiplicity (class-I) to lower multiplicity (class-X). This trend is attributed to the diminished energy transfer in higher multiplicity classes. Additionally, we observed that the transverse flow velocity ( ) experiences a decline from class-I to class-X. The normalization constant, which represents the multiplicity of produced particles, was observed to decrease as we moved toward higher multiplicity classes. While the effective and kinetic freeze-out temperatures, as well as the transverse flow velocity, show a mild dependency on multiplicity for lighter particles, this dependency becomes more pronounced for heavier particles. The multiplicity parameter for heavier particles was observed to be smaller than that of lighter particles, indicating a greater abundance of lighter hadrons compared to heavier ones. Various particle species were observed to undergo decoupling from the fireball at distinct temperatures: lighter particles exhibit lower temperatures, while heavier ones show higher temperatures, thereby supporting the concept of multiple freeze-out scenarios. Moreover, we identified a positive correlation between the kinetic freeze-out temperature and transverse flow velocity, a scenario where particles experience stronger collective motion at a higher freeze-out temperature. The reason for this positive correlation is that, as the multiplicity increases, more energy is transferred into the system. This increased energy causes greater excitation and pressure within the system, leading to a quick expansion.