Exploring nuclear matter phase transition through \(p_T\) spectra analysis using blast wave model with Tsallis statistics in proton–proton collisions

Abstract

The freeze-out parameters are extracted by analyzing the transverse momentum (\(p_T\)) spectra of \(\pi ^+\) and \(\pi ^-\) measured in proton–proton (pp) collisions at NA61/SHINE Collaboration using the blast wave model with Tsallis statistics (TBW) across various rapidity segments. We extracted the kinetic freeze-out temperature (\(T_0\)), transverse flow velocity (\(\beta _T\)), velocity flow profile, and the non-extensive parameter (q). We also calculated the initial temperature (\(T_i\)) of the emission source of the final state particles by the string percolation theory as well as the mean transverse momentum (\(\langle p_T \rangle \)) of the produced particles. We have attempted to gain some insights into the expansion parameters of the system formed in the final state of the collision. We observed that the \(T_i\), \(\langle p_T \rangle \), \(T_0\), and \(\beta _T\) decrease from mid-rapidity toward forward rapidity region, while the flow profile parameter increases. We observed the kinetic freeze-out to be the reflection of the emission source of the final state particles and mean \(p_T\). \(T_0\) along with the \(T_i\), mean \(p_T\) and the \(\beta _T\) increases from lower energies up to 8.8 GeV, and after that, they remain unchanged. However, the velocity flow profile has the opposite behavior with increasing energy up to 8.8 GeV. The increment in the temperatures from lower energies up to 8.8 GeV shows the increasing excitation degree of the interacting system with increasing energy, while 8.8 GeV energy is seen to be the energy where the system reaches a critical energy density and the phase transition is supposed to occur. Furthermore, the \(\beta _T\) is related to the equation of states, and its saturation evinces toward the conformal equation of state.