[Paper Review] Indication of Differential Kinetic Freeze-out at RHIC and LHC Energies

D. Thakur, S. Tripathy+3 more|arXiv (Cornell University)|Mar 16, 2016

High-Energy Particle Collisions Research1 references5 citations

TL;DR

This study uses Tsallis non-extensive statistics with and without radial flow to analyze transverse momentum spectra in A+A and p+p collisions at RHIC and LHC energies. It reveals mass-dependent freeze-out parameters, showing heavier particles freeze out earlier than lighter ones—evidence of differential kinetic freeze-out—while radial flow decreases with mass, confirming mass-ordering in collectivity and indicating similar thermodynamic behavior in peripheral heavy-ion and p+p collisions.

ABSTRACT

The transverse momentum spectra at RHIC and LHC for A+A and p+p collisions are studied with Tsallis distributions in different approaches i.e. with and without radial flow. The information on the freeze-out surface in terms of freeze-out volume, temperature, chemical potential and radial flow velocities for different particle species are obtained. These parameters are found to show a systematic behavior with mass dependence. It is observed that the heavier particles freeze-out early as compared to lighter particles and freeze-out surfaces are different for different particles, which is a direct signature of mass dependent differential freeze-out. Further, we observe that the radial flow velocity decreases with increasing mass. This confirms the mass ordering behavior in collectivity observed in heavy-ion collisions. It is also observed that the systems created in peripheral heavy-ion collisions and in proton-proton collisions are of similar thermodynamic nature.

Motivation & Objective

• To investigate the thermodynamic properties of particle production in heavy-ion and proton-proton collisions at high energies.
• To determine whether particle species exhibit different freeze-out conditions based on mass.
• To assess the role of radial flow and non-extensivity (via the q-parameter) in shaping transverse momentum spectra.
• To compare the thermodynamic nature of systems formed in peripheral A+A and p+p collisions.
• To establish whether differential freeze-out—where heavier particles decouple earlier—is a universal feature across collision systems and energies.

Proposed method

• Employing the Tsallis distribution function without radial flow (Eq. 2) to extract freeze-out temperature T, volume V, and non-extensivity parameter q from transverse momentum spectra.
• Using the Tsallis distribution with radial flow (Eq. 3), expanded in Taylor series up to first order in (q−1), to include radial flow velocity v and model momentum spectra more accurately.
• Applying the distribution to mid-rapidity data from Au+Au and Pb+Pb collisions at √sNN = 200 GeV and 2.76 TeV, respectively.
• Analyzing the mass dependence of extracted parameters: T, V, q, and v across identified particles (e.g., pions, kaons, protons).
• Comparing results from systems with different participant numbers (central vs. peripheral) and collision types (A+A vs. p+p).
• Verifying consistency of parameters via the relation T = T₀ + (q−1)μ, where μ is chemical potential, and T₀ is the Tsallis temperature at μ=0.

Experimental results

Research questions

• RQ1 Do different particle species exhibit distinct freeze-out conditions in heavy-ion collisions at RHIC and LHC energies?
• RQ2 Is there evidence of mass-dependent kinetic freeze-out, where heavier particles decouple earlier than lighter ones?
• RQ3 How does the inclusion of radial flow affect the description of transverse momentum spectra in non-equilibrium systems?
• RQ4 To what extent do peripheral A+A and p+p collisions share similar thermodynamic properties in terms of freeze-out parameters?
• RQ5 Does the q-parameter’s mass dependence suggest a dynamical origin for non-extensivity in high-energy collision systems?

Key findings

• Heavier particles (e.g., protons) exhibit earlier kinetic freeze-out compared to lighter particles (e.g., pions), indicating differential freeze-out.
• The freeze-out temperature T increases with particle mass, while the volume parameter V decreases, confirming mass-dependent freeze-out surfaces.
• The non-extensivity parameter q decreases with increasing particle mass, suggesting a dynamical origin for non-extensivity in the system.
• Radial flow velocity v decreases systematically with increasing particle mass, consistent with hydrodynamic models and collectivity trends.
• Peripheral A+A and p+p collisions at both RHIC and LHC energies show similar thermodynamic behavior, implying comparable freeze-out conditions.
• The extracted parameters from both Tsallis forms (with and without radial flow) satisfy the consistency relation T = T₀ + (q−1)μ, validating the theoretical framework.