Investigation of Nuclear Modification Factor from RHIC to LHC energies using Boltzmann Transport equation in conjunction with q-Weibull distribution

TL;DR

The study develops a Boltzmann Transport Equation framework in Relaxation Time Approximation to model the nuclear modification factor $R_{AA}$ in heavy-ion collisions from RHIC to LHC. It combines a Boltzmann-Gibbs equilibrium distribution $f_{eq}$ with a non-equilibrium final-state distribution $f_{fin}$ modeled by the $q$-Weibull form, deriving a master equation for $R_{AA}$ and fitting it to charged-hadron and identified-hadron data across energies and systems. The fits yield a near-unity $t_f/ au$ and reveal a linear mass dependence of the shape parameters $k$ and $ lambda$, indicating harder spectra and mass-dependent suppression patterns consistent with jet quenching and radial flow. The approach provides a consistent, broad-$p_T$ description of $R_{AA}$ and offers a framework to study the mass dependence of freeze-out and relaxation in QGP dynamics.

Abstract

The study of nuclear modification factor is crucial in advancing our knowledge of the hot and dense nuclear matter created during high energy heavy-ion collision. In this direction, we have developed a theoretical model for the nuclear modification factor using the Boltzmann Transport equation in relaxation time approximation with the q-Weibull distribution as the final state distribution and studied the experimental data of nuclear modification factor of charged hadrons as well as identified particles at various energies ranging from 7.7 GeV measured at RHIC upto the maximum value of 5.44 TeV studied in LHC. We observed a good agreement between the model and the experimental data as can be quantified using the $χ^2$/NDF values. We have also studied the mass dependence of different fit parameters that appears in the theoretical model and observe a linear mass dependence of some parameters.

Figures (6)

• Figure 1: Nuclear modification factor of identified hadrons produced in most central $PbPb$ collision at $2.76$ TeV ALICE:2014juv.
• Figure 2: Nuclear modification factor of different identified particles produced in most central $PbPb$ collision at $2.76$$\&$$5.02$ TeV fitted with the equation for $R_{AA}$ given in Eq. \ref{['RAA_final']}
• Figure 3: Nuclear modification factor of inclusive $J/\psi$ produced in most central $PbPb$ collision at $5.02~\&~2.76$ TeV fitted with the equation for $R_{AA}$ given in Eq. \ref{['RAA_final']}.
• Figure 4: Nuclear modification factor of charged hadrons produced in most central $XeXe$ collision at $5.44$ TeV, $PbPb$ collision at $5.02~\&~2.76$ TeV and $AuAu$ collision at $200~\&~130$ GeV fitted with the equation for $R_{AA}$ given in Eq. \ref{['RAA_final']}. Some of the data points are scaled for better visibility.
• Figure 5: Nuclear modification factor ($R_{CP}$) of charged hadrons produced in most central $AuAu$ collision at $62.4,~27,~19.6,~11.5~\&~7.7$ GeV fitted with the equation for $R_{AA}$ given in Eq. \ref{['RAA_final']}.