Transverse Momentum Spectra and Nuclear Modification Factor using Boltzmann Transport Equation with Flow in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

Abstract

In the continuation of our previous work, the transverse momentum ($p_T$) spectra and nuclear modification factor ($R_{AA}$) are derived using relaxation time approximation of Boltzmann Transport Equation (BTE). The initial $p_T$-distribution used to describe $p+p$ collisions has been studied with the pQCD inspired power-law distribution, the Hagedorn's empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the $p_T$-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, $K^{*0}$ and $\phi$. It is observed that the present formalism while explaining the transverse momentum spectra upto 5 GeV/c, explains the nuclear modification factor very well upto 8 GeV/c in $p_T$ for all these particles except for protons. $R_{AA}$ is found to be independent of the degree of non-extensivity, $q_{pp}$ after $p_T \sim$ 8 GeV/c.