Exploring Anisotropic flow via the Boltzmann Transport Equation Employing the Tsallis Blast Wave Description at LHC energies

Anisotropic flows $i.e.$ azimuthal anisotropies in particle production are one of the important probes in characterizing the properties of the strongly interacting matter created in the relativistic heavy-ion collisions. These observables are sensitive to both the transport properties as well as the equation of state (EOS) of Quantum Chromodynamics (QCD) matter. We have adopted the Boltzmann transport equation (BTE) in the relaxation time approximation (RTA) to describe the experimental data for harmonic flows such as elliptic flow ($v_2$), triangular flow ($v_3$), quadrangular flow ($v_4$) obtained in heavy-ion collisions at Large Hadron Collider (LHC) energies. In this analysis, we have used Tsallis statistics as an initial distribution and the Tsallis Blast wave (TBW) description is used as the equilibrium distribution function while describing the evolution of the particle production in BTE. We have fitted the transverse momentum spectra, $v_2$, $v_3$, and $v_4$ of identified hadrons such as pion, kaon, and proton for Pb-Pb and Xe-Xe collisions at the LHC energies of $\sqrt{s_{NN}}$ = 5.02 TeV and $\sqrt{s_{NN}}$ = 5.44 TeV, respectively for various centralities. Our study offers a comparative analysis between the two distinct collision systems operating at comparable collision energies. The present formulation successfully fits the experimental data for $p_T$-spectra upto $p_T$ = 8 GeV and effectively explains the anisotropic flows data upto $p_T$ = 10 GeV with a very favourable $\chi^2/ndf$. We observe that the average transverse flow velocity ($<\beta_r>$) and the kinetic freeze-out temperature ($T$) extracted in our analysis decrease as we go towards the peripheral collisions. The azimuthal modulation amplitudes ($\rho_a$) exhibit an increasing pattern as one moves from central to peripheral collisions in both the Pb-Pb and Xe-Xe nuclei interactions.