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Elliptic and Hexadecapole flow of charged hadron in viscous hydrodynamics with Glauber and Color Glass Condensate initial conditions for Pb-Pb collision at $\sqrt{s_{NN}}$=2.76 TeV

The experimentally measured elliptic ($v_{2}$) and hexadecapole ($v_{4}$) flow of charged particles as a function of transverse momentum ($p_{T}$) at midrapidity in Pb-Pb collisions at $\sqrt{s_{\mathrm NN}}$ = 2.76 TeV are compared with the relativistic viscous hydrodynamic model simulations. The simulations are carried out for two different initial energy density profiles obtained from (i) Glauber model, and (ii) Color Glass Condensate (CGC) model. Comparison to experimental data for 10-20% to 40-50% centrality, shows that a centrality dependent shear viscosity to entropy density ($η/s$) ratio with values ranging between 0.0 to 0.12 are needed to explain the $v_{2}$ data for simulations with the Glauber based initial condition. Whereas for the CGC based initial conditions a slightly higher value of $η/s$ is preferred, around 0.08 to 0.16. From the comparison of the $v_{4}$ simulated results to the corresponding experimental measurements we observe that for the centralities 20-30% to 40-50% the $η/s$ values lies between 0.0 to 0.12 for both the initial conditions studied. The $η/s$ values obtained from our studies for Pb-Pb collisions at $\sqrt{s_{\mathrm NN}}$ = 2.76 TeV are compared to other studies which uses both transport and hydrodynamic approaches.