Reexamination of eccentricity scaling of elliptic flow and incomplete thermalization scenario in heavy-ion collisions at energies available at CERN large hadron collider

Abstract In this article, we reexamine the formulation for extraction of Knudsen number ( K ), the ratio of shear viscosity to entropy density ( $$\eta /s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>η</mml:mi> <mml:mo>/</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> ), within the incomplete thermalization scenario, using eccentricity scaling of elliptic flow ( $$v_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>v</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> ) of final state hadrons. Data on centrality dependence of charged hadron $$v_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>v</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> in Xe–Xe and Pb–Pb collisions, measured by ALICE and CMS collaborations at LHC are analyzed for this purpose. Results have been compared using two different models of collision namely Glauber Monte Carlo and TRENTO. The measured $$v_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>v</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , even for $$\sqrt{s_{NN}}=5.02$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:mi>NN</mml:mi> </mml:mrow> </mml:msub> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>5.02</mml:mn> </mml:mrow> </mml:math> TeV most central Pb–Pb collisions is found to be below the ideal hydrodynamic limit by at least $$15 \%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>15</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> . Extracted $$\eta /s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>η</mml:mi> <mml:mo>/</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> of the medium exhibit heavy dependence on the employed initial conditions. Impact of the Pade approximants based alternative formulation of the functional relation between $$v_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>v</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> and K are also investigated in detail. Our studies reconfirm the importance of clarifying the initial state configuration as well as the inbuilt ambiguities in employing the transport approach based on incomplete equilibrium in a strongly coupled regime at LHC.