Constraining $\eta /s$ through high-p${}_{\perp }$ theory and data

Abstract

We study whether it is possible to use high-$p_{\perp }$ data/theory to constrain the temperature dependence of the shear viscosity over entropy density ratio $\eta /s$ of the matter formed in ultrarelativistic heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC). We use two approaches: i) We calculate high-$p_{\perp }$ $R_{AA}$ and flow coefficients $v_2$, $v_3$ and $v_4$ assuming different $(\eta /s)(T)$ of the fluid-dynamically evolving medium. ii) We calculate the quenching strength ($\hat{q}/T^3$) from our dynamical energy loss model and convert it to $\eta /s$ as a function of temperature. It turned out that the first approach can not distinguish between different $(\eta /s)(T)$ assumptions when the evolution is constrained to reproduce the low-$p_{\perp }$ data. In distinction, $(\eta /s)(T)$ calculated using the second approach agrees surprisingly well with the $(\eta /s)(T)$ inferred through state-of-the-art Bayesian analyses of the low-$p_{\perp }$ data even in the vicinity of $T_c$, while providing much smaller uncertainties at high temperatures.

Comments: 25 pages, 9 figures, Version published in Physical Review C