Quantitative and Conceptual Considerations for Extracting the Knudsen Number in Heavy Ion Collisions

TL;DR

This paper critically examines methods for extracting the Knudsen number and shear viscosity to entropy density ratio in heavy ion collisions, highlighting sensitivities to initial state parameters and methodological ambiguities.

Contribution

It analyzes the dependence of eta/s extraction on Glauber model parameters and explores alternative functional forms, including a minimum mean free path, to improve understanding.

Findings

eta/s is highly sensitive to Glauber parameters

Alternative flow-Knudsen relations affect physics conclusions

Including a minimum mean free path impacts results

Abstract

In this paper we examine the methodology for extracting the Knudsen number (K) and the ratio of shear viscosity to entropy density (eta/s) developed by Drescher et al. The final result for eta/s turns out to be quite sensitive to Glauber parameters, and particularly the parameter x which controls the balance between Npart and Ncoll. We also explore how alternative formulations of the functional relation between the elliptic flow and Knudsen number impacts the physics conclusions, based on Pade approximants. Finally, we extend the calculation to include a limiting minimum value on the mean free path proportional to the DeBroglie wavelength. These results emphasize the importance of clarifying the initial state used in different calculations, as well as the ambiguities inherent in using a transport approach in a strongly-coupled regime.