Temperature and net baryochemical potential dependence of $\eta/s$ in a hybrid approach

TL;DR

This study investigates how the shear viscosity to entropy density ratio $s$ depends on temperature and net baryochemical potential in hydrodynamic simulations, revealing minimal impact on elliptic flow but potential as a proxy for non-equilibrium shear viscosity.

Contribution

It introduces a parameterization of s that depends on temperature and baryochemical potential, incorporating constraints from transport coefficients and pQCD, and explores its effects in a hybrid hydrodynamic model.

Findings

Net baryon number dependence has negligible effect on elliptic flow.

The s parameterization aligns with transport coefficients in the hadronic phase.

The approach may serve as a proxy for shear viscosity during non-equilibrium stages.

Abstract

In this work, the qualitative impact of the net baryochemical potential dependence of the shear viscosity to entropy density ratio $\eta/s$ in hydrodynamical simulations is studied. The effect of a predicted non-constant $\eta/s$($\mu_B$) is largely unexplored in hydrodynamic simulations. Previous studies focus only on a temperature dependence or even only a constant effective shear viscosity. This work addresses this issue by studying qualitatively the effect of a generalized $\eta/s$($T,\mu_B$) in the hybrid approach SMASH-vHLLE, composed of the hadronic transport approach SMASH and the (3+1)d viscous hydrodynamic code vHLLE. In order to reduce the bias of the result on the equation of state used in the hydrodynamic part of the model, $\eta/s$ is parameterized directly in the energy density and net baryon number density. The parameterization takes into account the constraints of matching to the transport coefficients in the hadronic phase, as well as pQCD results. This work compares the impact of the density dependence for different system sizes and energies and compares the observables with experimental results in the RHIC - BES region $\sqrt{s_{NN}}$ =7.7 - 39.0 GeV, as the effect of this generalization is especially relevant for intermediate collision energies, for which the system is in equilibrium for a relevant amount of time, but the net baryochemical potential does not vanish. It is shown that the effect of an explicit net baryon number dependence on the elliptic flow is negligible and only relevant in the early stages of the collision. Additionally, we find that the proposed parameterization could be a good proxy for the shear viscosity in the non-equilibrium hadronic transport stage.