Constraints on shear stress tensor in viscous relativistic hydrodynamics

TL;DR

This paper investigates how different shear stress tensor constraints in viscous relativistic hydrodynamics affect observable predictions, highlighting the importance of constraint choice and revealing limitations in reproducing experimental data.

Contribution

It introduces an analysis of shear stress tensor constraints within Israel-Stewart hydrodynamics and their impact on observables in a hybrid model, comparing different constraint forms.

Findings

Constraint choice significantly affects sensitivity to shear viscosity ratio.

The vHLLE model's constraint shows high sensitivity but limited applicability at high viscosity.

No constraint tested could simultaneously fit pion and proton data.

Abstract

We extend our hybrid model HydHSD by taking into account shear viscosity within the Israel-Stewart hydrodynamics. The influence of different forms of $\pi^{\mu\nu}$ constraints on observables is analyzed. We show that the form of the corresponding condition plays an important role for the sensitivity of viscous hydrodynamics to the ratio of shear viscosity to the entropy density, $\eta/s$. It is shown that the constraint used in the vHLLE model, results in most sensitivity of rapidity distributions and transverse momentum spectra to a change of the $\eta/s$ ratio; however, their applicability for large values of $\eta/s$ is doubtful. On the contrary, the strict constraints from \cite{MNR2010} are very strong but most established. We also found that $\eta/s$ as a function of the collision energy probably has an extremum at $E_{\rm lab}=10.7$ AGeV. However, we obtain that any considered condition does not allow to reproduce simultaneously pion and proton experimental data within our model.