Viscosities of Gluon Dominated QGP Model within Relativistic Non-Abelian Hydrodynamics

TL;DR

This paper develops a relativistic non-Abelian hydrodynamics model for quark-gluon plasma, deriving viscosities analytically and revealing that bulk viscosity exceeds shear viscosity near hadronization.

Contribution

It introduces a novel Lagrangian incorporating viscosities for gluon-dominated QGP and analytically calculates shear and bulk viscosities based on first principles.

Findings

Bulk viscosity is larger than shear viscosity near hadronization.

The ratio of bulk to shear viscosity exceeds 4π under conjectured conditions.

Analytical expressions for viscosities are derived from the energy-momentum tensor.

Abstract

Based on the first principle calculation, a Lagrangian for the system describing quarks, gluons, and their interactions, is constructed. Ascribed to the existence of dissipative behavior as a consequence of strong interaction within quark-gluon plasma (QGP) matter, auxiliary terms describing viscosities are constituted into the Lagrangian. Through a "kind" of phase transition, gluon field is redefined as a scalar field with four-vector velocity inherently attached. Then, the Lagrangian is elaborated further to produce the energy-momentum tensor of dissipative fluid-like system and the equation of motion (EOM). By imposing the law of energy and momentum conservation, the values of shear and bulk viscosities are analytically calculated. Our result shows that, at the energy level close to hadronization, the bulk viscosity is bigger than shear viscosity. By making use of the conjectured values $\eta / s \sim 1 / 4\pi$ and $\zeta / s \sim 1$, the ratio of bulk to shear viscosity is found to be $\zeta / \eta > 4 \pi$.