Viscosities of gluon dominated QGP model within relativistic non-Abelian hydrodynamics

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 η/s ∼ 1/4π and ζ/s ∼ 1, the ratio of bulk to shear viscosity is found to be ζ/η > 4π.

Equation of state within gluon dominated QGP model in relativistic hydrodynamics approach

“…The Lagrangian of QGP that describes the unification of fermions and bosons from different gauge groups with preserving SU(3) F ⊗ U(1) G gauge symmetry can be written as [13,14] …”

“…The QCD Lagrangian in Eq. ( 1) is constructed with a purpose to reproduce the energy momentum tensor that has the same form as the energy momentum tensor of an ideal fluid [13]. In the succeeding step, the gluon field U a µ , that is designed to act as the flow field in the system is proposed to be formulated in a configuration that inherently contains the relativistic flow.…”

“…On the other hand, the gluon-dominated plasma motivated by the discoveries of jet quenching in the heavy-ion collision at Brookhaven's Relativistic Heavy Ion Collider (RHIC) indicates the shock waves in the form of Mach cone [11,12]. The present paper adopts the so-called fluid QCD model [13][14][15] to produce the equation of motion and energymomentum tensor for quark and gluon in a lump of QGP, and subsequently to investigate the distributions of the pressure and energy density. This paper is organized as follows.…”