Deciphering the viscous properties and the Bjorken expansion of the QGP medium at finite angular velocity

TL;DR

This work addresses how rapid rotation in noncentral heavy-ion collisions affects the viscous transport and Bjorken expansion of the quark-gluon plasma (QGP). It employs a relativistic Boltzmann framework with a novel relaxation time approximation (RTA) in which angular velocity $ω$ enters the distribution functions via $χ_{q,ar{q},g}(βω)$ and uses a quasiparticle description with thermal masses. The main findings are that rotation enhances both shear and bulk viscosities, but the novel RTA reduces $η$ and raises $ζ$ relative to the standard RTA, with $η/s$ approaching the lower bound $1/(4π)$ and $ζ/s$ increasing, signaling a departure from conformal symmetry; rotation also speeds up the Bjorken expansion, leading to faster cooling of the QGP. These results illuminate how vorticity in noncentral collisions can modify fluid behavior and have implications for interpreting flow observables in heavy-ion experiments.

Abstract

We have studied the viscous properties as well as the Bjorken expansion of a rotating QGP medium. In the noncentral events of heavy-ion collisions, the produced medium can carry a finite angular momentum with a finite range of angular velocity. This rotation can significantly affect various properties, including viscous properties and the expansion of the QGP medium. Using a novel relaxation time approximation for the collision integral in the relativistic Boltzmann transport equation at finite angular velocity, we have calculated the shear and bulk viscosities and compared them with their counterparts in the standard relaxation time approximation within the kinetic theory approach. Our results show that the angular velocity increases both shear and bulk viscosities, suggesting an enhanced momentum transfer within the medium and greater fluctuations in local pressure. This rotational effect on viscosities is more evident at lower temperatures than at higher temperatures. Our analysis also shows that, compared to the standard relaxation time approximation, the shear viscosity is lower while the bulk viscosity is higher in the novel relaxation time approximation for all temperatures. Additionally, some observables related to the flow characteristic, fluid behavior and conformal symmetry of the medium are markedly impacted due to rotation. We have also studied the hydrodynamic evolution of matter within the Bjorken boost-invariant scenario and have found that the energy density evolves faster in the presence of finite rotation than in the nonrotating case. Consequently, rapid rotation accelerates the cooling process of the QGP medium.

Figures (10)

• Figure 1: Variation of (a) shear viscosity and (b) bulk viscosity as a function of temperature for different angular velocities, comparing the RTA and the novel RTA methods.
• Figure 2: Variation of the Reynolds number: (a) as a function of temperature for different angular velocities, comparing the RTA and the novel RTA methods, and (b) as a function of angular velocity for different temperatures within the RTA approach.
• Figure 3: Variation of kinematic viscosity: (a) as a function of temperature for different angular velocities, comparing the RTA and the novel RTA methods, and (b) as a function of angular velocity for different temperatures within the RTA approach.
• Figure 4: Variation of entropy density: (a) as a function of temperature for different angular velocities and (b) as a function of angular velocity for different temperatures.
• Figure 5: Variation of the specific shear viscosity: (a) as a function of temperature for different angular velocities and (b) as a function of angular velocity for different temperatures.