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Hall Viscosity in the Quark-Gluon Plasma

Sukrut Mondkar, Giorgio Torrieri, Matthias Kaminski, René Meyer

Abstract

We study the Hall viscosity of the quark gluon plasma (QGP) created in non-central heavy-ion collisions. In the presence of a strong magnetic field or vorticity, rotational symmetry is broken from O(3) to O(2), allowing for two independent Hall viscosities associated with shear deformations transverse and parallel to the symmetry-breaking direction. We find the corresponding constitutive relations by extending the kinetic-theory mechanism to three spatial dimensions and provide parametric estimates of the Hall viscosities under realistic QGP conditions. Both kinetic-theory and holographic estimates indicate that Hall viscosities are comparable in magnitude to the shear viscosity at zero magnetic field. We further show that Hall viscous stresses at hydrodynamic initialization can be as large as standard viscous corrections and identify observable consequences in flow and event-plane correlations.

Hall Viscosity in the Quark-Gluon Plasma

Abstract

We study the Hall viscosity of the quark gluon plasma (QGP) created in non-central heavy-ion collisions. In the presence of a strong magnetic field or vorticity, rotational symmetry is broken from O(3) to O(2), allowing for two independent Hall viscosities associated with shear deformations transverse and parallel to the symmetry-breaking direction. We find the corresponding constitutive relations by extending the kinetic-theory mechanism to three spatial dimensions and provide parametric estimates of the Hall viscosities under realistic QGP conditions. Both kinetic-theory and holographic estimates indicate that Hall viscosities are comparable in magnitude to the shear viscosity at zero magnetic field. We further show that Hall viscous stresses at hydrodynamic initialization can be as large as standard viscous corrections and identify observable consequences in flow and event-plane correlations.
Paper Structure (12 sections, 95 equations, 3 figures, 3 tables)

This paper contains 12 sections, 95 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Generating Hall viscosity in the QGP
  3. Hall viscosities in three-dimensional non-relativistic hydrodynamics
  4. Estimated Hall viscosities from kinetic theory
  5. Estimated Hall viscosities from holography
  6. Observables
  7. Quantitative estimates of Hall viscosity effects on the QGP
  8. Observables and their quantitative estimates
  9. Conclusions and Outlook
  10. Hall viscosities
  11. The Alekseev mechanism in two-dimensional non-relativistic hydrodynamics
  12. Derivation of early-time velocity gradients

Figures (3)

  • Figure 1: (a) A qualitative illustration of the effect of the transverse Hall viscosity $\tilde{\eta}_\perp$ on a QGP fireball with elliptic flow. This viscosity couples vorticity to azimuthal shear, $T_{xx}-T_{zz}$, hence causing an elongation of the fireball due to longitudinal polarization. (b) A qualitative illustration of the effect the longitudinal Hall viscosity $\tilde{\eta}_\parallel$ on a QGP fireball with transverse polarization. This viscosity couples azimuthal to longitudinal shear, causing the fireball to spin, i.e. rotate perpendicular to the longitudinal vorticity.
  • Figure 2: Illustration of the distinct effect of the two Hall viscosities on the stress-energy tensor components $T^{\mu\nu}$ in response to different shear flows. The magnetic field points along the $y$-direction, the beamline is along $z$, and the fluid flow has been chosen to have a shear in either the $xz$-plane or the $xy$-plane.
  • Figure 3: Illustration of the effect of $\tilde{\eta}_\parallel$: Rotation around the $z$-axis induces a rotation around the $x$-axis. Left: The shear flow in the $xy$-plane generated by rotation around the $z$-axis is schematically displayed by blue arrows. Longitudinal Hall viscosity induces a stress response in the $zy$-plane, $T^{zy}$, indicated by the green arrows. Right: The stress response (shear flow), $T^{zy}$, is displayed in the $zy$-plane by green arrows, and the big arrow indicates the induced rotation around the $x$-axis resulting from that shear flow.