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Universal properties of bulk viscosity near the QCD phase transition

F. Karsch, D. Kharzeev, K. Tuchin

Abstract

We extract the bulk viscosity of hot quark-gluon matter in the presence of light quarks from the recent lattice data on the QCD equation of state. For that purpose we extend the sum rule analysis by including the contribution of light quarks. We also discuss the universal properties of bulk viscosity in the vicinity of a second order phase transition, as it might occur in the chiral limit of QCD at fixed strange quark mass and most likely does occur in two-flavor QCD. We point out that a chiral transition in the O(4) universality class at zero baryon density as well as the transition at the chiral critical point which belongs to the Z(2) universality class both lead to the critical behavior of bulk viscosity. In particular, the latter universality class implies the divergence of the bulk viscosity, which may be used as a signature of the critical point. We discuss the physical picture behind the dramatic increase of bulk viscosity seen in our analysis, and devise possible experimental tests of related phenomena.

Universal properties of bulk viscosity near the QCD phase transition

Abstract

We extract the bulk viscosity of hot quark-gluon matter in the presence of light quarks from the recent lattice data on the QCD equation of state. For that purpose we extend the sum rule analysis by including the contribution of light quarks. We also discuss the universal properties of bulk viscosity in the vicinity of a second order phase transition, as it might occur in the chiral limit of QCD at fixed strange quark mass and most likely does occur in two-flavor QCD. We point out that a chiral transition in the O(4) universality class at zero baryon density as well as the transition at the chiral critical point which belongs to the Z(2) universality class both lead to the critical behavior of bulk viscosity. In particular, the latter universality class implies the divergence of the bulk viscosity, which may be used as a signature of the critical point. We discuss the physical picture behind the dramatic increase of bulk viscosity seen in our analysis, and devise possible experimental tests of related phenomena.

Paper Structure

This paper contains 10 sections, 25 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Kubo's formula for bulk viscosity
  3. Low energy theorems at finite $T$
  4. Bulk viscosity from the lattice data
  5. Spectral density
  6. Uncertainties of the method
  7. Universality
  8. The case of zero baryon density
  9. Chiral Critical Point
  10. Summary and discussion

Figures (1)

  • Figure 1: Bulk viscosity in the high temperature phase of QCD versus temperature in units of the transition temperature. Part (a) of the figure shows various contributions to $9\omega_0(T)\zeta/Ts$ given in (\ref{['ze']}). In part (b) of the figure we show the bulk viscosity in units of the entropy density for $\omega_0 = 0.5,\, 1,\, 1.5$ GeV (top to bottom) which reflects the uncertainty in the determination of this scale parameter.