HYDRODYNAMICS AND HEAVY ION COLLISIONS

1
HYDRODYNAMICS AND HEAVY ION COLLISIONS

• EFFECT OF SPONTANEOUS BREAKING OF CHIRAL SYMMETRY

Frankfurt, NCRH2007, April 2007
2
INTRODUCTION

• IDEAL HYDRODYNAMICS
• Available at local equilibrium
• ? after thermalization
• Mean free path small compared to system size
• ? before freeze-out
• Small  window ???
• No most of the experimental data at RHIC
• are well described

3
INTRODUCTION

• HYDRODYNAMICS
• Quark-gluon phase
• strongly interacting particles (? small
  viscosity)
• ? / s lower bound reached? (µ 0)
• Same quantity for the hadronic phase
  information on transition temperature?

4
INTRODUCTION

• ULTRARELATIVISTIC HEAVY ION COLLISIONS
• Hadron gas pion gas
• ? symmetry breaking
• ?modification of hydrodynamics!
• Why increase the number of hydrodynamical modes
  Goldstone modes

5
HYDRODYNAMICS AND SYMMETRY BREAKING
BASICS

• Hydrodynamics
• Local equilibrium (time and length scales)
• Collective modes (infinite relaxation time when k
  0)
• Conserved quantities / Goldstone modes

6
HYDRODYNAMICS AND SYMMETRY BREAKING
HYDRODYNAMICS MODES
CONSERVED QUANTITIES

7
HYDRODYNAMICS AND SYMMETRY BREAKING
HYDRODYNAMIC MODES
GOLDSTONE MODES

8
HYDRODYNAMICS AND SYMMETRY BREAKING
HYDRODYNAMIC EQUATIONS
Normal fluid Superfluid Chiral fluid ?
Hydrodynamic equations particles, momentum,
entropy

9
HYDRODYNAMICS AND SYMMETRY BREAKING
HYDRODYNAMIC MODES

Normal fluid 5 modes Superfluid 5 1
(breaking of U(1)) second
sound Chiral fluid 14 modes !!! (breaking of
SU(2)L X SU(2)R )
10
HYDRODYNAMICS AND SYMMETRY BREAKING
RELATIVISTIC HEAVY ION COLLISIONS
Temperature profile

ideal
11
HYDRODYNAMICS AND SYMMETRY BREAKING
DISSIPATION
1/ Introduce dissipative terms 2/ Compute entropy
production 3/ Determine dissipative fluxes
Normal fluid 3 coefficients Superfluid 5
coefficients Chiral fluid 39 coefficients

12
HYDRODYNAMICS AND SYMMETRY BREAKING
DISSIPATION
Spontaneous fluctuations around equilibrium

• Fluctuations to
• reach equilibrium

• Relation between transport coefficients
  and correlation function

Example shear viscosity
13
HYDRODYNAMICS AND SYMMETRY BREAKING
SHEAR VISCOSITY
Correlation function
Boltzmann
14
HYDRODYNAMICS AND SYMMETRY BREAKING
CONCLUSION

• Spontaneous symmetry breaking ? modification of
  hydrodynamics (Goldstone modes)
• 11 D Bjorken model no quantitative effect
• Near the transition point other modifications!