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The speed of sound in a magnetized hot Quark-Gluon-Plasma Based on: 0905.2097. Neda Sadooghi Department of Physics Sharif University of Technology Tehran-Iran MIDEAST 2009. QCD Phase Diagram. Main Goals: Physics of the Early Universe In general

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the speed of sound in a magnetized hot quark gluon plasma based on 0905 2097

The speed of sound in a magnetized hot Quark-Gluon-PlasmaBased on: 0905.2097

NedaSadooghi

Department of Physics

Sharif University of Technology

Tehran-Iran

MIDEAST 2009

qcd phase diagram
QCD Phase Diagram

Main Goals:

  • Physics of the Early Universe

In general

  • Behavior of nuclear matter under extreme T,μ,B,E …

Specific Goals:

  • Interplay between various phase transitions
    • Confinement-Deconfinement
    • Chiral Symmetry Restoration

Two different aspects:

  • Static aspects
  • Dynamical aspects
qcd phase diagram1
QCD Phase Diagram

Static aspects:

  • Thermodyn. properties of new phases

T dependence of

    • Energy density
    • Pressure

 Various aspects of phase transition

  • Type of phase transitions
    • 1st order phase transition
    • 2nd order phase transition
  • Position of the critical end points
    • Critical T, μ
qcd phase diagram2
QCD Phase Diagram

Static aspects:

Nonperturbative Methods (low energy physics)

  • Lattice QCD
  • Thermal Field Theory

Phenomenological Model Building

    • Hadron resonance gas model  Statistical Model
    • Linear and nonlinear sigma model  Chiral (effective) Field Theory
    • Polyakov-NJL model  Chiral (effective) Field Theory + Lattice QCD
qcd phase diagram3
QCD Phase Diagram

Static aspects:

Lattice QCD (deficits)

  • It is difficult to implement dynamical (physical) quarks
  • It is difficult to implement a finite and large μ in MC calculations

Nevertheless:

Lattice QCD predictions

Tc =180-200 MeV

Crossover

 Trace anomaly Є-3P

(Bazavov et al., 0903.4379 [hep-lat])

lattice qcd predictions bazavov et al 0903 4379 hep lat
Lattice QCD Predictions (Bazavov et al., 0903.4379 [hep-lat])

Trace anomaly Є-3P

The speed of sound

KEYWORD: THERMAL EQUILIBRIUM

(Time plays no major role)

qcd phase diagram4
QCD Phase Diagram

Dynamical (non-equilibrium) aspects:

Methods

  • Real-time thermal field theory
  • Relativistic hydrodynamics (Rel. fluid dynamics  Landau ‘1950)
    • Non-dissipative (non-viscous) hydrodynamics
    • Dissipative hydrodynamics

Transport properties

T-dependence of shear and bulk viscosities

T-dependence of the speed of sound

 e.g. Study the new strongly correlated QGP phase created at RHIC

rhic relativistic heavy ion collider
RHIC: Relativistic Heavy Ion Collider

 The sQGP phase behaves as a nearly perfect fluid

    • Jet quenching
    • Elliptic flow
  • Au-Au collisions with the energy of 100 GeV per nucleon
  • The motion of particles is relativistic
  • The nuclei are Lorentz contracted by a factor of
  • Enormous entropy production (~7000 particles are produced)
  • Very short equilibration time ~6 fm/c
rhic relativistic heavy ion collider1
RHIC: Relativistic Heavy Ion Collider
  • Magnetic field production in off-central HI collisions
    • Due to very large relative angular momentum
    • Due to electrically charged ions in the initial state, and due to the electric charge asymmetry in the distributions of the produced hadrons

(Kharzeev et al. 2007)

  • The produced magnetic field is perp. to the reaction plane

 Event to event P and CP violation (Kharzeev et al. 2008)

our goal here
Our goal here:

Study the effect of a constant and strong magnetic field on the speed of sound in a magnetized hot QGP

N.S., 0905.2097 [hep-ph]

our method
Our Method
  • Consider an effective field theory model of QCD (NJL model) in the presence of a constant (fixed) and strong magnetic field
  • Integrate out the fermions  An effective theory in a background strong magnetic field and consisting of massive mesons
  • The mesons are massive due to dynamical chiral symmetry breaking in the presence of strong magnetic field [Magnetic Catalysis]
  • The resulting system can be regarded as a magnetized fluid consisting of massive mesons and exhibiting chiral phase transition at some Tc 

It mimics a magnetized hot QGP near the chiral critical point

our method1
Our Method
  • Extend the thermodynamical and hydrodynamical relations  ChiralMagnetohydrodynamical (CMHD) formulation
  • Performing a 1st order stability analysis  Dispersion relation of plane waves propagating in this magnetized hot medium
  • Linearizing the dispersion relation  Speed of sound v_s

What we expect here:

  • An anisotropy in the velocity distribution in this medium due to the presence of a fixed external magnetic field
  • Similar T dependence of v_s as was observed in Lattice QCD
slide13
v_12 has a maximum at T~0.4-0.45 Tc

v_12 remains constant for T>Tc

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