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

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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


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

    v_12 has a maximum at T~0.4-0.45 Tc

    v_12 remains constant for T>Tc


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

    v_13 has, independent on θ, a minimum at T~0.4-0.45 Tc

    v_13 remains also constant for T>Tc


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