The speed of sound in a magnetized hot Quark-Gluon-Plasma

Based on: 0905.2097

Neda SadooghiDepartment of Physics

Sharif University of TechnologyTehran-Iran

MIDEAST 2009

QCD Phase Diagram

Main Goals:• Physics of the Early UniverseIn 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 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 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 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])

Trace anomaly Є-3P The speed of sound V

s d

dPc

2

KEYWORD: THERMAL EQUILIBRIUM (Time plays no major role)

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

The sQGP phase behaves as a nearly perfect fluid Jet quenchingElliptic 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

100

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:

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

– 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 Method

– Extend the thermodynamical and hydrodynamical relations Chiral Magnetohydrodynamical (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_sWhat we expect here:1. An anisotropy in the velocity distribution in this medium due to the

presence of a fixed external magnetic field2. Similar T dependence of v_s as was observed in Lattice QCD

• v_12 has a maximum at T~0.4-0.45 Tc• v_12 remains constant for T>Tc

• v_13 has, independent on θ, a minimum at T~0.4-0.45 Tc • v_13 remains also constant for T>Tc