Quark Matter Under Extreme Conditions

Neda SadooghiSharif University of Technology

Tehran-IranMunich-January 2011

Force Strength

Theory Mediator

Strong 1 Chromodynamics Gluon

Electromagnetic

10-2 Electrodynamics Photon

Weak 10-7 Flavordynamics W+, W-, Z0

Gravitational 10-39 Geometrodynamics

Graviton

Four Fundamental ForcesStrong nuclear force Electromagnetic force

Weak nuclear force Gravitational force

Theory of Everything

Standard Model of Cosmology

Big Bang

1019 GeV 1014 GeV 100 GeV ~10-4 eV

Inflationary Epoch

QCD Phase Transition

100 MeV

QGP

EW Phase Transition

Interaction Couples to Gauge Bosons

Mass (GeV/c2)

Strong Color charge Gluon 0

Electromagnetic

Electric charge

Photon 0

Weak Weak charge W+, W-, Z0 ~100

Standard Model of Particle Physics

Fermions

Family E- Charge

Color Weak Isospin

Spin

1 2 3 LH RH

Leptonsνe νμ ντ 0 - 1/2 - 1/2e μ τ -1 0

Quarksu c t +2/3 r g

b1/2 0 1/2

d s b -1/3 0

SU(3) x SU(2) x U(1)

Quark flavors Quark colors

Quantum Electrodynamics (QED) describes the force between electrically charged particles in terms of exchange of massless and neutral photons

Elementary process (three point vertex):

QED vs. QCD

Quantum Electrodynamics (QED)

QED vs. QCD

Coulomb Repulsion

Coulomb Attraction

QED vs. QCDQuantum Chromodynamics (QCD)

Elementary process(es)

Gluons carry color-charge

Gluon-Gluon Self-Interaction

QED vs. QCDFlux Lines

Electric flux between a pair of equal and opposite charges Dipole field pattern

Chromoelectric flux between a quark and an antiquark Flux tube

Quantum Chromodynamics (QCD) Static potential between a quark-antiquark pair

QED vs. QCD

r 0 ↷ A(r) 0 ↷ V(r) 0

Asymptotic Freedom

rrrArV )()(

rrA

ln1)(

fmMeV /880~

Small r

Large r

String Tensionσ~ 880 MeV/fm

A force sufficient to lift three elephants !!!

Hadrons: Mesons and Baryons

Confining Potential Hadrons are color singlet

Color Confinement

Helicity:

For massless particles, helicity and chirality are the same

Right handed particles have positive helicity (chirality) Left handed particles have negative helicity (chirality) Up and down quarks can be regarded as massless A

theory including only up and down quarks should be symmetric under global chiral transformation

Chiral SymmetrySpontaneous Chiral Symmetry Breaking

QCD at low energy ∋ (u,d)

Proton

Neutron

Pion

Spontaneous Symmetry Breaking

Spontaneous Chiral Symmetry Breaking:(Pseudo) Goldstone Mechanism: SUL(2)

x SUR(2)

SUL+R(2)π+

π-π0

The mysteries of Mexican Hat Potential

15

Standard Model of Cosmology

Big Bang

QCD Phase Transition

100 MeV

QGP

QCD phase transition at TQCD~2.4 x1012 K~ 200 MeV

Extreme Temperature

Core of our Sun ~ 1.57 x 107 K ~1.3 keV

Room temperature ~ 27 C ~ 300 K ~ 25 meV

NTe

mpe

ratu

re

Baryonic Chemical Potential

d

u

ss

d

u u

s

d

s

d

u

u

d

s

u s

d

us

ud

sd

QCD Phase Diagram

Hadronic Phase

Quark Gluon Plasma Phase

Color Superconducting phase

Confinement-

Deconfinement phase transition

Tc~170 MeV

Chiral Symmetry Restoratio

n

Earl

y U

nive

rse

RHI

C

LHC

SP S

2SC CFL

Neutron Stars

Hadron gas Nuclear Matter

Hadronic Fluid

μc~310 MeV

Neutron stars:Laboratories of Matter

under Extreme Conditions

Neutron star is a type of stellar remnant that can result from gravitational collapse of a massive star during a supernova event

When a giant star dies, it can collapse into a black hole or implode into an ultra-dense neutron star

Pauli exclusion principle supports the neutron star against further collapse (they are made almost entirely of neutrons)

Neutron Stars Natural laboratory for extreme conditions

Neutron Stars: Structure

Outer crust 0.3-0.5 kmIons and electrons

Inner crust 1-2 kmElectrons, neutrons,

nuclei

Outer core ~9 kmNeutron-proton Fermi

liquidFew % electron Fermi gas

Inner core 0.3 kmQuark-Gluon Plasma/

CFL Color Superconductor ???

0.3-0.4 ϱ0

0.5-2.0 ϱ0

>2ϱ0

Neutron star radius: 12 km

Radius 6.4x103 km ~6.96 x105 km 12 km

Mass 6x1024 kg 2x1030 kg 2.4x 1030 kg

Density 5 g/cm3

(Mean density)

162.2 g/cm3

(Core) 2.7 x1014 g/cm3

(Core)

Surface gravity

g ~28 g 7x1011 g

Escape velocity

11 km/s 617.7 km/s 1.3x105 km/s

Temperature(Core)

5700 K 1.57 x 107 K 1011 K~ 1-10 MeV

108 x Earth

~3x106 x Earth

56 x Earth

1.2-2 Solar mass

~104 Solar T

1/3 c

Neutron Stars

Extreme Density

kg12105.5 900

Neutron Stars:Pulsars

Pulsars are highly magnetized, rotating neutron stars that emit a beam of electro-magnetic radiation

Because neutron stars are very dense objects, the rotation period and thus the interval between observed pulses is very regular Atomic Clocks

The observed periods of the pulses range from 1.4 msec to 8.5 sec

Extremely large magnetic fields MagnetarsSurface: B~1014-1015 GInner field: B~1018-1020 G

 

0.6 G100 G

4000 G

4.5 X 105 G~ 45 T

108 G

1014-1015 G

1018-1020 G

Measured at the magnetic pole The Earth’s B fieldHand-held magnet

The magnetic field in strong sunspots

The strongest, sustained magnetic fields

achieved in the labThe strongest fields ever detected on non-neutron

stars

Typical surface magnetic fields of radio

pulsars

Magnetars: Inner fields

Like those used to stick papers on a refrigerator

Within dark, magnetized areas on the solar surface

Generated by huge electromagnets

Strongly-magnetized, compact white dwarf stars

The most familiar kind of neutron star

Soft gamma repeaters and anomalous

X-ray pulsars

Extreme Magnetism

Vacuum Birefringence (double refraction)Polarized light waves change speed and hence wavelength when they enter a very strong magnetic field

Photon SplittingX-rays split in two or merge together. This process is important in fields stronger than 1014 G

Scattering SuppressionA light wave can glide past an electron with little hindrance if the field is large enough to prevent the electron from vibrating with the wave

Distortion of AtomsFields above 109 G squeeze electron orbitals into cigar shapes. In a 1014 G field, a hydrogen atom become 200 times narrower

Effects of Extreme Magnetism

Calcite crystal: Some letters showing the double refractionLiquid Crystal Displays are also birefringent

NTe

mpe

ratu

re

Baryonic Chemical Potential

Effects of Extreme Magnetism on Quark Matter

Hadronic PhaseChiral-SB phase

Quark Gluon Plasma Phase

Color Superconducting phase

Tc~170 MeV

Earl

y U

nive

rse

RHI

C

LHC

Neutron Stars

Relativistic Heavy Ion Colliders

Center of mass energy √s=200 AGeV for Au+Au collision

Collision with 99.7% speed of light Ultra-RHIC The energy density

ε= 5.5 GeV/fm3

The pressure generated at the time of impact 1030 atmospheric pressure

Question:Deconfinement Phase Transition

Color Glass Condensate (CGC) sheets

Initial singularity at the time of collision

Glasma phase (Out of Equilibrium Physics)

Not expected: Strongly correlated QGP (Perfect Fluid)

Mixed phase (quarks, gluons and hadrons)

Hadron Gas

?

CGC

Initial Singularity

Glasma

sQGP

Hadron Gas

?

Big Bang vs. Little Bang:

The evolution of matter produced in the Little Bang is comparable with the Big Bang (same evolution equations)

t=10-21-10-20sec

t=10-22-10-21sec

t=0-10-22sec

Perfect Liquid: Strongly Correlated QGP

Electric Plasmam- strongly correlated ??Deconfinement

Dual superconductivitym-correlatione-confined

Magnetized Plasmae-strongly correlated

Confinement

sQGP

(Color) Superconductivitye-correlationm-confined ??

CS

T

μB

T~ 2 Tc

Idea supported by the conjecture of AdS/CFT duality

Tc

1101.1120 Shifman et al

Chiral Magnetic Effect

Parity Violation in QCD Strong CP ProblemQuestion: Is the world distinguishable from its mirror image?Answer(s): Weak interaction violates P and CP Strong interaction: Experimentally: No evidence of global strong CP violation

C: Matter↔Antimatter

P: Mirror symmetry

Neutron’s EDM ~ 0Theoretically: QCD θ ≠ 0 ( topological charge)

Experimental bound for θ < 3x10-10 Strong CP problemThe existence of topological charge Matter-Antimatter asymmetry in the Early Universe !!

Chiral Magnetic Effect

Local (event by event) P and CP Violation in QCDTheory: Fukushima, Kharzeev, Warringa, McLerran, (2007-09)Lattice: Polikarpov et al. (2009-10)B~L→ →

Charge separation stems from the interpaly between the strong magnetic field in the early stage of heavy ion collision and the presence of topological configurations in hot matter

BJ

~

Charge separation Electric current

QGP in the deconfined phase

Chiral Magnetic Effect

Local Parity Violation in QCD Chiral magnetic Effect

B

uR

uL

p

dR

dL

dR

uR

uR

dR

0

L RCharge SeparationBJ

~

Chiral Magnetic Effect

RHICNon-Central HIC

√sNN ~ 200 GeV b~4 fm eB ~1.3 mπ2 ↷ B~ 4x1018

G

LHCNon-Central HIC

√sNN ~ 4.5 TeV b~4 fm eB ~15 mπ2 ↷ B~ 5x1019

G

D.E. Kharzeev, L.D. McLerran, and H.J. Warringa (0711.0950)

Very Strong Magnetic FieldRHICNon-Central HIC

√sNN ~ 200 GeV b~4 fm eB ~1.3 mπ2 ↷ B ~ 4x1018

G

1019 Gauss

1014 Gauss

eB (M

eV2 )

The strength of B is comparable with Magnetic Field in Neutron Stars

N

Tem

pera

ture

Baryonic Chemical Potential

Hadronic PhaseChiral-SB phase

Quark Gluon Plasma Phase

Color Superconducting phase

Tc~170 MeV

RHI

C

LHC

Neutron Stars

Effect of Strong Magnetic Fields on Color Superconductivity

Effect of Strong Magnetic Fields on Color Superconductivity

QED Superconductivity vs. Color Superconductivity

q

qIngredients: (QED) A liquid of fermions with electric charge(QCD) Quarks with electric and color charges

(QED) An attractive electromagnetic interaction between the fermions (QCD) An attractive strong interaction between two quarks (QED) Low temperature: T<Tc

(QCD) Low temperature: In neutron stars T<100 MeV ≪ Big Bang T~1019GeV

(QED) QED Meissner Effect Photons acquire mass (QCD) QCD Meissner Effect Gluons acquire mass

Results:

Effect of Strong Magnetic Fields on Color Superconductivity

Effects on QCD Phase Diagram (I):Sh. Fayazbakhsh and NS: PRD (2010)

NormalChSB CS

C

Normal

CSC

ChSB

NormalChSB

CSC

NormalNormal

ChSB

ChSB

ChSB

Effect of Strong Magnetic Fields on Color Superconductivity

Effects on QCD Phase Diagram (II):

De Haas-van Alphen oscillations before the system enters the regime of LLL dominance

Low μ: Only chiral phase transion

2nd order phase transition from chiral SB to the Normal phase

Effect of Strong Magnetic Fields on Color Superconductivity

Effects on QCD Phase Diagram (III):Low T: Chiral and Color phase transions

Results1. The type of the phase transition between chiral SB and

the Normal phase changes with B: 2nd Order 1st Order

2. Increasing B has no effect on the type of phase transition between the color symmetry breaking and the normal phase (2nd order)

3. De Haas-Van Alphen oscillations CSC-Normal-CSC phase transition

4. For eB>eBt: The effect of T and μ are partly compensated by B

5. For eB>eBt ~ 0.5 GeV2: System is in the LLL dominant regime

Effect of Strong Magnetic Fields on Color Superconductivity

Effects on QCD Phase Diagram (II):Intermediate μ: Chiral and Color phase transions

45

Effect of Strong Magnetic Fields on Color Superconductivity

Effects on QCD Phase Diagram (II):Large μ: Only Color phase transion

Effect of Strong Magnetic Fields on Color Superconductivity

Effects on QCD Phase Diagram (III):Intermediate T: Chiral and Color phase transions

Effect of Strong Magnetic Fields on Color Superconductivity

Effects on QCD Phase Diagram (III):Large T: Only Chiral phase transion