Hot and Dense QCD

T. Hatsuda (Univ. Tokyo)

Present (2001-):Two major experimentsto probe the early Universe

WMAP (2001-)

RHIC (2001- )

Future (2007-):LHC (CERN) & Planck (ESA)

Outline of this talkOutline of this talk

1. Origin of masses– a major challenge in modern physics

2. Recent progress in hot QCD– strongly interacting plasma

3. Recent progress in dense QCD– new phases dense matter

4. Summary

Origin of masses

“Origin of masses” Structure of the vacuum“Origin of masses” Structure of the vacuum

Cosmological constantEinstein (1917)

Universe

baryons

QCD condensateNambu (1960)

baryon

quark

EW condensateAnderson (1963)Englert-Brout, Higgs (1964)

quark

barequark

WMAP (2001-), Planck (2007-) RHIC (2001-), LHC (2007-) LHC(2007-)

Birth of QCDBirth of QCD

’65 SUc(3) YM theory as a model of strong interactionNambu (’65)

(Nobel foundation)

’65-’72 First indication of asymptotic freedomVanyashin & Terenteev (’65), Khriplovich (’69), ’t Hooft (’72)

Late ’60-early ’70 Discovery of quarks in DIS Friedman, Kendall & Tayler Nobel Prize 1990

’73 Discovery of asymptotic freedomGross & Wilczek, Politzer Nobel Prize 2004

’74 Discovery of heavy QCD bound state (J/ψ)Richter, Ting Nobel Prize 1976

Asymptotic freedom Asymptotic freedom

qqmqAtiqGGL aaa

a g −−∂+−= )(41

µµµµν

µν γ

Energy scale （ＧｅV)

Effective coupling(αs = ｇ２/４π）

αs

ColorConfinement

Asymptotic freedom

(int)/(kin) << 1

Asymptotic freedom = Pauli para-magnetismAsymptotic freedom = Pauli para-magnetism Nielsen (’81)Hughes (’81)

Electric property Magnetic property

QED > 1 (screening) < 1 (dia-magnetism)

QCD < 1 (anti-screening) > 1 (para-magnetism)

sum of Landau levels

BVacuum energy under uniform B

Pauli para-magnetismvs Landau dia-magnetism

Color confinement

Nobel foundation

Seven Prize Problems ($1 million allocated to each)

Important classic questions in mathematics that have resisted solution over the years (Clay Mathematics Institute, May 24, 2000)

1. Birch and Swinnerton-Dyer Conjecture2. Hodge Conjecture 3. Navier-Stokes Equations4. P vs NP5. Poincare Conjecture6. Riemann Hypothesis7. Yang-Mills Theory

Official description by A. Jaffe and E. Witten

Lattice QCD approach to confinementLattice QCD approach to confinement

Wilson (’74)

Lattice QCD simulationsLattice QCD simulations

Quenched QCDFull QCD

Integration : Monte Carlo with importance sampling

hypercube

slab

Why lattice ?

• Well defined QM (finite a and L) • Gauge invariant • Fully non-perturbative

0.1 fm 2-3 fm

Continuum and thermodynamic limits

• Equation of state of hot plasma• Phase transition (critical temperature, order etc)• Static and dynamic correlations near equilibrium

What one can do in principle

• Cold degenerate plasma • Phenomena far from equilibrium

What one cannot do (at present)

Examples (quenched QCD)Examples (quenched QCD)

R

0.5 fm 1.0 fm

Linear confining string

Bali, Phys. Rep. 343 (’01) 1

Heavy-quark bound states

CP-PACS, Phys. Rev. D65 (’02) 094508

2S+1LJ

Color Deconfinementn

T<Tc T~Tc T>Tc

http://boojum.hut.fi/research/theory/typicalpt.html

4HeH2Oλ

-line

QCD Phase DiagramQCD Phase Diagram

T

μB

Quark-Gluon Plasma

ColorSuperconductor

Hadronic Fluid

Vacuum

CriticalEnd point

Triplepoint ?

Equation of State at finite T (full QCD)Equation of State at finite T (full QCD)

Black-body radiation for massless particles :

Karsch, Lect.Notes Phys.583 (’02) 209

SB limit

Nf = 2

Nf = 2+1

Nf = 3

Tc = 173±8 MeV (Nf=2)= 154±8 MeV (Nf=3)

Fate of the color string (full QCD)Fate of the color string (full QCD)

Karsch, Laermann, Peikert, Nucl. Phys.B605 (’01) 579

T=0

Order of the finite T transitionOrder of the finite T transitionPisarski and Wilczek (’84)

Yaffe & Svetizky (’83)

m u,d

ms

1st

1st

cross over

2nd

∞

∞

Nf=3

Nf=2

Nf=1

Nf=0∞

0

(Quenched QCD)

μB QCD Phase DiagramQCD Phase Diagram

Colorsuperconductor

Quark-gluon plasma

~ 1 GeV

Hadronic fluid

Vacuum T ~ 170 MeV

Static plasma properties at T > Tc

QGP for g << 1 ( T >> 100 GeV )QGP for g << 1 ( T >> 100 GeV )

Inter-particledistance

Electric screening

Magneticscreening

1/T

1/gT

1/g2T

Relativistic plasma :

“Coulomb” coupling parameter :

Debye number :

S. Ichimaru, Rev. Mod. Phys. 54 (’82) 1071

Problems of high T perturbation

I. Strong coupling problem

g ~ 2 for T=200-400 MeV

badly behaved perturbation series

soft magnetic gluons are always non-perturbativeeven if g 0

pertubation theory

II. Non-Abelian magnetic problem

I. Strong coupling problemI. Strong coupling problem

T=100GeV T=1 GeV T=0.2 GeVQCD Pressure (Nf=4)

naive perturbation: meaningful only for T>100 GeV

II. Non-Abelian magnetic problem II. Non-Abelian magnetic problem

EOS : A. Linde, Phys. Lett. B96 (’80) 289

μ ν

magnetic screening :

“Debye” screening :

Kraemmer & Rebhan, Rept.Prog.Phys.67 (’04)351

QCD is non-perturbative even at T =∞ ( L3x(1/T) L3 )

soft magnetic gluons are always non-perturbativeeven if g 0 (T ∞)

pertubation theory from O(g6)

(mmag~ g2T)

Screening masses at T>Tc on the lattice Screening masses at T>Tc on the lattice

Quenched SU(3)20×20×32×6Lorenz gauge

m = gT

Nakamura, Saito & Sakai, Phys.Rev.D69 (’04) 014506

8133 ⊕=⊗

3633 ⊕=⊗

0.5fm0.25fm

243×6Lorenz gauge

T/Tc=3.04

Heavy quark “potentials” at T>Tc (quenched)Heavy quark “potentials” at T>Tc (quenched)

Nakamura & Saito, Prog.Theor.Phys.111, 112 (’04) hep-lat/0406038, 0404002

Heavy quark “potentials” at T>Tc (quenched)Heavy quark “potentials” at T>Tc (quenched)

8133 ⊕=⊗ 3633 ⊕=⊗

Dynamic plasma properties at T > Tc

Dynamic structure factor of the vacuumvacuum

γ*

PDG(’04)

plasma

γ*Dynamic structure factor of the plasma

system

probeMethod in lattice QCDMethod in lattice QCD

∫∫

=

= +

ωωωτ

ττ

dpAK

xdeJxJpD xpi

),(),(

)0,0(),(),( 3

r

rr rr

Maximum Entropy Method

latticeQCD data

knownkernel

spectral function= dynamic structure factor

Asakawa, Nakahara & T.H, Phys. Rev. D60 (’99) 091503 Prog. Part. Nucl. Phys. 46 (’01) 459

D = K×A

D A D A

Image reconstruction by MEM

D = K×A

D A D A

Image reconstruction by MEM

Quark-anti-quark ound state above Tc ? Quark-anti-quark ound state above Tc ?

charmstrange

Spec

tral

func

tion ρ

(ω)

J/ψ(3.1GeV)

1. J/ψ survivesup to 1.6 Tc

2. J/ψ disappears in 1.6 Tc < T < 1.7 Tc

see also,Umeda et al, hep-lat/0401010Datta et al., PRD 69 (’04) 094507

Asakawa & T.H., PRL 92 (’04) 012001

cc bound state above Tc (quenched) cc bound state above Tc (quenched)

Spec

tral

func

tion ρ

(ω)

J/ψ(3.1GeV)

1. J/ψ survivesup to 1.6 Tc

2. J/ψ disappears in 1.6 Tc < T < 1.7 Tc

see also,Umeda et al, hep-lat/0401010Datta et al., PRD 69 (’04) 094507

Asakawa & T.H., PRL 92 (’04) 012001

cc bound state above Tc (quenched) cc bound state above Tc (quenched)

ss bound state above Tc (quenched) ss bound state above Tc (quenched) A

(ω）/ω

2Mφ(T=0)=1.03 GeV

T/Tc= 1.4

Asakawa & T.H., Prog. Theor. Phys. Suppl. 149 (‘03) 42

Possible mechanisms of supporting “hadrons” above Tc

Possible mechanisms of supporting “hadrons” above Tc

1. Strong correlationsin JP=0+ (σ) and JP=0- (π) channels above Tc

Kunihiro and T.H., Phys. Rev. Lett. 55 (’85) 88

2. Dynamical confinementin all color singlet channels above Tc

DeTar, Phys. Rev. D32 (’85) 276

3. Strong Coulomb interactionin color singlet and non-singlet bound statesabove Tc

Shuryak and Zahed, Phys. Rev. D70 (2004) 054507Brown, Lee, Rho and Shuryak, Nucl. Phys.A740 (’04) 171

Shear viscosity (quenched)Shear viscosity (quenched)

1.0 1.5 2.0 2.5 3.0 T/Tc

Nakamura and Sakai, PRL 94 (’05) 072305

Baym, Monien,Pethick & Ravenhall (’90)

Arnold, Moore & Yaffe, (’03)

Kovtun, Son & Starinets (’04)

Viscous fluidR << 1

Perfect fluidR >> 1

“Reynolds number”

Possible structure of QCD plasmaPossible structure of QCD plasma

Chiral dynamics pQCDLattice QCD

RHIC, LHC

Weakly int.pion plasma

Strongly int.Resonanceplasma

Strongly int.q+g+”hadron”plasma

weakly int.q+g plasma

q+g plasma

viscous fluid ?perfect fluid ?

Relativistic Hydrodynamcsfor High-Energy Hadron Collisions

Relativistic Hydrodynamcsfor High-Energy Hadron Collisions

Expansion

Freezeout(T = 1.95 K neutrino)T = 2.73 K photon

Tchem = 170 MeVTtherm = 120 MeV

ObservablesCMB & anisotropy(CνB, CGB & anisotropy)

Collective flow & anisotropyJets, leptons, photons

Big Bang Mini Bang

Initial state Inflation ? (10-35 sec) Color glass ? (10-1 fm)

Thermalization Inflaton decay decoherence

Parametersto be

determined

8~10 cosmological parameters・ Initial density fluctuation・ Cosmological const. Λ etc

QGP parameters・ Initial energy density・ Equation of state etc

Evolution Code e.g. CMBFAST 3D-hydro ?

WMAP: Astrophys. J. Suppl. 148 (2003) 1, 175

Precision cosmologyPrecision cosmology

CGC + 3D-hydro + jet simulationCGC + 3D-hydro + jet simulation Hirano and Nara, nucl-th/0404039

-- First complete & sucessful study from intial to final --

Au+Au sNN1/2 = 200 GeV

Extract QGP parameters with errors

Dense QCD

10 km

？

？

N. Itoh (’70), E. Witten (’84)Baade-Zwicky (’34)

T

μB

Quark-gluon plasma

~ 1 GeV

Hadronic fluid

Vacuum

Colorsuperconductor

High density QCD High density QCD

~ 170 MeV

Color Superconductivity in Quark MatterColor Superconductivity in Quark Matter

Variety of phasesCFL, 2SC, dSC, uSCgapless phase, …

1. Highly relativisiticLong range magnetic int.

2. Color-flavor entanglement

Major differences from BCS

High Tc superconductorTc/pF ~ 0.1

Compact Cooper pairsize ~ 1-10 fm

Three fundamental phases in quark matterThree fundamental phases in quark matter

∆ 3

∆1

∆ 2

CFLdSC

2SC

(ds)

(us)

(du)

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

∆∆

∆=∆

3

2

1

000000

ia

2SC: Bailin, Love, Phys. Rep. 107 (’84)CFL : Alford, Rajagopal, Wilczek, Nucl. Phys. B537 (’99)dSC: Iida, Matsuura, Tachibana & Hatsuda, Phys. Rev. Lett. 93 (’04)

T

μB

~ 1 GeV

Hadronic fluid

Vacuum

High Density QCDHigh Density QCD

CFL

2SC

dSC

~ 170 MeV

μBdq

ξc

Abuki, Itakura & T.H., PRD65 (’02)

100

101

102

103

104

105

⌧ c/d

q

103 104 105 106

[MeV]

to BEC ?

BCS

pF(MeV)

ξc/dq

BCS BEC RBECcrossovers ?

Nishida and Abukihep-ph/0504083 (’05)

40K : JILA, PRL 92 (2004) 0404036Li : Innsbruck, PRL 92 (2004) 120401

MIT, PRL 92 (2004) 120403

40KCond. of Fermionic-Atom Pairs

N0/N = 1% 5% 10%

Neutron Star StructureNeutron Star Structure

M-R relation in APR EoSM-R relation in APR EoS (ρmax ～ 6ρ0)

Vela-X1Cyg-X2

PSR1913+16

J0751+1807

Neutron starbinary

X-ray binaries

Neutron star- WD binary

EXO0748-676(X-ray bursts)

astro-ph/0411207 i

Nature 420 (’02)

M-R relation in APR EoS + CFL quark matter M-R relation in APR EoS + CFL quark matter

Free QM

Int. QM

Alford et al., nucl-th/0411016

Cooling of neutron stars Cooling of neutron stars St

anda

rdEx

otic

quen

chin

g

n superfluidityQ color super

exp(-Δ/T)

Cooling of neutron stars Cooling of neutron stars St

anda

rdEx

otic

quen

chin

g

n superfluidityQ color super

exp(-Δ/T)

log (time/yr)

log (Ts /K

)log

(Ls /(e

rg/s

))

Weber, astr-ph/0407155 (’04)

Future Experimental Facilities for hot/dense QCDFuture Experimental Facilities for hot/dense QCD

LHC (2007-)

2.8 TeV/A

・ Hottest matter ・ Precision QGP

J-PARC (2007-)

50 GeV PS

Phase I・ Dense mesic nuclei・ Exotic hadrons

Phase II・ Primary beam phys.

SIS100/300 (201? -)

90 GeV PS

・ Densest matter ・ In-medium hadrons

SummarySummary

Hot QCD is becoming a mature field

(3+1)-dim.Hydro. Code

pQCD (jet, CGC)

LQCD (EoS, SPF)

Heavy Ion data

Key questions

1. Why & how thermalization happens? Perfect fluid ?

2. How complex is QGP ? How we can characterize it ?

3. Direct evidence of the evaporation of QCD condensates ?

RHIC LHC : temperature scan, precision QGP

Big Bang

(1992-)

SPS (1994-)

(2001-)

RHIC (2001-)

Planck (2007-)

LHC (2007-)

Q.G

.P.

Little Bang

Dense QCD is still an open field

BoseNova (JILA)BCS-BEC (JILA)

1. New phases in color superconductor, e.g. CFL, 2SC, dSC (how to access?)

2. Transition from HM QM still unclear(need new idea to solve dense QCD)

3. Obs. progresses in studying M and R of the neutron stars (2 solar mass?)

4. Common physics with atomic condensates (e.g. BCS-BEC crossover)

Present and future

1. What is quark-gluon plasma

Part I. Basic Concept of Quark-Gluon Plasma:

2. Introduction to QCD3. Physics of quark-hadron phase transition 4. Field theory at finite temperature 5. Lattice gauge approach to QCD phase transitions 6. Chiral phase transition 7. Hadronic states in hot environment

Part II. QGP in Astrophysics:

8. QGP in the early universe9. Compact stars

Part III. QGP in Relativistic Heavy Ion Collisions:

10. Introduction to relativistic heavy ion collisions 11. Relativistic hydrodynamics for heavy ion collisions 12. Transport theory for pre-equilibrium process 13. Formation and evolution of QGP 14. Fundamentals of QGP diagnostics 15. Results from CERN-SPS experiments 16. First results from BNL-RHIC 17. Detectors in relativistic heavy ion experiments

Appendices A-H: 120 Exercises

to appear in a few months

Дякую !

Back up slides

Quark flavorsQuark Flavors Quark Flavors

Heavy quarks mc~1.5 GeVmb~5 GeVmt~178 GeV

Light quarks

mu~3MeVmd~7MeVms~100MeV

Tc ~ 170 MeVμc ~ 400 MeVms~100MeV

same order

More on QCD Phase Transition at finite T (full)More on QCD Phase Transition at finite T (full)

(i) String fluctuation and breaking(ii) Restoration of broken symmetries

)1()3()3( BRL USUcSU ×× +

0≠qq

low D : Hadronic phase

Low T

2)3( ZSU RLC ×++

0≠qq

high D : color supercond.

Low T

)1()]3()3([)3( BRLC USUSUSU ×××Quark gluon plasma

High T

?

Pisarski & Wilczek, PRD29 (’84) e.g. Matsuura, Iida, Baym and T.H.,PRD69 (’04)

H2O

4He 3He

PhaseDiagrams

PhaseDiagrams

http://boojum.hut.fi/research/theory/typicalpt.html

sign problem:

Dense QCD (T~0, μ large)Dense QCD (T~0, μ large)

Complex

Complete new idea necessary

History of our Universe

History of our Universe