High Density QCD

H2O

T. Hatsuda(Univ. Tokyo)

Outline
Outlineofof thisthistalktalk

1. Phase structure of QCD– what we know and what we do not know
2. Phases in hot QCD
3. Phases in dense QCD
4. Future
5. Summary

Quantum
Quantum phases
phasesof
of
33He & 44He
He & He

4He

H2O

3He

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

Phases
Phasesin
inQCD
QCD?? ––aaschematic
schematicpicture
picture----QGP (quark-gluon plasma)~170 MeV

χSB(chiral symmetry breaking)

CSC (color superconductivity)~1 GeVTheoryTheorybehind:behind:Quantum
Quantum Chromo
ChromoDynamics
Dynamics
1965 SUc(3) YM theory as a model of strong interactionaColor
L = − 14 GµνGaµν + qγ µ (i ∂µ − g t a Aµa )q − mqq
Nambu (’65)
Confinement
Running coupling(αs = ｇ２/４π）

1965-1972 Precursors of asymptotic freedom
Vanyashin
αs & Terenteev (’65), Khriplovich (’69), ’t Hooft (’72)

1973 Discovery of asymptotic freedom
Gross & Wilczek, Energy
Politzer(’73)
scale（ＧｅV)

Asymptoticfreedom(int)/(kin) << 1Origin
Originofof each
each“phase”“phase”
strong residual force
 pre-formed pairs

Asymptotic freedom+ Debye screening deconfinement

Hatsuda & Kunihiro,
Phys.Rev.Lett. 55 (1985)

Collins & Perry,Phys.Rev.Lett. 34 (1975)

QGP

χSB

quark - anti-quark pairing
 chiral instability
Nambu & Jona-Lasinio,
Phys.Rev. 122 (1961)

CSC

quark-quark pairing
 Cooper instability
Bailin & Love,
Phys.Rep.107 (1984)

Symmetry
Symmetryofof eacheach“phase”“phase” (case(caseforforsmallsmallmmududwithwith mmss=∞)=∞)
SUC (3) ×[SUL (2) × SUR (2)]×UB (1)

QGP

χSB

CSC

SUC (3) × SU L+ R (2) ×U B (1)~SUC (2) ×[SUL (2) × SUR (2)]×U B+C (1)qq ≠ 0qq ≠ 0

Similarity
Similaritywith
withhigh
highTTccsuperconductors
superconductors

QGP

χSB

CSC

Bi2Sr2CaCuO8+δ

1. insulator – superconductor transition
2. strong coupling  pre-formed pairs?
3. similar physics in “cold-atoms” tooHighlyundedoped

HTS – BEC – QCD connection ?
• Babaev, PRD (’00)• Abuki, Itakura & Hatsuda, PRD (’02)• Kitazawa, Koide, Kunihiro & Nemoto, PRD (’02)• Chen, Stajic, Tan & Levin, Phys. Rep. (’05)

optimally
doped

underdoped

Experimental/Observational
Experimental/Observational probes
probesHeavy ion collisions• low energies : (1-20) GeV/A,

SIS (GSI), AGS (BNL), SPS (CERN)SIS100/300 (GSI), J-PARC (Japan)

 dense matter• high energies : (200-) GeV/A, hot matter

RHIC (BNL), LHC (CERN)

Compact stars : dense matterPhases in hot QCD
BRAHMSPHOBOSQGP

1.2 kmPHENIXSTARχSB
STAR@RHICCSC
QCDPAXEquation
Equationof
ofstatestate(EoS)(EoS) (lattice(latticeQCDQCDsimulation)
simulation)
Ideal gaslimit

Nf = 3
Nf = 2+1
Nf = 2

Karsch,Lect.Notes Phys.
583 (’02) 209

1. Crossover for (2+1)-flavors
SPS

2. Tc = 173±8 MeV(massless Nf=2)
RHIC
εcrit = 1.2 GeV/ fm3

LHCby CP-PACS., Columbia and Bielefeld groupsプラズマ診断
プラズマ診断ハドロン放出熱・化学平衡エネルギー密度
流体発展
火の玉サイズ

γ線
内部温度
プラズマ反応過程

レプトン対
カイラル対称性
色デバイ遮蔽

ジェット放出時空発展
e.g. Relativistic hydrodynamics-- full (3+1)-dim. Simulations -Hirano, PRL86 (’01), Hirano & Nara, PRL91 (’03)

プラズマ密度• Asakawa & Hatsuda,
Phys. Rev. Lett. (’04)• Nakamura & Sakai,Phys. Rev. Lett. (’05)

LHC, RHIC

Lattice QCD

SPSChiral dynamics

Pion gas

viscous fluid

Resonance
gas

perfect fluid

Strongly int.
Q+G+PFP
plasmapQCDq+g plasma

viscous fluid

weakly int.
q+g plasma

AAmodern
modern“picture”“picture”
ofof hot
hotQCD
QCD
fromfromlattice
latticeQCD
QCD

化学平衡
化学平衡@
@RHIC
RHIC

T

QGP相

ハドロン相

ｔ

T = 177 MeV,
化学凍結 μ = 29 MeV
Bジェット抑制の発見@RHIC
ジェット抑制の発見@RHIC

Bjorken’s formula

Bj

εBj > 5 GeV/fm3~ 5 εcrit~ 30 ε01. What is quark-gluon plasma

Part I. Basic Concept of Quark-Gluon Plasma:
2. Introduction to QCD
3. 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 universe
9. Compact stars

Part III. QGP in Relativistic Heavy Ion Collisions:published, Dec. 15, 2005

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

http://utkhii.px.tsukuba.ac.jp/cupbook/index.html

Appendices A-H:
120 Exercises

Phases in dense QCD

Baade-Zwicky (’34)

N. Itoh (’70), E. Witten (’84)

http://chandra.harvard.edu/resources/illustrations/neutronStars.html

Structure
Structureof
ofcompact
compact starsstarsQGPχSBCSC

Akmal, Pandharipande & Ravenhall, PRC58 (’98)

E/A (MeV)

State-of-the-art nuclear EoS

Z=0
N=Z

APR’s EoS

ρ(fm-3)

Variational method

ρ0= 0.16 fm-3

3ρ05ρ0EoS of nuclear matter (N=Z)
from ab initio calculations

Hard EoS

Soft EoS

Fuchs and Walter, nucl-th/0511070

Collective flow in low-energy heavy ion collisions and EoS
semi-classical Boltzmann-Vlasov approach
D f(x,p,t) = C[f]dN/dφ= 1 + v1 cosφ+v2cos2φ+ ….

Au + Au, Elab = 2GeV/A
Danielewicz et al, Science 298 (2002)

Constraint from Flow Datain SIS-AGS energies

Soft EOS is preferred

Danielewicz et al, Science 298 (2002)

Sub-threshold K+ production at SIS

Soft EOS is preferred

Fuchs and Walter, nucl-th/0511070

Glendnning, PRC64 (’01)

J-PARC (’08)

ρ0

3ρ0

5ρ0

QGP

χSBCSCHeiselberg & Pandharipande,Ann. Rev. Nucl. Part. Sci. 50 (’00)

APR
QM

quark matter EOS

3ρ05ρ07ρ0

9ρ0

NM-QM mixture

Heiselberg & Hjorth-Jensen, Phys.Rept.328 (’00)

Maxwellconstruction

Mixed phase(droplet etc)3ρ0-+-+-+--

5ρ0

7ρ0

9ρ0(Coulomb + surface) energy
vssymmetry energy

QGPχSBCSC

Bailin & Love, Phys. Rep. 107 (1984)
Iwasaki & Iwado, PL B350 (1995)
Alford, Rajagopal & Wilczek, PL B422 (1998)
Rapp, Schafer, Shuryak & Velkovsky, PRL81 (1998)

Origin
Originofof Color
Color Superconductivity
Superconductivity(CSC)(CSC)

flavor color

Major differences from BCS
1. Highly relativistic
Long range magnetic int.

2.

High Tc superconductor
Tc/εF ~ 0.1
Compact Cooper pairsize ~ 1-10 fmSon PRD59 (’99),
Schafer & Wilczek, PRD60 (’99)Variety of phases
Color-flavor
entanglement
Pisarski & Rischke, PRD61 (’00)(such as ice and 3He)
0  ∆1 0CFL, 2SC, dSC, uSC, etc= 0 0∆200 ∆ 3 PhasePhase structure
structure relevant
relevant toto compact
compact starsstars
withwithcharge-neutrality
charge-neutrality&&β-equilibrium
β-equilibriumund > nu > nsuds

2SCduusuSCddss

CFLdSCdSC

χSB2SCFFLOuSC

2SC : Bailin and Love, Phys. Rep. (’84)
CFL : Alford, Rajagopal and Wilczek, NPB (’99)
dSC : Iida, Matsuura, Tachibana and Hatsuda, PRL (’04)
uSC : Ruster, Werth, Buballa, Shovkovy and Rischke, PRD (’05)
FFLO, gapless phase, CSL, K-cond. etc

CFLThermal
Thermal transitiontransition :: 2SC2SC  normalnormalGinzburg-Landau parameter :• Weak coupling analyses

Matsuura, Iida, Hatsuda & Baym, PRD 69 (’04)• Lattice simulations :Digal, Hatsuda & Ohtani, hep-lat/0511018

gluon dominanceweak 1st order

Criticalend pointType IχSB

Type II(κGL> 1)

2SC(κGL< 1)BCS-BEC
BCS-BEC crossovercrossover ??

ξc/dq

410BCS-like

⌧
/dc q

310210110
N0/N = 10%5%

BEC-like

40K : 0 JILA group,

106Li :

ξc

Abuki, Itakura & Hatsuda,Hatsuda, PRD65 (’02)( 02)
Abuki,

Ladder
QCD at finitePairsµ5Cond.
ofFermionic-Atom101%

PRL 92 (2004) 040403
6Innsbruck group,
PRL 10925 (2004) 120401
101010MIT group,
PRL 92 (2004) 120403
μ(MeV)
[MeV]
34dq

40KPossible
Possible phasephase structurestructure

QGP
χSB

CSC

See Kitazwa, Koide, Kunihiro & Nemoto, PTP108 (’02)

Probing Dense QCD

J-PARCSIS100/300

M-R
M-Rrelation
relationin
inAPR
APREoS
EoS

Neutron star
- WD binary

J0751+1807

Cyg-X2 Vela-X1
PSR1913+16
EXO0748-676(X-ray bursts)(ρρmax ～ 6ρρ0)

X-ray binaries

Neutron starbinaryM-R
M-Rrelation
relationin
inAPR
APREoS
EoS++ CFL
CFLquark
quarkmattermatterInt. QM

Free QM

Alford, Braby, Paris & Reddy, ApJ 629 (2005)

Cooling
Coolingof
ofneutron
neutronstarsstars

Exoticquenchingn superfluidity
Q color superlog (Ts /K)log (Ls /(erg/s))

Standard

Weber, astr-ph/0407155 (’04)

exp(-ΔΔ/T)

log (time/yr)

HeavyHeavy ion
ion collisioncollision atat J-PARC
J-PARC && SIS
SIS energies
energies[25A GeV Au] +Au
JAM(Hadronic cascade model)
Y. Nara et al, PRC61 (2000)

ρB > 6 ρ0
for about 3 fm/c

Figure taken from JHF report (2002) by A.OhnishiSummary
Summary“phase”

theoryexp./obs.

χSB(low T & low µ)

Mature (precision physics)
lattice QCD
effective theories

variety of data

QGP(high T)

Developing
lattice QCD
effective theories

data accumulation
RHIC  LHC

QM and CSC(low T & high µ)

Developing
effective theories
Need lattice inputs• Neutron stars (M-R)• SIS, J-PARC, Nuclotron“PG”(intermediate T & µ)Not- fully exploredInteresting connection toHTS, cold atoms

Relevant region
to RHIC, SIS, J-PARC,
Nuclotron ?

QGP~170 MeVχSBnuclearπ, Κsuperfluidity cond.

~1 GeVCSC

Back up slides

astro-ph/0411207i

Nature 420 (’02)

CP-PACS, PRD 67 (’03) 034503

323 x 56 – 643 x 112
a=0.1-0.05 fm
La=3 fm

0.5 fm

1.0 fmBali, Phys. Rep. 343 (’01) 1

QuarkQuark number
number susceptibility
susceptibility

χq2

 µq (µ q ) = +2c2 + 12c4   + O µq4
4T
T Kunihiro,Phys. Lett.
Kunihiro,Lett. B271 (’(’92) 395
HattaHatta-Ikeda, Phys.Rev.D67 (’(’03) 014028( )Ejiri et al. (Bielefeld(BielefeldBielefeld-Swansea Coll.)

Lattice
LatticeQCD
QCDsimulations
simulationshypercube
slabComplex
Sign problem !

ScaleScaleofof eacheach“phase”“phase”

QGPχSBCSCTheoretical
Theoretical status
status

Lattice QCD
Perturbative QCD
Ginzburg-Landau + RG
Nuclear theory
effective models

QGP

χSB

CSC

Svetitsky & Yaffe, NPB210 (’82)

Order
Order ofofthe
thethermal
thermaltransitiontransition(µ=0)(µ=0)

Pisarski and Wilczek, PRD29 (’84)

O(4) GL theory

LGL

large

LGL

1st

2ndZ(3) GL theory

msSUL(3)xSUR(3) GL theorysmall

cross overQGP

1stLGL

smallmu,dlarge

χSBCSCScaleScaledegeneracydegeneracynear
near TTcc
1/(g2T)

1/(gT)
1/T

Running coupling at finite T

2.5

Inter-particle distance

2.0

Electric screening length
Magnetic screening length1.0Pre-formed
Pre-formedpairs
pairs(PFP)(PFP)forfor TTcc<<TT <<T*
T*
Hatsuda & Kunihiro, PRL (’85)

σ and πat T > Tc

Asakawa & Hatsuda, PTP (’04)

ss mesonsat T/Tc= 1.4(LQCD+MEM)(NJL model)

Asakawa & Hatsuda, PRL (’04), Datta et al., PRD (’04)

J/ψψ(3.1GeV)(LQCD+MEM)

Tc: absence of coherence

T*: dissociation of PFP
BEC-BCS crossover:Leggett (’80), Nozieres & Schimitt-Rink (’85)

Master
Masterformula
formulanear
near TTcc

T

Symmetric matter

Asymetric matternormalnormal

CFL

2SC
dSC
mCFL

Iida, Matsuura,
Tachibana and Hatsuda,
PRL (’04)