Static/Dynamic Correlations in Hot QCD -- Tickling the QCD Vacuum -- T. Hatsuda

(Univ. Tokyo)

　 Two major experimentsto probe the early Universe

RHIC (2000- )

WMAP (2001-)

WMAP data(3x105 years)

Inflation

Present (13.7 x 109 years)

Hot Era

Big Bang

CGC

QGP

RHIC data

Little Bang

Expansion

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

Tchem ~ 170 MeV

Ttherm ~ 120 MeV

Observables CMB & anisotropy (CνB, CGB & anisotropy)

Collective flow & anisotropy Jets, leptons, photons

Parameters to be determined

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

QGP parameters 　・ Initial energy density 　・ Equation of state etc

Big Bang Little Bang

Initial state Inflation ? 　 (10-36 sec) Color glass ? (< 10-1 fm)

Thermalization Inflaton decay decoherence

Evolution Code CMBFAST 3D-hydro

[1] Origin of Masses　　 -- one of the big questions in modern physics

[2] QCD Phase Structure　　　 -- similarity to High Tc superconductivity – anomaly induced critical point at high density

[3] Dynamics of QCD Phase Transition -- climbing the Hagedorn slope

[4] Strongly Correlated QCD Plasma ? -- electric/magnetic screening and viscosity -- heavy flavor as a probe

[5] Summary

Contents

Origin of Masses

“Origin of masses” Structure of the vacuum

WMAP (2001-), Planck (2007-)

Cosmological constantEinstein (1917)

Universe

baryons

RHIC (2000-), LHC (2007-)

“Chiral” condensateNambu (1960)

baryon

quark

LHC(2007-)

“Higgs” condensate Anderson (1963) Englert-Brout, Higgs (1964)

quark

barequark

QCD Phase Structure

4He 3He

CSC (Color Superconductivity)

QGP (Quark-Gluon Plasma)

SB (Chiral Symmetry Breaking)

Origin of each “phase”

Asymptotic freedom + Debye screening deconfinement Collins & Perry, Phys.Rev.Lett. 34 (1975)

quark - anti-quark pairing chiral instability

Nambu & Jona-Lasinio, Phys.Rev. 122 (1961)

SB CSC

QGP

T

B

strong residual force pre-formed pairs Hatsuda & Kunihiro, Phys.Rev.Lett. 55 (1985) DeTar, PRD32 (1985)

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

&

SB CSC

QGP

Similarity with high Tc superconductivity

1. Competing order parameters2. strong coupling effect pre-formed pairs in Tc < T < T*

　　　　 　 Tc = decoherence temp. T* = dissociation temp. 　

Highly undedoped

underdoped

optimallydoped

Bi2Sr2CaCuO8+δ

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)

Anomaly Induced Critical Point

SB

CSC

QGP

CP

SB

CSC+SB

QGP

SB+CSC

CP-T

CP-D

Most General Ginzburg-Landau Potential with the symmetry:

+ …

Emergence of a high-density critical point (CP-D)

Yamamoto, Tachibana, Baym & Hatsuda, hep-ph/0605018

Hadron-quark continuitySchafer & Wilczek (’99)

Dynamics of QCD phase transition

SB CSC

QGP

T (MeV)

Yukawa regime Hagedorn regime

* QCD in a finite box : V

QCD Level Density and Hagedorn slope

* Laplace transform of = partition function Z

E

Information of the Phase Transition is encoded in the QCD leverl density (E,V)

Hagedorn (1965)Ejiri & Hatsuda, hep-lat/0509119

s() ∝ ln (E,V) ~

~ T0

~ 3/4

E

I

II

III

= E/ V

s()

Lattice Thermodynamics

Quenched QCDFull QCD

Integration : Monte Carlo with importance sampling

hypercube

slab

Nf =0 1st orderTc = 271±2 MeV

Equation of State (EoS) on the lattice

Strongly Correlated QCD Plasma ?

Inter-particledistance

Electric screening

Magneticscreening

1/T

1/gT

1/g2T

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

Relativistic plasma :

“Coulomb” coupling parameter :

Debye number :

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

1/T

1/(gT)

1/(g2T)

Scale degeneracy near Tc

Inter-particle distance

Electric screening length

Magnetic screening length

Running coupling at finite T

1.0

2.0

2.5

・ naive perturbation: meaningful only for T>100 GeV ・ resummation may improve the situation

QCD Pressure near Tc

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

Screening masses at T>Tc on the lattice

Quenched SU(3)20×20×32×6Lorenz gaugeelectric

magnetic

m/T

Nakamura, Saito & Sakai, Phys.Rev.D69 (’04) 014506T/Tc

1/T

1/gT

1/g2T

|)|exp(~)0()( xmAxA

Viscosity 　 updated (quenched QCD)

)0,0(),(R TxtT

24x24x24x8 Nakamura & Sakai, Phys.Rev.Lett.94:072305,2005 updated: hep-lat/0510100

T/Tc

/s

Kovtun, Son & Starinets (’04) AdS/CFT

Baym, Monien, Pethick & Ravenhall (’90)Arnold, Moore & Yaffe, (’03)pQCD

　

Probing QCD plasma By Heavy Flavors

Matsui & Satz, PLB (’86)Miyamura et al., PRL (’86)

Static probe Dynamic probe

Gluon matter (quenched QCD)Quark-gluon matter (full QCD)

r

g,u,d

Nf= 2, Wilson sea-quarks, 243x40a= 0.083 fm, L= 2 fm, mp/mr= 0.704SESAM Coll., Phys.Rev.D71 (2005) 114513

1fm0.5fm 1.5fm

[ V(r

) - 2

mH

L ] a

Static Probe at T=0 : heavy-quark potential (full QCD)

g,u,d,s

Dynamic Probe at T=0 : charmonia spectra (full QCD)

MILC Coll., PoS (LAT2005) 203 [hep-lat/0510072]

Nf= 2+1, staggered sea-quarks, 163x48, 203x64, 283x96 a = 0.18, 0.12, 0.086 fm, L= 2.8, 2.4, 2.4 fm

spin ave. 1S energy

Note: connection between spectroscopy and V(r)through 1/mc expansion: Eichten-Feinberg (’79) Brown-Weisberger(’79)

g,u,d

r

Heavy Quark Free-energy at Finite T (full QCD)

Note: connection between spectroscopy and F(r)not established yet Kaczmarek & Zantow, PoS (LAT2005) 192 [hep-lat/0510094]

Nf= 2, staggered sea-quarks, 163x4 ,m/m= 0.7

Heavy-quark free energy at T >Tc

in varous channels (full QCD)

quenched, 243x32, Coulomb gaugeNakamura & Saito,Phys. Lett. B621 (’05) 171

g,u,d

r

g,u,d

r

Tsukuba-Tokyo Coll. (Maezawa, Ukita, Ishii, Ejiri, Hatsuda, Aoki, Kanaya, Taniguchi)

Nf= 2, Wilson sea-quarks, 163x4 mp/mr= 0.8 (& 0.65), Coulomb gauge

preliminary

preliminary

singlet

anti-triplet

gr

Umeda, Katayama, Miyamura & Matsufuru, Int.J.Mod.Phys.A16 (2001) 2215 [hep-lat/0011085]

quenched, 162x24x(96,26,22,16) x=3.95, as=0.12 fm, at=0.03 fm

r (G

eV-1)

2

3

5

4

free

T/Tc=1.53

T/Tc=0.93

t (GeV-1)

Charmonium “Wave Function” at Finite T (quenched QCD)

PDG(’04)

Charmonium Spectral Function at Finite T

dpAK

xdeJxJpD xpi

),(),(

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

Lattice data

)1/(),( / TeeK

“Laplace” kernel

All information on hadronic correlations at T=0 and T≠0

Spectral Function

MEM (Maximum Entropy Method)

・　 First applications of MEM to lattice QCD: 　 Asakawa, Nakahara & Hatsuda, Phys. Rev. D60 (’99) 091503 Prog. Part. Nucl. Phys. 46 (’01) 459 　

1. No parameterization necessary for A2. Unique solution D A3. Error estimate for A possible

Advantages of MEM

D = K×A

D A D A

Image reconstruction by MEM

JP=1/2+

Asakawa, Nakahara & Hatsuda, Phys. Rev. D60 (’99) 091503

Sasaki, Sasaki & Hatsuda, Phys.Lett.B623 (’05) 208

MEM : Examples at T=0 (quenched QCD)

quenched, anisotropic lattice, 323 x (96,54,46,40,32)=4.0, as=0.04 fm, at=0.01 fm, (Ls=1.25fm)

Asakawa and Hatsuda, Phys.Rev.Lett.92 (2004) 012001.g

J/ c

MEM applied to Charmonia at Finite T (quenched QCD)

quenched, isotropic lattice, 483 x (24,16,12)a=0.04 fm (Ls=1.9 fm)

Datta, Karsch, Petreczky & Wetzorke, Phys. Rev. D69 (2004) 094507.g

MEM applied to Charmonia at Finite T (quenched QCD)

Asakawa, Nakahara & Hatsuda, [hep-lat/0208059]

Is heaviness essential for bound states aboveTc ?

mud << ms~Tc << mc < mb

A(ω

）/ω

2

mφ(T=0)=1.03 GeV at T/Tc= 1.4ss-channel

Full QCD ?

Hatsuda, hep-ph/0509306

Net dissociation rate may even be smaller in full QCD

Aarts, et.al., [hep-lat/0511028]

Nf=2, anisotropic lattice, 83 x (48,32,24,16)=6.0, as=0.2 fm, at=0.033 fm, (Ls=1.6 fm) m/m=0.55

2Tc

1.3Tc

Tc

0.7Tc

2Tc

1.3Tc

Tc

0.7Tc

J/

c g,u,d

Pion gas

Resonance gas

Strongly int.Q+G+PFPplasma

weakly int.q+g plasma

q+g plasma

viscous fluid perfect fluid

viscous fluid

Chiral dynam

icspQ

CD

Lattice QC

D

SP

SLH

C, R

HIC

A possible “picture”

of hot QCD

Summary

2. Several critical points in (T,μ)-plane ? Chiral CP at high T, Chiral-super CP at high μ, Liquid-gas CP at low μ

3. Progress in spectral analysis on the lattice Heavy and light bound states above Tc

Small viscosity even up to 30 Tc ? Full QCD study is started RHIC LATTICE

AdS/CFT HTS/BEC

1. Hot QCD is strongly interacting: Tc < T* ? Just like high Tc superconductor

BEC regime of systems of atomic fermions

(1992-)

SPS (1994-)

(2001-)

RHIC (2000-)

Planck (2007-)

LHC (2007-)

Q.G

.P.

Big Bang

Little Bang

　 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:

　 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

published, Dec., 2005 (Cambridge Univ. Press)

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

Back up slides

Physics Today, Dec. vol.58 (2005) http://www.lsbu.ac.uk/water/phase.htmlMore on H2O

Scale of each “phase”

cSB CSC

QGP

Filled:Nt=4, Open:Nt=6

173±8 MeV

Small mud

Tc in 2-favor lattice QCD Ejiri (’04)

Dilute gasPercolationtransition Closely packed

Volume fraction:

Percolation picture

T.H., (’97)

1/3

Super Computer: IBM BlueGene at KEK(March, 2006-) 57.3 Tflops

Lattice QCD simulations

Color Confinement

Examples in full lattice QCD

Heavy bound states

MILC Coll., hep-lat/0510072

Nf= 2+1, staggered, 163x48, 203x64, 283x96 a = 0.18, 0.12, 0.086 fm L= 2.8, 2.4, 2.4 fm

Mas

s-(s

pin

avar

aged

1s)

[MeV

]

Confining string

R

SESAM Coll., Phys.Rev.D71 (2005) 114513

1fm0.5fm 1.5fm

[ V(R

) - 2

mH

L ] a

Nf= 2, Wilson, 243x40 a= 0.083 fm L= 2 fm mp/mr= 0.704

R/a