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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-)
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WMAP data(3x105 years)
Inflation
Present (13.7 x 109 years)
Hot Era
Big Bang
CGC
QGP
RHIC data
Little Bang
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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
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[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
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Origin of Masses
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“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
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QCD Phase Structure
4He 3He
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CSC (Color Superconductivity)
QGP (Quark-Gluon Plasma)
SB (Chiral Symmetry Breaking)
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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)
&
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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)
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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)
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Dynamics of QCD phase transition
SB CSC
QGP
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T (MeV)
Yukawa regime Hagedorn regime
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* QCD in a finite box : V
QCD Level Density and Hagedorn slope
* Laplace transform of = partition function Z
E
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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()
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Lattice Thermodynamics
Quenched QCDFull QCD
Integration : Monte Carlo with importance sampling
hypercube
slab
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Nf =0 1st orderTc = 271±2 MeV
Equation of State (EoS) on the lattice
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Strongly Correlated QCD Plasma ?
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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
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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
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・ 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)
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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
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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
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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)
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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)
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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)
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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
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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
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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)
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PDG(’04)
Charmonium Spectral Function at Finite T
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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
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D = K×A
D A D A
Image reconstruction by MEM
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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)
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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)
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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)
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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
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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
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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
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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
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(1992-)
SPS (1994-)
(2001-)
RHIC (2000-)
Planck (2007-)
LHC (2007-)
Q.G
.P.
Big Bang
Little Bang
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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
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Back up slides
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Physics Today, Dec. vol.58 (2005) http://www.lsbu.ac.uk/water/phase.htmlMore on H2O
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Scale of each “phase”
cSB CSC
QGP
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Filled:Nt=4, Open:Nt=6
173±8 MeV
Small mud
Tc in 2-favor lattice QCD Ejiri (’04)
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Dilute gasPercolationtransition Closely packed
Volume fraction:
Percolation picture
T.H., (’97)
1/3
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Super Computer: IBM BlueGene at KEK(March, 2006-) 57.3 Tflops
Lattice QCD simulations
Color Confinement
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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