Many-body Problems in QCD · 2010. 11. 8. · Hot matter:T ~1012K Dense matter:ρ ~1012...
Transcript of Many-body Problems in QCD · 2010. 11. 8. · Hot matter:T ~1012K Dense matter:ρ ~1012...
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T ~1012K Hot matter: ρ ~ 1012 kg/cm3Dense matter:
Neutronliquid
QuarkMatter?
Lattice QCD confronts experiments
Japanese-German Seminar 2010 Nov. 6 (2010) at Mishima
T. Hatsuda (University of Tokyo)
Many-body Problems in QCD
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1. Introduction to QCD phase structure
2. Hot QCD confronts RHIC/LHC experiments
3. Dense QCD confronts neutron star observations
4. Dense QCD confronts ultracold atomic experiments ?
5. Summary
Recent review:
“The Phase Diagram of Dense QCD”K. Fukushima and T. Hatsuda, Rep. Prog. Phys. 73 (2010)
arXiv: 1005.4814 [hep-ph]
contents
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Symmetry realization in hot/dense QCD(for mu,d,s=0 case)
QGP
BRLC USUSUSU )1(])3()3([)3(
QGP :
Cabibbo & Parisi, PLB 59 (1975)Collins & Perry, PRL 34 (1975)
0 Rt
RL
t
L CqqCqqCFL :
Alford, Rajagopal & Wilczek, NPB 537 (1999)
RLRLC ZZSU )2()2()3(
cSB :
Nambu, PRL 4 (1960)
BRLC USUSU )1()3()3(
0RLqq
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QCD vs. condensed matters
cSB CSC
QGP
1. Competition between different orders
2. Strong coupling
Common features
• Kitazawa, Nemoto, Kunihiro, PTP (‘02)
• Abuki, Itakura & Hatsuda, PRD (’02)
• Chen, Stajic, Tan & Levin, Phys. Rep. (’05) Dirac
Fermi
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Transition at Finite T
cSB CSC
QGP
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Chiral field: ~
Chiral transformation:
Pisarski & Wilczek (‟84)
Symmetry:
Ginzburg-Landau-Wilson analysis in hot QCD
SU(Nf)LxSU(Nf)RxU(1)A
SU(Nf)LxSU(Nf)R
quark mass term
Axial anomaly
X
AfNZ )2(
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Pisarski and Wilczek, PRD29 (‟84)
Svetitsky & Yaffe, NPB210 (‟82)Order of the thermal QCD transition (μ=0)
1st
1st
cross over
2nd
ms
small
larg
e
m u,dsmall large
Nf=0
Nf=1
Nf=2
Nf=3
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Transition at Finite T
cSB CSC
QGP
Asakawa-Yazaki CP
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by T.D.Lee Tsinghua University, Beijing (photo by G. Baym)
Relativistic Heavy Ion Collisions
particle
productionFreezeoutthermalization QGP hydrodynamic
expansion
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RHIC & LHC
PHENIX@RHIC STAR@RHIC ALICE@LHC
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Hot QCD confronts RHIC/LHC experiments
Theoretical Inputs
for equation of state
for local correlations
・ Lattice QCD・ pQCD・ AdS/QCD
Relativistic hydrodynamics
for space-time evolution
∂μTμν =0
Laudau (1953), Namiki & Iso (1957)・ 1D hydro by Bjorken (1983) ・ 3D hydrodynamics by
Hirano, Muroya, Nonaka (2000-)
lepton
hadron
jet
charm
bottom
photon
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Initial energy density
Energ
y D
ensity
(GeV
/fm
3 )
AGS
SPS
RHIC
c.m. energy / nucleon
(GeV)
Lattice QCD
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3D hydrodynamics with lattice EOS
http://www.youtube.com/watch?v=p8_2TczsxjMby T. Hirano
http://www.youtube.com/watch?v=p8_2TczsxjM
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・ State-of-the-art lattice EOS・ Full 3D hydrodynamics・ Experimental SPF at T=0
Akamatsu, Hatsuda, Hamagaki, & Hirano (2010)
Dilepton emission with lattice EOS
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Predictions for LHC
Hirano, Huovinen and Nara,arXiv:10106222 [nucl-th] Nov.1 (2010)
・State-of-the-art lattice EOSgiven by HOT QCD Coll.
・Full 3D hydrodynamics+ hadron cascade
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Transition at finite μ
cSB CSC
QGP
CP
Neutronliquid
QuarkMatter?
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Nuclear Force and Neutron Star
(ρmax ~ 6ρ0)
PSR1913+16
Neutron star binary
Pressure balance
gravity
Repulsive core
Fermi pressure
Oppenheimer-Volkov(1939)
NN
NNN
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Ozel, Baym & Guver, arXiv: 1002.3153 [astro-ph.HE]Steiner, Luttimer & Brown, arXiv: 1005.0811 [astro-ph.HE]
From TOV to EOS
M-R relation fromthermonuclear Burst in X-ray Binaries
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Color superconductivity
major differences from the standard BCS superconductor
1. Relativistic fermi system
color-magnetic int. dominant High Tc : Tc/eF ~ 0.1
Compact pair : r~ 1-10 fm
2. Color-flavor entanglementVarious phases (c.f. Ice, 3He)
2SC, uSC, dSC, CFL etc
flavor color
u
d s
u
d s
u
d s
u
d s
CFLdSCuSC2SC
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Pisarski & Wilczek, PRD29 (‟84) Iida & Baym, PRD63 (‟01) Yamamoto, Tachibana, Baym & Hatsuda, PRL97 (‟06)
GL analysis for chiral-super interplay in QCD (Nf=3)
Symmetry:
Chiral field: diquark field:
AZ )6(
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Complete classification of the GL potential (mu,d,s=0)Yamamoto, Tachibana, Baym & Hatsuda, PRL 97 (‟06), PRD 76 („07)
Axial anomaly
RL ZZ )2()2( broken explicitly
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Chiral-CFL interplay in Nf=3
Natural parameter relations
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phase diagram (without d-σ coupling)
μ
T
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phase diagram (with d-σ coupling)
Low T critical point driven by the axial anomaly
T
μ
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phase diagram (with d-σ coupling & quark mass)
h
Low T critical point driven by the axial anomalyHigh T critical point driven by Higgs condensate
T
μ
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Critical points from symmetry point of view
Original idea : Hatsuda and Alford (2010)
Figure taken fromSchmitt, Stetina & Tachibana, arXiv: 10104243 [hep-ph]
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Spectral continuity at finite μ
cSB CSC
QGPCP induced by Higgs
CP induced by anomaly
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mco
ndensa
tes
Continuity in the ground state
Generalized Gell-Mann-Oakes-Renner relation :
Yamamoto, Tachibana, Baym & T.H., PR D76 (‟07)
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Tachibana, Yamamoto and T.H.,PRD78 (2008)
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Continuity in excitation modes
Vector meson – CFL gluon continuity (QCD sum rules):
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diquark
BCS
Baryon
BCSdiquark
BEC
Dense QCD confronts UCA experiments?
“Simulating dense QCD matter with Ultracold atoms”Maeda, Baym and Hatsuda, Phys. Rev. Lett. 103 (2009) 085301
Neutron
matter
quark
Matter?
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Ultracold Atoms (UCA)
・T ~ 10-7 K
・hyperfine states
magnetically controllable
・density 1014 - 1015 cm-3
( cf. Air ~ 1019cm-3 )
10 12
10 9
10 7
T[K]
10 2
10
1
10 -3
10 -7
Quark-gluon plasma
Superfluid neutron matter
Center of sun
Boiling waterFreezing water
Liquid nitrogen
Superfluid, superconductor
Superfluid of 3He
Ultracold atoms
Neutron
matter
quark
Matter?
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b fσ
s-wave boson-fermion
scattering length
strong weak
0
Maeda, Baym and Hatsuda, Phys. Rev. Lett. 103 (2009) 085301Atomic Boson-Fermion mixture
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Induced superfluidity of composite fermions
-- a novel analogy between cold atoms and QCD --
Maeda, Baym & Hatsuda,Phys. Rev. Lett. 103 (‟09)
Composite
Fermion
cold atoms dense QCD
weak (bf)-(bf) attraction ⇔ strong b-f attraction baryon superfluidity ⇔ strong diqark correlation
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Y. Nambu, Nobel Lecture (Dec.8, 2008), page 24/25
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1. QCD phase structure・ Three major phases in QCD: χSB, QGP and CSC
・ Axial anomaly plays crucial roles everywhere
・ Close similarity to high Tc supercond. & multi-comp. cold atoms
2. Chiral-super interplay driven by axial anomaly・ A new critical point at low T and high μ
・ Continuity of χSB phase and CSC phase
3. Spectral continuity in high density QCD・ Pions are pions.
・ Vector mesons are gluons.
4. Near future・ Hot QCD confront LHC experiments
・ Dense QCD confronts neutron star observations
・ Dense QCD confronts ultracold atomic experiments
Summary and Future
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1. QCD phase structure・ Three major phases in QCD: χSB, QGP and CSC
・ Axial anomaly plays crucial roles everywhere
・ Close similarity to high Tc supercond. & multi-comp. cold atoms
2. Chiral-super interplay driven by axial anomaly・ A new critical point at low T and high μ
・ Continuity of χSB phase and CSC phase
3. Spectral continuity in high density QCD・ Pions are pions.
・ Vector mesons are gluons.
4. Near future・ Hot QCD confront LHC experiments
・ Dense QCD confronts neutron star observations
・ Dense QCD confronts ultracold atomic experiments
Summary and Future
RHIC/LHC
LQCD Neutron
stars
UCA