Post on 08-Feb-2021
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
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
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
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
Transition at Finite T
cSB CSC
QGP
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(
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
Transition at Finite T
cSB CSC
QGP
Asakawa-Yazaki CP
by T.D.Lee Tsinghua University, Beijing (photo by G. Baym)
Relativistic Heavy Ion Collisions
particle
productionFreezeoutthermalization QGP hydrodynamic
expansion
RHIC & LHC
PHENIX@RHIC STAR@RHIC ALICE@LHC
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
Initial energy density
Energ
y D
ensity
(GeV
/fm
3 )
AGS
SPS
RHIC
c.m. energy / nucleon
(GeV)
Lattice QCD
3D hydrodynamics with lattice EOS
http://www.youtube.com/watch?v=p8_2TczsxjMby T. Hirano
http://www.youtube.com/watch?v=p8_2TczsxjM
・ State-of-the-art lattice EOS・ Full 3D hydrodynamics・ Experimental SPF at T=0
Akamatsu, Hatsuda, Hamagaki, & Hirano (2010)
Dilepton emission with lattice EOS
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
Transition at finite μ
cSB CSC
QGP
CP
Neutronliquid
QuarkMatter?
Nuclear Force and Neutron Star
(ρmax ~ 6ρ0)
PSR1913+16
Neutron star binary
Pressure balance
gravity
Repulsive core
Fermi pressure
Oppenheimer-Volkov(1939)
NN
NNN
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
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
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(
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
Chiral-CFL interplay in Nf=3
Natural parameter relations
phase diagram (without d-σ coupling)
μ
T
phase diagram (with d-σ coupling)
Low T critical point driven by the axial anomaly
T
μ
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
Critical points from symmetry point of view
Original idea : Hatsuda and Alford (2010)
Figure taken fromSchmitt, Stetina & Tachibana, arXiv: 10104243 [hep-ph]
Spectral continuity at finite μ
cSB CSC
QGPCP induced by Higgs
CP induced by anomaly
mco
ndensa
tes
Continuity in the ground state
Generalized Gell-Mann-Oakes-Renner relation :
Yamamoto, Tachibana, Baym & T.H., PR D76 (‟07)
○
Tachibana, Yamamoto and T.H.,PRD78 (2008)
○
Continuity in excitation modes
Vector meson – CFL gluon continuity (QCD sum rules):
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?
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?
b fσ
s-wave boson-fermion
scattering length
strong weak
0
Maeda, Baym and Hatsuda, Phys. Rev. Lett. 103 (2009) 085301Atomic Boson-Fermion mixture
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
Y. Nambu, Nobel Lecture (Dec.8, 2008), page 24/25
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
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