Naoki Yamamoto (University of Tokyo) 高高高 QCD 高高高高 高高高高高高高 contents • Introduction: color superconductivity • The role of U(1)A anomaly and chiral symmetry breaking • Partition function zeros and chiral symmetry breaking • Summary & Outlook (1) T. Hatsuda, M. Tachibana, N.Y. and G. Baym, Phys. Rev. Lett. 97 (2006) 122001. (2) N.Y., JHEP 0812 (2008) 060. (3) N.Y. and T. Kanazawa, Phys. Rev. Lett. 103 (2009) 032001. KEK 理理理理理理理理理 理理理理 理理理理理理理 「・」 2009.8.11.
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Naoki Yamamoto (University of Tokyo) 高密度 QCD における カイラル対称性 contents Introduction: color superconductivity The role of U(1) A anomaly and chiral symmetry.
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Naoki Yamamoto (University of Tokyo)
高密度 QCD におけるカイラル対称性
contents
• Introduction: color superconductivity• The role of U(1)A anomaly and chiral symmetry
breaking• Partition function zeros and chiral symmetry
breaking• Summary & Outlook(1) T. Hatsuda, M. Tachibana, N.Y. and G. Baym, Phys. Rev. Lett. 97 (2006) 122001.(2) N.Y., JHEP 0812 (2008) 060.(3) N.Y. and T. Kanazawa, Phys. Rev. Lett. 103 (2009) 032001.
KEK 理論センター研究会「原子核・ハドロン物理」 2009.8.11.
QCD phase diagram
T
mB
Quark-Gluon Plasma
Hadrons
RHIC/LHC
CFL
Color superconductivity
quark matter
Neutron star
Color Superconductivity
QCD at high density → asymptotic free Fermi surface
Attractive channel → Cooper instability
[3]C×[3]C=[6]C+[3]C
E
p
μ
q q
3
“diquark condensate”
“Fermi sea”
“Dirac sea”
Color-Flavor Locking (CFL)
ud s
r,g,bu,d,s
Pairing channel • s-wave pairing, spin singlet → Dirac antisymmetric• Attractive channel → color antisymmetric• Pauli principle → flavor antisymmetric• U(1)A anomaly → Lorentz scalar
Consider the Kobayashi-Maskawa-’t Hooft (KMT) vertex with quark mass:
VKMT is minimized when
and the positive parity state is energetically favored.
Alford-Rajagopal-Wilczek (NPB1999)
Kobayashi-Maskawa (PTP1970);‘t Hooft (PRD1976)
G G
T. Schafer (PRD2002)
Chiral symmetry breaking in CFL
The chiral condensate:
Exactly calculated thanks to the screening of instantons at high μ:
[Point]
1. Chiral symmetry is broken not only by the diquark condensate but also the chiral condensate in CFL.
2. Nonzero chiral condensate in CFL is model-independent.
3. Chiral-super interplay of the type is inevitable.
Alford-Rajagopal-Wilczek (NPB1999)
T. Schafer (PRD2002); NY (JHEP2008)
Possible phase structure I
Anomaly-induced critical point at high μ. Hatsuda-Tachibana-NY-Baym (PRL2006) A realization of quark-hadron continuity. Schafer-Wilczek (PRL1999) Critical point(s) of other origins. Kitazawa-Koide-Kunihiro-Nemoto
(PTP2002); Zhang-Fukushima-Kunihiro (PRD2009);
Zhang-Kunihiro, arXiv:0904.1062.
T
mB
Quark-Gluon Plasma
HadronsColor
superconductivity
Possible phase structure III
Is there this possibility? [see also Hidaka-san’s talk]
T
mB
Quark-Gluon Plasma
Hadrons CFLquark matter
Phase diagram of “instantons” (Nf=3)
T
mB
“instanton liquid”
“instanton molecule”
“instanton gas“
Chiral phase transition at high μ: instanton-induced crossover. 4-dim. generalization of Kosterlitz-Thouless transition.
NY (JHEP2008)
Another viewpoint: Lee-Yang zeros
The partition function zeros in the complex plane at V<∞ reflects the information of the chiral condensate at V=∞:
Nonzero chiral condensate at V=∞ requires a cut through m=0.
Halasz-Jackson-Verbaarschot (PRD97)
[Lee-Yang zeros at μ=0] Leutwyler-Smilga (PRD92)
Predictions of Random Matrix Theory (RMT)
Halasz-Jackson-Verbaarschot (PRD97); Halasz, et al. (PRD98) RMT predictions:
1. Chiral symmetry restores at μ=μc.
2. The cut will move away from origin as μ increases.
→ Is it consistent with the chiral symmetry breaking at high μ?
[Random Matrix Theory → Ohtani-san’s talk]
Finite-volume QCD at high density
QCD in a large but finite torus:
ε-regime:
Elementary excitations in CFL;• 9 quarks: mass gap~Δ due to the color superconductivity. • 8 gluons: mass gap~Δ due to the Higgs mechanism.• 8+1(+1) Nambu-Goldstone (NG) modes: nearly (or exactly) massless.
In ε-regime,• Non-NG modes negligible since . • Kinetic terms of NG modes negligible.
NY-Kanazawa (PRL2009)
Partition functions in ε-regime
Chiral Lagrangian at high μ (flavor-symmetric): Son-Stephanov (PRD2000)
Exact partition function at high μ:
a novel correspondence between hadronic phase and CFL phase
related to quark-hadron continuity!
Dirac spectrum...
at μ=0.
at high μ.
NY-Kanazawa (PRL2009)
Exact Lee-Yang zeros at high density
Asymptotic partition function and Lee-Yang zeros at μ=∞:
Chiral condensate vanishes at μ=∞. However, many Lee-Yang zeros exist near origin even at high μ
and the chiral condensate can be nonzero for μ<∞.
NY-Kanazawa (PRL2009)
1. Phases in dense QCD• The U(1)A anomaly (or instanton) plays crucial role.• Non-vanishing chiral condensate even at high μ.• Chiral-super interplay is inevitable.• Possible critical point(s) in dense QCD.
2. Partition function zeros in dense QCD• Exact X-shaped cut in the complex mass plane at μ=∞.• Chiral condensate can be nonzero for μ<∞.
3. Future problems• Phases at lower or intermediate densities?• Anomaly-induced interplay in NJL. Baym-Hatsuda-NY, in progress.
• Confinement-deconfinement transition?• Microscopic understanding based on QCD?
Summary & Outlook
Back up slides
Chiral vs. Diquark condensates
E
p
pF
-pF
Diquark condensate Chiral condensate
Y. Nambu (‘60)
Hadrons (3-flavor)
SU(3)L×SU(3)R
→ SU(3) L+R
Chiral condensate
NG bosons (π etc)
Vector mesons (ρ etc)
Baryons
Color-flavor locking
SU(3)L×SU(3)R×SU(3)C×U(1)B
→ SU(3)L+R+C
Diquark condensate
NG bosons
Gluons
Quarks
Phases
Symmetry breaking
Order parameter
Elementaryexcitations
quark-hadron continuity
Continuity between hadronic matter and quark matter (color-flavor locking)
Conjectured by Schäfer & Wilczek, PRL 1999
Instantons and chiral symmetry breaking
Why instanton? : mechanism for chiral symm. breaking/restoration