chiral symmetry breaking in dense qcd
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Chiral symmetry breaking in dense QCD. contents Introduction: QCD critical point at high T Chiral-super interplay QCD phase structure from instantons QCD phase structure at large N c Summary & Outlook. Naoki Yamamoto (University of Tokyo). - PowerPoint PPT PresentationTRANSCRIPT
Naoki Yamamoto (University of Tokyo)
Chiral symmetry breaking in dense QCD
contents• Introduction: QCD critical point at high T• Chiral-super interplay• QCD phase structure from instantons• QCD phase structure at large Nc• Summary & Outlook(1) T. Hatsuda, M. Tachibana, G. Baym & N.Y., Phys. Rev. Lett. 97 (2006) 122001.(2) N.Y., JHEP 0812 (2008) 060.
駒場原子核理論セミナー
April 15, 2009
QCD phase diagram
T
mB
Quark-Gluon Plasma
Color superconductivity
Hadrons Neutron star & quark star
?
Early universe
RHIC/LHC
..But, 2-flavor NJL rather than QCD
QCD critical point at high T
QCD critical point?
First predicted by 2-flavor NJL model Asakawa-Yazaki, ‘89 Confirmed by other models, e.g., random matrix model Halasz et al. ‘98 Lattice results: still controversial de Forcrand-Philipsen ‘06, ‘08 But models have many ambiguities!
e.g.) NJL-type Lagrangian:
Parameters (to be fitted with pion mass/decay const.): Λ, G, m
→ Calculate phase diagram numerically.
Thermodynamic potential:
QCD (tri)critical point (Nf=2)
T
μ
: 1st order: 2nd order
c.f.) Coefficient in NJL: N.Y. et al., ‘07
Potential at lowest order (m=0):
No critical point in massless 3-flavor limit
1st order
Pisarski-Wilczek (‘84)
μ
T
Chiral field:
U(1)A anomaly
QCD critical point in 2+1 flavor
μ
T T
μ
0 = mu,d,s 0 = mu,d m≪ s
T
μ
0<mu,d<ms
<
As ms increases,
<
Note) CP in 2-flavor limit is also model-dependent.
Some comments Unknown medium effects on model parameters easily smear out CP!
QCD critical point at high T from 2+1 flavor PNJL model with gD~c0
K. Fukushima, PRD (‘08), N. Bratovich, T. Hell, S. Rößner + W. Weise (’08)
4-fermi interaction etc. also has medium effects 3-flavor random matrix model with axial anomaly?
Sano-Fujii-Ohtani, (‘09)
c.f.)
Location of QCD critical point?
Taken from hep-lat/0701002, M. Stephanov
Chiral-super interplay
Chiral vs. Diquark condensates
E
p
pF
-pF
Diquark condensate Chiral condensate
Y. Nambu (‘60)
Chiral-super interplay in models
Phase diagram in 2-flavor NJL modelBerges-Rajagopal, ‘99
Examples of phase diagrams in 2-flavor random matrix model Vanderheyden-Jackson, ‘00
Notes Many ambiguities in NJL:
With vector interaction → coexistence phase appearsKitazawa et al, ‘02
Possible higher interactionsKashiwa et al. ‘07
Medium effects on interactions (remember 3-flavor PNJL) Chen et al. ’09
Favor-dependence, quark masses, ...
However, their topological structures look similar, why?→ Because all models have QCD symmetries!
Ginzburg-Landau approach (Nf=2) GL potential:
T
μ
Most general phase diagram Hatsuda-Tachibana-Yamamoto-Baym (‘06)
Precise medium effects on GL coefficients needed
Anomaly-induced interplay (Nf=3)Hatsuda-Tachibana-Yamamoto-Baym (‘06)
T
μ
: 1st order: 2nd order
Non-vanishing chiral condensate at high μ due to U(1)A anomaly The possible 2nd critical point at high μ Anomaly-induced interplay in NJL Yamamoto-Hatsuda-Baym in progress
0 ≾ mu,d<ms ∞ (realistic quark masses)≪
Realistic QCD phase structure?
2nd critical point
Critical pointAsakawa & Yazaki, 89
mu,d,s = 0 (3-flavor limit) mu,d = 0, ms=∞ (2-flavor limit)≿ ≿T
μ
T
μT
μ
Hatsuda, Tachibana, Yamamoto & Baym 06
QCD phase structurefrom instantons
Instantons and chiral symmetry breaking
Why instanton? : mechanism for chiral symm. breaking/restoration
T=0 T>Tc
“instanton liquid” (metal) “instanton molecule” (insulator)
Schäfer-Shuryak, Rev. Mod. Phys. (‘97)
See, e.g., Hell-Rößner-Cristoforetti-Weise, arXiv: 0810.1099
nonlocal NJL model
Origin of NJL model:
Then, χSB in dense QCD from instantons?
Dense QCD : U(1)A is asymptotically restored.
Low-energy dynamics in dense QCD
convergent!
Low-energy effective Lagrangian of η’
Manuel-Tytgat, PL(‘00)Son-Stephanov-Zhitnitsky, PRL(‘01)Schäfer, PRD(‘02)
Coulomb gas representation
: topological charge
: 4-dim Coulomb potential
Instanton density, topological susceptibility
Witten-Veneziano relation :
Renormalization group analysis
Fluctuations :
Change of potential after RG :
RG trans. :
RG scale :
kinetic vs. potential
D = 2 : potential irrelevant → vortex molecule phase potential relevant → vortex plasma phase
D 3≧ : potential relevant → plasma phase
Phase transition induced by instantons
Unpaired instanton plasma in dense QCD→Coexistence phase:
Actually,
System parameter α Topological excitations Order of trans.
2D O(2) spin system vortex 2nd
3D compact QED magnetic monopole crossover
4D dense QCD instanton crossover
D-dim sine-Gordon model :
Note: weak coupling QCD:
Phase diagram of “instantons” (Nf=3)
T
mB
QGP
CFLχSB“instanton liquid”
“instanton molecule”
“instanton gas“
Chiral phase transition at high μ: instanton-induced crossover. 4-dim. generalization of Kosterlitz-Thouless transition.
N. Yamamoto, JHEP 0812:060 (2008)
QCD phase structureat large Nc
QCD phase diagram at large Nc
McLerran-Pisarski, NPA (‘07)
see also, Horigome-Tanii, JHEP (‘07)
Gluodynamics (~Nc2) dominates independent of μB (~Nc).
CSC at large Nc? qq scattering
qq scattering
Double-line notation
★ Diquarks are suppressed at large Nc!
Deryagin-Grigoriev-Rubakov (‘92)Shuster-Son (‘00)Ohnishi-Oka-Yasui (‘07)
Conjectured Phase Diagram for Nc = 3
RHIC
LHC
SPS
FAIR
AGS
Confined
N ~0(1)
Not Chiral
Confined
Baryons
N ~ NcNf
Chiral
Debye Screened
Baryons Number
N ~ Nc 2
Chiral
Color Superconductivity
Liquid Gas Transition
Critical Point
Quark Gluon Plasma
Quarkyonic Matter
Confined Matter
T
From McLerran at QM2009
Not correct for 3-flavor limit: deconfinement earlier than χSR. Note that large Nc leads to
No color superconductivity Weak axial anomaly indep. of μ
A dynamical question: subtleness of quark masses. (flavor-dep.) A puzzle: how χSB occurs after χSR?
1. QCD phase structure• Consensus is highly model-dependent.• The QCD critical point at high T?• Possible 2nd critical point at high μ.
2. Instanton plasma from low μ to high μ• Instantons play crucial roles everywhere.• Non-vanishing chiral condensate even at high μ.
3. Future problems• Quarkyonic vs. CSC?• QCD phase structure from QCD itself?• AdS/CFT application?
Summary & Outlook
Finite-volume QCD at high μ
microscopic regime:
Exact analytical results;I. Partition function (zero topological sector): a novel correspondence!
II. Spectral sum rules: Dirac spectra at high μ are governed by the CSC gap Δ.
III. Lee-Yang zeros: conventional random matrix model fails to reproduce CSC.
Application to dense 2-color QCD is also possible.T. Kanazawa, T. Wettig, N. Yamamoto, to appear soon.
N. Yamamoto, T. Kanazawa, arXiv:0902.4533.
at μ=0.
at high μ.
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 superconductivitySU(3)L×SU(3)R×SU(3)C×U(1)B
→ SU(3)L+R+C
Diquark condensate
NG bosons
Gluons
Quarks
PhasesSymmetry breaking
Order parameter
Elementaryexcitations
Hadron-quark continuity
Continuity between hadronic matter and quark matter (Color
superconductivity)
Conjectured by Schäfer & Wilczek, PRL 1999
Back up slides
Order of the thermal transition Z(3) GL theoryO(4) GL theory
SUL(3)xSUR(3) GL theory
Color Superconductivity
QCD at high density asymptotic freedom Attractive channel [3]C×[3]C=[3]C+[6]C
Fermi surface
Cooper instability
E
p
pF
-pF
3-flavor case
ud s Color-Flavor Locking
(CFL) phase
r,g,b
q q
3
dL,R :diquark
u,d,s
Alford-Rajagopal-Wilczek (‘99)
2nd order
Color superconductivity phase transition
Iida-Baym (‘00)
μ
T
Diquark field: