Naoki Yamamoto (University of Tokyo)

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New Critical Point and Hadron-Quark Continuity
in Dense QCD

• Naoki Yamamoto (University of Tokyo)

• contents
• Introduction
• Ginzburg-Landau theory QCD phase structure(1,2)
• Pion at intermediate density(2)
• Vector meson at intermediate density(3)
  (from in-medium QCD sum rule)
• Summary Outlook

(1) Hatsuda, Tachibana, Yamamoto, Baym, PRL 97
(2006) 122001. (2) Yamamoto, Tachibana, Hatsuda,
Baym, PRD 76 (2007) 074001. (3) Hatsuda,
Tachibana, Yamamoto, in preparation.
7th Heavy Ion Café 2008.1.12.
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QCD????
????QCD?????????
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What is the color superconductivity?

• QCD at high density
• asymptotic freedom
• Attractive channel
• 3C3C3C6C

Fermi surface
Cooper instability
3-flavor case
a,b,cr,g,b, i,j,ku,d,s
Color-Flavor Locking (CFL) phase
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?????? vs. ????????
????????
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• Hadron-quark continuity (Schäfer Wilczek,
  1999)

?????? ? ?????? (??????) ?????
?????? (3-flavor) SU(3)LSU(3)R ? SU(3)
LR ?????? NG bosons (p etc) vector mesons (?
etc) baryons
?????? (CFL) SU(3)LSU(3)RSU(3)CU(1)B ?
SU(3)LRC ???????? NG bosons gluons quarks
? ?????? ???? ???
Ginzburg-Landau (GL) approach
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Ginzburg-Landau (GL) approach

• Model-independent approach based only on the
  symmetry.
• Free-energy is expanded in terms of the order
  parameter F
• (such as the magnetization) near the phase
  boundary.

Z(2) symmetry m ?-m
2nd order phase transition
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????????QCD??????

• Symmetry
• Order parameters
• Transformations

Topological structure of the phase diagram
Two simple cases 3-flavor (mumdms0),
2-flavor (mumd0, ms8)
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Transformations
????????
??????
GL????????
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???????
Pisarski-Wilczek (84)
First order phase transition
2nd order phase transition
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Massless 3-flavor???
??????
Hatsuda-Tachibana-Yamamoto-Baym (06)
New critical point
Mass term for d external field for s
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massless 3-flavor???
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massless 3-flavor???
Hatsuda-Tachibana- Yamamoto-Baym (06)
See also, Kitazawa, Koide, Kunihiro Nemoto (02)
A realization of hadron-quark continuity
Schäfer Wilczek, (99)
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????QCD????
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????QCD????
T
Quark-Gluon Plasma
Hadrons
Color superconductivity
mB
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????????pion
T
Quark-Gluon Plasma
Hadrons
Color superconductivity
?
mB
??????????p?? ????????????????
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Ginzburg-Landau (GL) effective Lagrangian
Effective Lagrangian
Kinetic term
Mixing term
Mass term
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A toy model
Lagrangian
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generalized pion??????
generalized Gell-Mann-Oakes-Renner (GOR) relation
Hadron-quark continuity ? pion ????????????!
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????????vector meson?????
Hadron-quark Continuity

• ?????? gluon ?? ? (mg1.362?, Gusynin-
  Shovkovy, 2001)
• ???? vector meson ? nonet. ??????? gluon ?
  octet.
• ????? vector singlet ????????
• NG boson ???????????????????????

In-medium QCD sum rule
Hatsuda, Koike Lee, NPB (2001)
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QCD sum rule
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Operator Product Expansion (OPE) for vector meson
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Finite energy sum rule (FESR)
?????????
Octet vector meson ???
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Vector singlet??????

• CFL??? U(1)B ?????????????? NG scalar (H) ????
• flavor singlet ? channel ???? H ???????? (Im?) ?
  ??

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Continuity of vector meson
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Summary Outlook

• 1. Interplay between chiral and diquark
  condensate in model-independent Ginzburg-Landau
  approach
• 2. We found a new critical point at low T
• 3. Hadron-quark continuity in QCD phase
  structure
• Continuity of elementary excitations
• Pion/vector meson at low density and
  generalized
• pion/gluon at high density are
  continuously connected.
• Mystery of vector singlet at high density
  is resolved.
• 5. Future problems
• Real location of the new critical point in T-µ
  plane?
• Hadron-quark continuity for baryon (? quark) ?
• Its relevance to neutron star and heavy ion
  collision?