1. Naoki Yamamoto (Univ. of Tokyo) Tetsuo Hatsuda (Univ. of Tokyo) Motoi Tachibana (Saga Univ.) Gordon Baym (Univ. of Illinois) Phys. Rev. Lett. 97 (2006)122001 (hep-ph/0605018 ) (hep-ph/0605018 ) Quark Matter 2006 Nov. 15. 2006 Hadron-quark continuity induced by the axial anomaly in dense QCD

2. Introduction T  Quark-Gluon Plasma Colorsuperconductivity Hadrons 1st Critical point Asakawa & Yazaki, ’89 Standard picture

3. Introduction T  Quark-Gluon Plasma Colorsuperconductivity Hadrons 1st ? hadron-quark continuity? (conjecture) Schäfer & Wilczek, ’99 Critical point Asakawa & Yazaki, ’89

4. Introduction T  Colorsuperconductivity Hadrons New critical point Yamamoto et al. ’06 What is the origin? Quark-Gluon Plasma 1st Critical point Asakawa & Yazaki, ’89

5. ・ Symmetry of the system ・ Order parameter Φ Symmetry:Symmetry: Order parameters :Order parameters : 1.φ 4 theory in Ising spin system 2.O(4) theory in QCD at T≠0 2.O(4) theory in QCD at T≠0 Pisarski & Wilczek ’84 What about QCD at T≠0 and μ≠0? What about QCD at T≠0 and μ≠0 ? Topological structure of the phase diagram Interplay Ginzburg-Landau (GL) model-independent approach e.g. Axial anomaly

6. Most general Ginzburg-Landau potential Instanton effects ＝ Axial anomaly （ breaking U(1) A ） Axial anomaly （ breaking U(1) A ） η’ mass New critical point

7. Massless 3-flavor case Possible condensates ＝ Axial anomaly （ breaking U(1) A ） Axial anomaly （ breaking U(1) A ）,

8. : 1 st order : 2 nd order Phase diagram with realistic quark masses

9. Z 2 phase Phase diagram with realistic quark masses New critical point A realization of hadron-quark continuity

10. Summary & Outlook 1. Interplay between and in model-independent Ginzburg-Landau approach in model-independent Ginzburg-Landau approach 2. We found a new critical point at low T 3. Hadron-quark continuity in the QCD ground state 4. QCD axial anomaly plays a key role 5. Exicitation spectra? at low density and at high density at low density and at high density are continuously connected. are continuously connected. 6. Future problems Real location of the new critical point in T-μ plane? How to observe it in experiments?

11. Back up slides

12. Crossover in terms of QCD symmetries COE phase : Z 2 CSC phase : Z 4 γ-term : Z 6 COE & CSC phases can ’ t be distinguished by symmetry. → They can be continuously connected. COE phase : Z 2

13. G = SU(3) L ×SU(3) R ×U(1) B ×U(1) A ×SU(3) C Hyper nuclear matter SU(3) L ×SU(3) R ×U(1) B → SU(3) L+R chiral condensate broken in the H-dibaryon channel Pseudo-scalar mesons (π etc) vector mesons (ρ etc) baryons CFL phase SU(3) L ×SU(3) R ×SU(3) C ×U(1) B → SU(3) L+R+C diquak condensate broken by d NG bosons massive gluons massive quarks (CFL gap) PhaseSymmetrybreakingPatternOrderparameter U(1) B Elementaryexcitations Hadron-quark continuity Hadron-quark continuity (Schäfer & Wilczek, 99) Continuity between hyper nuclear matter & CFL phase

14. GL approach for chiral & diquark condensates Chiral cond. Φ: Chiral cond. Φ: Diquark cond. d : 3 3★3★3★3★1 13 1 3 33 ＝ Axial anomaly （ breaking U(1) A to Z 6 ） Axial anomaly （ breaking U(1) A to Z 6 ） 6-fermion interaction

15. Realistic QCD phase structure m u,d = 0, m s =∞ (2-flavor limit) m u,d,s = 0 (3-flavor limit) Critical point 0 ≾ m u,d <m s ≪ ∞ (realistic quark masses) New critical point ≿≿ Asakawa & Yazaki, 89 hadron-quark continuity Schäfer & Wilczek, 99

16. Leading mass term Leading mass term (up to ) Mass spectra for lighter pions Generalized GOR relation including σ & d Pion spectra in intermediate density region Mesons on the hadron side Mesons on the CSC side Interaction term Axial anomaly Axial anomaly

17. Apparent discrepancies of “hadron-quark continuity” On the CSC side, extra massless singlet scalarextra massless singlet scalar (due to the spontaneous U(1) B breaking) 8 rather than 9 vector mesons (no singlet)8 rather than 9 vector mesons (no singlet) 9 rather than 8 baryons (extra singlet)9 rather than 8 baryons (extra singlet)

18. More realistic conditions Finite quark massesFinite quark masses β-equilibriumβ-equilibrium Charge neutralityCharge neutrality Thermal gluon fluctuationsThermal gluon fluctuations Inhomogeneity such as FFLO stateInhomogeneity such as FFLO state Quark confinementQuark confinement Can the new CP survive under the following?

19. Basic properties Why ? Why ? assumption: ground state → parity + assumption: ground state → parity + The origin of η’ mass The origin of η’ mass QCD axial anomaly ( Instanton induced interaction) QCD axial anomaly ( Instanton induced interaction)

20. Phase diagram (3-flavor) Crossover between CSC & COE phases & New critical point A γ>0 γ=0 : 1 st order : 2 nd order

21. Phase diagram (2-flavor) b>0b<0

22. The emergence of the point A Modification by the λ-term The effective free-energy in COE phase stationary condition

23. The origin of the new CP in 2-flavor NJL model Kitazawa, Koide, Kunihiro & Nemoto, 02 & their TP pFpF p pFpF p NG CSC This effect plays a role similar to the temperature, and a new critical point appears. As G V is increased, COE phase becomes broader.  becomes larger at the boundary between CSC & NG. → The Fermi surface becomes obscure.

24. Coordinates of the characteristic points in the a-α plane 3-flavor 2-flavor 2-flavor (b>0)

25. Crossover in terms of the symmetry discussion homogenious & isotropic fluid Typical phase diagram symmetry broken

26. Ising model in Φ 4 theory Model-independent approach based only on the symmetry. Free-energy is expanded in terms of the order parameter Φ (such as the magnetization) near the phase boundary. Ising model h=0 Z(2) symmetry : m ⇔－ m

27. GL free-energy Z(2) symmetry allows even powers only. This shows a minimal theory of the system. b(T)>0 is necessary for the stability of the system. a(T) changes sign at T=T C. → a(T)=k(T － T c ) k>0, T c : critical temperature unbroken phase (T>T c )broken phase (T<T c ) Whole discussion is only based on the symmetry of the system. (independent of the microscopic details of the model) GL approach is a powerful and general method to study the critical phenomena. This system shows 2 nd order phase transition.