Hadron-quark continuity induced by the axial anomaly in dense QCD

1. Hadron-quark continuity induced by the axial anomaly in dense QCD 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) Quark Matter 2006 Nov. 15. 2006

2. Critical point Asakawa & Yazaki, ’89 Introduction T Quark-Gluon Plasma 1st Color superconductivity Hadrons mB Standard picture

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

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

5. Interplay Axial anomaly Ginzburg-Landau (GL) model-independentapproach ・ Symmetry of the system ・ Order parameter Φ Topological structure of the phase diagram e.g. • φ4 theory in Ising spin system • O(4)theory in QCD at T≠0 Pisarski & Wilczek ’84 What about QCD at T≠0 and μ≠0? • Symmetry: • Order parameters :

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

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

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

9. Phase diagram with realistic quark masses New critical point Z2 phase A realization of hadron-quark continuity

10. Summary & Outlook 1. Interplay between and 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 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. COE phase : Z2 Crossover in terms of QCD symmetries COE phase : Z2 γ-term : Z6 CSC phase : Z4 COE & CSC phases can’t be distinguished by symmetry. → They can be continuously connected.

13. G = SU(3)L×SU(3)R×U(1)B×U(1)A×SU(3)C Continuity between hyper nuclear matter & CFL phase Hadron-quark continuity(Schäfer & Wilczek, 99) 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) Phase Symmetry breaking Pattern Order parameter U(1)B Elementary excitations

14. GL approach for chiral & diquark condensates 3 3★ 1 3 1 3 1 3 3 Chiral cond. Φ: Diquark cond. d : Axial anomaly（breakingU(1)Ato Z6） ＝ 6-fermion interaction

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

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

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

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

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

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

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

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

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

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

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

26. Ising model in Φ4 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. This system shows 2nd order phase transition. unbroken phase (T>Tc) broken phase (T<Tc) 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=TC. → a(T)=k(T－Tc) k>0, Tc: critical temperature 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.