Presentation Transcript

1. 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 Naoki Yamamoto (University of Tokyo) (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.
2. QCDphase diagram T Quark-Gluon Plasma RHIC/LHC Hadrons Color superconductivity quark matter CFL mB Neutron star
3. E p Color Superconductivity QCD at high density →asymptotic free Fermi surface Attractive channel → Cooper instability [3]C×[3]C=[6]C+[3]C 3 q “diquark condensate” q μ “Fermi sea” “Dirac sea”
4. u s d Color-Flavor Locking (CFL) Pairing channel s-wave pairing, spin singlet → Dirac antisymmetric Attractive channel → color antisymmetric Pauli principle → flavor antisymmetric U(1)A anomaly → Lorentz scalar 3-flavor limit: Color-Flavor Locking (CFL) Alford-Rajagopal-Wilczek (NPB1999) Gauge-invariant order parameter e.g.) Symmetry breaking pattern: u,d,s r,g,b
5. CFL is positive parity Alford-Rajagopal-Wilczek (NPB1999) ... due to the presence of U(1)A anomaly. Consider the Kobayashi-Maskawa-’t Hooft (KMT) vertex with quark mass: VKMT is minimized when and the positive parity state is energetically favored. G G Kobayashi-Maskawa (PTP1970); ‘t Hooft (PRD1976) T. Schafer (PRD2002)
6. Chiral symmetry breaking in CFL Alford-Rajagopal-Wilczek (NPB1999) The chiral condensate: Exactly calculated thanks to the screening of instantons at high μ: [Point] Chiral symmetry is broken not only by the diquark condensate but also the chiral condensate in CFL. Nonzero chiral condensate in CFL is model-independent. Chiral-super interplay of the type is inevitable. T. Schafer (PRD2002); NY (JHEP2008)
7. Possible phase structure I T Quark-Gluon Plasma Color superconductivity Hadrons mB 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.
8. Possible phase structure III T Quark-Gluon Plasma Hadrons CFL quark matter mB Is there this possibility? [seealsoHidaka-san’s talk]
9. T mB Phase diagram of “instantons” (Nf=3) “instanton molecule” “instanton liquid” “instanton gas“ Chiral phase transition at high μ: instanton-induced crossover. 4-dim. generalization of Kosterlitz-Thouless transition. NY (JHEP2008)
10. Another viewpoint: Lee-Yang zeros Halasz-Jackson-Verbaarschot (PRD97) 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 cutthrough m=0. [Lee-Yang zeros at μ=0] Leutwyler-Smilga (PRD92)
11. Predictions of Random Matrix Theory (RMT) RMT predictions: Chiral symmetry restores at μ=μc. 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] Halasz-Jackson-Verbaarschot (PRD97); Halasz, et al. (PRD98)
12. Finite-volume QCD at high density NY-Kanazawa (PRL2009) 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.
13. Partitionfunctions 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... NY-Kanazawa (PRL2009) at high μ. at μ=0.
14. Exact Lee-Yang zeros athigh 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 highμ and the chiral condensate can be nonzero for μ<∞. NY-Kanazawa (PRL2009)
15. Summary & Outlook 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<∞. 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?
16. Back up slides
17. Chiralvs. Diquark condensates Diquark condensate Chiral condensate pF E p -pF Y. Nambu (‘60)
18. Continuity between hadronic matter and quark matter (color-flavor locking) quark-hadron continuity 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 Elementary excitations Conjectured by Schäfer & Wilczek, PRL 1999
19. Instantons and chiral symmetry breaking Why instanton? : mechanism for chiral symm. breaking/restoration “instanton liquid” (metal) “instanton molecule” (insulator) T=0 T>Tc Schäfer-Shuryak, Rev. Mod. Phys. (‘97) Origin of NJL model: nonlocal NJL model See, e.g., Hell-Rößner-Cristoforetti-Weise, arXiv: 0810.1099 Then, χSBin dense QCD from instantons?
20. Low-energy dynamics in dense QCD Dense QCD: U(1)A is asymptotically restored. Low-energy effective Lagrangian of η’ Manuel-Tytgat, PL(‘00) Son-Stephanov-Zhitnitsky, PRL(‘01) Schäfer, PRD(‘02) convergent!
21. Coulomb gas representation Instanton density, topological susceptibility Witten-Veneziano relation： : topological charge : 4-dim Coulombpotential
22. Renormalization group analysis Fluctuations： RG scale： Change of potential after RG： RG trans.： kineticvs.potential D＝2：potential irrelevant → vortex molecule phase potential relevant → vortex plasma phase D≧3： potential relevant → plasma phase
23. Phase transition induced by instantons D-dimsine-Gordonmodel： 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 Note: weak coupling QCD:
24. Color superconductivity at large Nc qq scattering Double-line notation qq scattering Deryagin-Grigoriev-Rubakov (‘92) Shuster-Son (‘00) Ohnishi-Oka-Yasui (‘07) ★ Diquarks are suppressed at large Nc!
25. ≿ ≿ 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 2nd critical point Realistic QCD phase structure? T T T μ μ μ Hatsuda, Tachibana, Yamamoto & Baym 06
26. Possible phase structure II T Quark-Gluon Plasma Color superconductivity Hadrons mB Of course, 1st order chiral phase transition at T=0 is still possible.