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Chiral symmetry breaking in dense QCD

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).

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Chiral symmetry breaking in dense QCD

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  1. 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 Naoki Yamamoto (University of Tokyo) (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

  2. QCDphase diagram ..But, 2-flavor NJL rather than QCD Early universe T Quark-Gluon Plasma ? RHIC/LHC Color superconductivity Hadrons Neutron star & quark star mB

  3. QCD critical point at high T

  4. 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: • Thermodynamic potential: • Parameters (to be fitted with pion mass/decay const.): Λ, G, m • → Calculate phase diagram numerically.

  5. : 1st order : 2nd order QCD (tri)critical point (Nf=2) T • Potential at lowest order (m=0): μ c.f.) Coefficient in NJL: N.Y. et al., ‘07

  6. No critical point in massless 3-flavor limit Chiral field: T Pisarski-Wilczek (‘84) U(1)A anomaly μ 1st order

  7. QCD critical point in 2+1 flavor T T T 0 = mu,d,s < 0 =mu,d≪ms < 0<mu,d<ms As msincreases, μ μ μ Note) CP in 2-flavor limit is also model-dependent.

  8. Some comments • Unknown medium effects on model parameters easily smear out CP! • QCD critical point at high T from 2+1 flavor PNJL modelwith gD~c0 • K. Fukushima, PRD (‘08), • N. Bratovich, T. Hell, S. Rößner + W. Weise (’08) c.f.) • 4-fermi interaction etc. also has medium effects • 3-flavor random matrix model with axial anomaly? • Sano-Fujii-Ohtani, (‘09)

  9. Location of QCD critical point? Taken from hep-lat/0701002, M. Stephanov

  10. Chiral-super interplay

  11. Chiralvs. Diquark condensates • Diquark condensate • Chiral condensate pF E p -pF Y. Nambu (‘60)

  12. Chiral-super interplay in models Phase diagram in 2-flavor NJL model Berges-Rajagopal, ‘99 Examples of phase diagrams in 2-flavor random matrix model Vanderheyden-Jackson, ‘00

  13. Notes • Many ambiguities in NJL: • With vector interaction → coexistence phase appears • Kitazawa et al, ‘02 • Possible higher interactions • Kashiwa 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!

  14. Ginzburg-Landau approach (Nf=2) T • GL potential: • Most general phase diagram Hatsuda-Tachibana-Yamamoto-Baym (‘06) μ • Precise medium effects on GL coefficients needed

  15. : 1st order : 2nd order Anomaly-induced interplay (Nf=3) Hatsuda-Tachibana-Yamamoto-Baym (‘06) T μ • 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

  16. ≿ ≿ 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

  17. QCD phase structurefrom instantons

  18. 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?

  19. 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!

  20. Coulomb gas representation • Instanton density, topological susceptibility • Witten-Veneziano relation： • : topological charge • : 4-dim Coulombpotential

  21. 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

  22. 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:

  23. T QGP χSB CFL 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. N. Yamamoto, JHEP 0812:060 (2008)

  24. QCD phase structureat large Nc

  25. QCD phase diagram at large Nc Gluodynamics (~Nc2) dominates independent of μB(~Nc). McLerran-Pisarski, NPA (‘07) see also, Horigome-Tanii, JHEP (‘07)

  26. CSC 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!

  27. Conjectured Phase Diagram for Nc= 3 Debye Screened Baryons Number N ~ Nc2 Chiral T Quark Gluon Plasma RHIC LHC Critical Point SPS Confined N ~0(1) Not Chiral Confined Baryons N ~ NcNf Chiral From McLerran at QM2009 • Not correct for 3-flavor limit: deconfinement earlier than χSR. • Note that large Ncleads 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? FAIR AGS Confined Matter Quarkyonic Matter Color Superconductivity Liquid Gas Transition

  28. Summary & Outlook • 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 lowμ to high μ • Instantons play crucial roles everywhere. • Non-vanishing chiral condensate even at high μ. • Future problems • Quarkyonic vs. CSC? • QCD phase structure from QCD itself? • AdS/CFT application?

  29. Finite-volume QCD at high μ N. Yamamoto, T. Kanazawa, arXiv:0902.4533. • microscopic regime: • Exact analytical results; • Partition function (zero topological sector): a novel correspondence! • Spectral sum rules: Dirac spectra at high μ are governed by the CSC gap Δ. • 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. at μ=0. at high μ.

  30. Continuity between hadronic matter and quark matter (Color superconductivity) Hadron-quark 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 superconductivity 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

  31. Back up slides

  32. Order of the thermal transition Z(3) GL theory O(4) GL theory SUL(3)xSUR(3) GL theory

  33. pF E u s d p -pF Color Superconductivity Fermi surface • QCD at high density asymptotic freedom • Attractive channel [3]C×[3]C=[3]C+[6]C Cooper instability dL,R:diquark 3 q 3-flavor case q u,d,s r,g,b Color-Flavor Locking (CFL) phase Alford-Rajagopal-Wilczek (‘99)

  34. Color superconductivity phase transition T Diquark field: Iida-Baym (‘00) μ 2nd order

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