1 / 34

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).

kele
Download Presentation

Chiral symmetry breaking in dense QCD

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related