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T. Hatsuda (University of Tokyo)

QCD Phase Structure at High Baryon Density. T. Hatsuda (University of Tokyo). contents Introduction Ginzburg-Landau approach to Dense QCD (1) Continuity in Dense QCD (2,3) UCA/QCD Correspondence (4) Summary.

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T. Hatsuda (University of Tokyo)

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  1. QCD Phase Structure at High Baryon Density T. Hatsuda (University of Tokyo) • contents • Introduction • Ginzburg-Landauapproach to Dense QCD (1) • Continuity in Dense QCD(2,3) • UCA/QCD Correspondence(4) • Summary • Tachibana, Yamamoto, Baym & T.H., PRL 97 (2006) 122001; PRD 76 (2007) 074001. • Tachibana, Yamamoto & T.H., PRD78 (2008) 011501. • Maeda, Baym and T.H., PRL 103 (2009) 085301 • (4) Abuki, Baym, Yamamoto and T.H., arXiv: 1003.0408 [hep-ph] NFQCD, March 10, 2010

  2. Physics Today, Dec. vol.58 (2005) http://www.lsbu.ac.uk/water/phase.html H2O 4He

  3. Collins & Perry, PRL 34 (1975) QGP : QGP cSB : CFL : Nambu, PRL 4 (1960) Alford, Rajagopal & Wilczek, NP B537 (1999) Symmetry realizationin hot/dense QCD（for mu,d,s=0 case）

  4. QGP cSB CSC Common features 1. Competition between different orders 2. Strong coupling • Kitazawa, Nemoto, Kunihiro, PTP (‘02) • Abuki, Itakura & Hatsuda, PRD (’02) • Chen, Stajic, Tan & Levin, Phys. Rep. (’05) QCD and high temperature superconductivity Fermi Dirac

  5. QGP cSB CSC Transition at Finite T

  6. ~ SU(Nf)LxSU(Nf)RxU(1)A SU(Nf)LxSU(Nf)R quark mass term Ginzburg-Landau-Wilson analysis in hot QCD Pisarski & Wilczek (’84) Symmetry: X Chiral field: Chiral transformation: Axial anomaly

  7. Svetitsky & Yaffe, NPB210 (’82) Pisarski and Wilczek, PRD29 (’84) m s 1st 2nd large cross over m u,d 1st small large small Order of the thermal QCD transition (μ=0) Nf=0 Nf=2 Nf=3 Nf=1

  8. QGP cSB CSC Transition at Finite T Asakawa-Yazaki CP

  9. QGP cSB CSC Transition at finite μ CP

  10. Mass-Radius relation of Neutron Stars and dense EOS Thermonuclear Burst in X-ray Binaries 4U 1608-248 EXO 1745-2484U 1820-30 (i) Apparent surface area (ii) Eddington limit Ozel, Baym & Guver, arXiv: 1002.3153 [astro-ph.HE]

  11. u u u u d d d d s s s s major differences from the standard BCS superconductor High Tc:Tc/eF ~ 0.1 Compact pair : r~ 1-10 fm Color superconductivity at high density CFL 2SC uSC dSC flavorcolor 1. Relativistic fermi system color-magnetic int. dominant Son, PRD59 (’99), Schafer & Wilczek, PRD60 (’99) Pisarski & Rischke, PRD61 (’00) Hong, Miransky, Shovkovy & Wijewardhana, PRD61 (’00) • Color-flavor entanglement Various phases(c.f. Ice, 3He) 2SC, uSC, dSC, CFL etc

  12. GL analysis for chiral-super interplay in QCD (Nf=3) Symmetry: diquark field: Chiral field: Pisarski & Wilczek, PRD29 (’84) Iida & Baym, PRD63 (’01) Yamamoto, Tachibana, Baym & T.H., PRL97 (’06)

  13. Yamamoto, Tachibana, Baym & T.H., PRL 97 (’06), PRD 76 (‘07) Complete classification of the GL potential (mu,d,s=0) Axial anomaly broken explicitly

  14. Chiral-CFL interplay in Nf=3 Natural parameter relations

  15. phase diagram (without d-σcoupling) T μ

  16. phase diagram (with d-σ coupling) T μ Low T critical point driven by the axial anomaly

  17. phase diagram (with d-σ coupling & quark mass) T μ Low T critical point driven by the axial anomaly High T critical point driven by Higgs condensate

  18. NJL model with axial anomaly (mu=md=ms) Abuki, Baym, Yamamoto and T.H., arXiv: 1003.0408 [hep-ph]

  19. QGP cSB CSC Spectral continuity at finiteμ CP induced by Higgs CP induced by anomaly

  20. Continuity in the ground state condensates m ○ Generalized Gell-Mann-Oakes-Renner relation : Yamamoto, Tachibana, Baym & T.H., PR D76 (’07) ○ Tachibana, Yamamoto and T.H., PRD78 (2008) Continuity in excitation modes Vector meson – CFL gluon continuity (QCD sum rules):

  21. UCA/QCD correspondence Baryon BCS diquark BEC diquark BCS “Simulating dense QCD matter with Ultracold atoms ?” Maeda, Baym and Hatsuda, Phys. Rev. Lett. 103 (2009) 085301 Neutron matter quark Matter?

  22. Maeda, Baym and Hatsuda, Phys. Rev. Lett. 103 (2009) 085301 fσ b Atomic BF mixture s-wave boson-fermion scattering length strong 0 +0 weak 0 -0 weak strong

  23. Induced superfluidity of composite fermions -- a novel analogy between cold atoms and QCD -- Maeda, Baym & Hatsuda, Phys. Rev. Lett. 103 (’09) weak (bf)-(bf) attraction ⇔ strong b-f attraction baryon superfluidity ⇔ strong diqark correlation cold atoms dense QCD Composite Fermion

  24. Phase structure and symmetry T b,f normal gas b,f normal gas b-BEC N normal gas N-BCS strong coupling weak coupling 0 Broken and residual symmetries (continuous symmetries) The Hamiltonian density has symmetry. broken residual

  25. Y. Nambu, Nobel Lecture (Dec.8, 2008), page 24/25

  26. Summary and Future • QCD phase structure ・ Three major phases in QCD: χSB,QGPand CSC ・ Axial anomaly plays crucial roles everywhere ・ Close similarity with high Tc supercond. & multi-comp. cold atoms • Chiral-super interplay driven by axial anomaly ・ A new critical point at low T and high μ ・ Continuity of χSBphase and CSC phase • Spectral continuity in high density QCD ・ Pions are pions. ・ Vector mesons are gluons. 4. Future ・ Real location of the new critical point ? ・ How to detect critical lines and points in lab. experiment ? ・ Tabletop simulations of high density QCD using cold atoms ?

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