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Hot and dense lattice QCD in the strong coupling limit

Hot and dense lattice QCD in the strong coupling limit. Yusuke Nishida University of Tokyo Seminar @ Tokyo Institute of Technology May 14, 2004. hep-ph/0306066, 0312371. Introduction. Extreme dense matter e.g. neutron star interiors Neutron superfluidity Pion/kaon condensation

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Hot and dense lattice QCD in the strong coupling limit

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  1. Hot and dense lattice QCD in the strong coupling limit Yusuke Nishida University of Tokyo Seminar@Tokyo Institute of Technology May 14, 2004 hep-ph/0306066, 0312371

  2. Introduction • Extreme dense matter e.g. neutron star interiors • Neutron superfluidity • Pion/kaon condensation • Color superconductivity Finite density QCD Complex fermion determinant Monte-Carlo lattice simulations

  3. Strong coupling lattice QCD QCD Lagrangian Effective action analytic! • SCL-QCD for finite density system • 3-color QCD with mB Damgaard, Hochberg and Kawamoto, PLB (1985) Bilic, Demeterfi and Petersson, NPB (1992)with T • 2-color QCD with mB Dagotto, Karsch and Moreo, PLB (1986) Dagotto, Moreo and Wolff, PLB (1987)with T

  4. Table of contents • Introduction -- finite density QCD -- • 2-color SCL-QCD with T, mB • 3-color SCL-QCD with T, mB and/or mI • Summary and outlook -- Formulation -- -- Phase diagrams -- -- Formulation -- -- Phase diagrams --

  5. SCL-QCD applied to 2-color QCD with T, m Why 2-color QCD ? Formulation of SCL-QCD Condensates and density Phase diagram in (T, m, m) Short summary

  6. Finite density QCD • 3-color vs. 2-color at finite density hint 3-color QCD 2-color QCD T T ? ? m m

  7. 2-color QCD • Medium density region • Chiral phase vs. BEC superfluid • Strong coupling lattice QCD • Phase structure at finite T, m, m • Comparison with lattice simulations 2-color QCD

  8. Formulation • Lattice action with m Hasenfratz and Karsch,PLB125, 308 (1983)

  9. Global symmetry at m=0 • Continuum limit a=0 • 4 flavor chiral symmetry • Chiral symmetry (a=0) • Pauli-Gursey symmetry (a=0) / and .. /

  10. How to derive effective action • Strong coupling limit : • 1/d expansion and integration over • Bosonization with and • Mean field approximation • Exact integration over , and Dagotto et al.,PLB186, 395 (1987)

  11. Effective action Quark excitation energy gap energy Dynamical quark mass spatial dimension

  12. Symmetry at m=m=0 Meson-diquark symmetry .. Pauli-Gursey symmetry s D

  13. Effect of m and/or m m Chiral condensate s is favored s D Diquark condensate D is favored m s D Competition between s and D

  14. Condensates and density Minimizing effective action : chiral and diquark condensates : density empty fully occupied

  15. Condensates vs. m • m=0 and T=0 m=0,m>0=>s=0, D>0 D : decrease/disappear r : increase/saturated Saturation effect

  16. Condensates vs. m • m=0.02T=0 m

  17. Condensates vs. m • m=0.02 and T=0.7 Thermal excitationof q and q pairs

  18. Lattice data • Diquark condensate vs. m Saturation effectoccurs at m~1 D diquark condensate Qualitative agreementwith our results Kogut et al.,NPB642, 181 (2002) chemical potential m

  19. Condensates vs. T • m=0.02 and m=0.2 D(T) : 2nd order phase transition s increases as D decreases => cusp shape Competition between s and D

  20. Lattice data • Condensates vs. b Phase transitionof diquark cond.is 2nd order condensate Cusp forchiral condensate? Kogut et al.,NPB642, 181 (2002) coupling (~temperature)

  21. Phase diagram • (m,m)-plane at T=0 Saturated systemevery site isoccupied by two quarks Diquarksuperfluidity Vacuumwith no baryonnumber present

  22. What is saturation ? cf. Hardcore boson Hubbard model Full density Hopping SC current=0 Condensate=0 cond-mat/0110024 Analogical phenomenon with Mott-insulator

  23. Phase diagram • (T,m,m)-space All of the phasetransition is2nd order

  24. Short summary • Chiral phase vs. BEC superfluid • Effect of T, m and m on (s, D) • Continuum rotation from s to D • Saturation effect -- diquark vs. density • Qualitative success in 2-color QCD Kogut et al., NPB642, 181 D m m Finite density 3-color QCD !

  25. SCL-QCD applied to 3-color QCD with T, mB, mI Formulation of SCL-QCD Phase diagram in T-mB plane Phase diagram in T-mI plane Summary and outlook

  26. Formulation • KS lattice action with m 2 species of KS fermion ～ Nf=4×2 continuum flavors

  27. How to derive effective action • Strong coupling limit : • 1/d expansion and integration over • Bosonization of with • Mean field approximation : • Exact integration over , and

  28. Effective action for Nf=8 • At T=0 p=0 Effective action for Nf=4 Non-trivial coupling between “up” and “down” due to U0 integration at T=0 /

  29. Phase diagram in T-mB plane • Nc=3, Nf=8, mI=0 • Existence of TCP → CEP (m=0) • Positive gradient at TCP • Nf↑⇒Tc↓ / Nf=4 Increasing thermal excitations m=0 m=0.4

  30. Effect of small mI • mI=0.2, m=0.4 • 1st order line splits • Tc increases Coupling between“u” and “d” mI mI

  31. Pion condensation with mI • Effective action at mB=0 • At T=0 Effective action for 2-color QCDp⇔D, mI⇔mB

  32. 3-color QCD with mI Chiral symmetry at m=mI=0 NG boson : pion Pion condensation for mI>mp 2-color QCD with mB Pauli-Gursey sym. at m=mB=0 NG boson : diquark Diquark cond. for mB>mp 3c-QCD(mI) vs. 2c-QCD(mB) ..

  33. Condensates vs. mI • T=0m=0.02 (2-color with mB) mI

  34. Kogut & Sinclair, PRD 66, 034505 (2002) Lattice data • T=0, m=0.025 Pion condensate Chiral condensate mI mI Qualitative agreement with our results Saturation effect occurs at mI~2

  35. Condensates vs. T • mI=0.4, m=0.02 p(T) : 2nd order phase transition sincreases as p decreases ⇒ cusp shape Competition between sand p T

  36. Kogut & Sinclair, PRD 66, 034505 (2002) Lattice data • mI=0.8, m=0.05 Pion condensate Thermal transitionof pion condensateis 1st order for large mI ? 2nd order inmean field analysis b

  37. Phase diagram • (T,mI)-plane 2nd order critical line m=0 : m=0.02 : Normal phase Pioncondensationphase

  38. 3D phase diagram • (T,mI,m)-space All of the phasetransition is2nd order Saturatedsystem Vacuum

  39. Summary 1 • Phase structures in T-mB at m=0 • Existence of TCP • Positive gradient at TCP • Including mI with finite m • mI splits 1st order line and increases Tc of CEP T s=0 / TCP p=0 / mB T-mB-mI at m=0 mI

  40. Summary 2 • Phase structures in T-mI-m • 3c-QCD(mI) ⇔ 2c-QCD(mB) • Agreement with MC simulations • p=0 with saturation ⇒Mott insulating phenomena • Future problem • Chiral/pion cond. at mB,mI=0 T s=0 / TCP mB p=0 ? / / mI

  41. Backup slides

  42. 1/d expansion • integration Higher order terms contain more quark fields = more 1/d

  43. Density / entropy jump • T=0.8, m=0 • Generalized Clapeyron-Clausius relation Nf=4 <Halasz et al., PRD58, 096007 (1998)> Positive gradientnear TCP/CEP

  44. Density / entropy jump • Leading order of 1/d expansion • integration • Entropy of static baryons baryonic mesonic Baryons are static!

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