1. Topological Structure of Dense Hadronic Matter October, 2004 Seoul V. Vento Universitat de València Colaborators: Heejung Lee (Universitat de València), Byung-Yung Park (Chungnam Nat’l Univ.), Dong-Pil Min (Seoul Nat’l Univ.) and Mannque Rho(Saclay & Hanyang)

2. 1.Introduction 2.Dense Skyrmion Matter 3.Pions in Dense Skyrmion Matter 4.Sliding Vaccua 5.Vector Mesons 6.Ongoing work 7.Concluding remarks

3. 1. Introduction

4. Theory Effective Relevant degrees of freedom? Dynamics?

5. Effective Theory QCD Observation

6. Quantum Chromo-Dynamics Effective Theory at zero Temp./Density Effective Theory at finite Temp./Density

7. Skyrme’s Old Idea 1960, T. H. R. Skyrme

8. Skyrme’s Old Idea U(x) : mapping from R 3 -{ }=S 3 to SU(2)=S 3 8 topological soliton 1960, T. H. R. Skyrme R ~ 1 f m M ~ 1.5 GeV BARYON

9. 2. Dense Skyrmion Matter B.-Y. Park, D.-P. Min, M. Rho, V. Vento, Nucl. Phys. A707 (2002) 381

10. Two Skyrmions Product Ansatz 1960, T. H. R. Skyrme

11. 1988, Braaten & Carson, 1995, Leese, Manton & Schroers Toroidal B=2 Skyrmion

12. Multi-Skyrmion System http://www.damtp.cam.ac.uk/user/hep/research.html#solitons

13. 1985, I. Klebanov (E/B) min =1.078 at L C =5.56 Simple Cubic Skyrmion Crystal U(x+L C,y,z) =  y U(x,y,z)  y y Y z xz x x x X y LCLC o

14. Half-Skyrmion Crystal U(x+L C,y,z) =  y U(x,y,z)  y 1987, A. S. Goldhaber & N. S. Manton y zx X LCLC  =-1  =+1 (L c /2 above) + additional symmetry (E/B) min =1.076 at L C =5.56

15. 1989, L. Castillejo et al. & M. Kugler et al. y Y x x X y z=L F /2 plane Y o z z z X z LFLF z=0 plane FCC Skyrmion Crystal

16. Y X (E/B) min =1.038 at L f =4.72 o z Y z z X z LFLF y x x y Half-Skyrmion CC

17. E/B vs. L F

18. Chiral symmetry restoration in dense matter?

19. 3. Pions in Dense Skyrmion Matter H.-J. Lee, B.-Y. Park, D.-P. Min, M. Rho, V. Vento, Nucl. Phys. A723 (2003) 427; Nucl. Phys. A741 (2004) 161

20. nuclear matter density  -N sigma term Chiral Symmetry Restoration pion properties in dense medium?

21. GellMann-Oakes-Renner Relation Chiral symmetry restoration

22. GellMann-Oakes-Renner Relation pion condensation?

23. Brown-Rho scaling ?

24. Deeply Bound Pionic States Yamazaki et al., 1998

25. Skyrme Model ( m  =0 ) \

26.  dynamics (  =0) \ +  - skyrmion matter interactions Skyrmion matter Pion fluctuations on top of the skyrmion matter

29.  dynamics (  =0) \ Wavefunction renormalization constant Z -1

30. Pion effective mass Pseudogap phase?

31. Pion velocity in medium

32. ff   Pseudogap? Zarembo, hep-ph/0104305 U still remains on the Chiral Circle But =0 Chiral Symmetry Restoration

33. Zarembo, hep-ph/0104305

34. 4. Sliding Vacuua H.-J. Lee, B.-Y. Park, M. Rho, V. Vento, Nucl. Phys. A723 (2003) 427

35. Skyrme Lagrangian Trace Anomaly of QCD m  ~ 720 MeV, f  ~240 MeV Ellis & Lanik, PLB(1985) Brown-Rho scaling, PRL(1992)

36. ff  V  Vacuum (  =0) U=1  =f 

37. Naive Estimate E/B=M 2 (L)  2 +M 4 (L) +M m (L)  3 +V(  )

38. E/B

40. In-medium quantities

41. Without 

42. In-medium pion velocity

43. 5. Vector Mesons B.-Y. Park, M. Rho, V. Vento, Nucl. Phys. A736 (2004) 129

44. Hidden Local Gauge Symmetry dilaton Trace Anomaly rho & omega vector mesons HLG + Vector Meson Dominance

45. KSRF relation : m V =af  g 2 22 Bando, Kugo, Yamawaki, Phys. Rep. (1988) pions, chi, rho and omega

46. E/B without Omega

47. E/B with Omega

48. E/B

49. & without Omega

50. & with Omega

51. 6. Ongoing work

52. position  orientation size Introduce variables describing the single skyrmion dynamics Classical mechanics Statistical mechanics Quantum mechanics Skyrmion from Instanton 1989, M. F. Atiyah & N. S.Manton

53. time component of SU(2) gauge potential for the instanton field of charge N time-ordering constant matrix to make U approach 1 at infinity constant rotation matrix

54. E/B vs. L F

57. 7. Concluding remarks

58. The skyrmions role in dense matter

59. 1. Construct dense skyrmion matter 2. Fluctuations on top of this skyrmion matter. Properties and Dynamics of hadrons in dense medium.

60. Skyrme model Universal theory of baryons and mesons Nuclei and meson fluctuations Nuclear matter and mesons in the medium …….. Nuclear physicists dream! Caveats: Still very primitive! Crystal structures which should be Fermi liquids  Quantum effects! Approach to QCD