Topological Structure of Dense Hadronic Matter

1. October, 2004 Seoul Topological StructureofDense Hadronic Matter 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. Introduction • Dense Skyrmion Matter • Pions in Dense Skyrmion Matter • Sliding Vaccua • Vector Mesons • Ongoing work • Concluding remarks

3. 1. Introduction

4. Relevant degrees of freedom? Effective Theory Dynamics?

5. QCD Effective Theory Observation

6. QuantumChromo-Dynamics Effective Theory atzero Temp./Density Effective Theory at finite Temp./Density

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

8. Skyrme’s Old Idea topological soliton U(x) : mapping fromR3-{ }=S3toSU(2)=S3 8 BARYON R ~ 1 f m M ~ 1.5 GeV 1960, T. H. R. Skyrme

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

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

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

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

13. Simple Cubic Skyrmion Crystal Y x z x LC o y y X z x x 1985, I. Klebanov U(x+LC,y,z) =ty U(x,y,z) ty (E/B)min=1.078 atLC=5.56

14. Half-Skyrmion Crystal z x LC y X s=-1 s=+1 (Lc/2 above) 1987, A. S. Goldhaber & N. S. Manton U(x+LC,y,z) =tyU(x,y,z)ty + additional symmetry (E/B)min=1.076 at LC=5.56

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

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

17. E/B vs. LF

18. <tr(U)> 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. Chiral Symmetry Restoration p-Nsigma term nuclear matter density pion properties in dense medium?

21. Chiral symmetry restoration GellMann-Oakes-Renner Relation

22. pion condensation? GellMann-Oakes-Renner Relation

23. Brown-Rho scaling ?

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

25. Skyrme Model(mp=0) \

26. pdynamics(r=0) Skyrmion matter Pion fluctuations on top of the skyrmion matter \ + p-skyrmion matter interactions

29. pdynamics(r=0) \ Wavefunction renormalization constant Z-1

30. Pseudogap phase? Pion effective mass

31. Pion velocity in medium

32. Pseudogap? Chiral Symmetry Restoration p fp s U still remains on the Chiral Circle But <U>=0 Zarembo, hep-ph/0104305

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 Ellis & Lanik, PLB(1985) Brown-Rho scaling, PRL(1992) mc ~ 720 MeV, fc~240 MeV

36. V(c) c fc Vacuum (r=0) U=1 c=fc

37. Naive Estimate E/B=M2(L)C2+M4(L) +Mm(L)C3+V(C)

38. E/B

40. In-medium quantities

41. Without c

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 HLG Trace Anomaly rho & omega vector mesons dilaton + Vector Meson Dominance

45. pions, chi, rho and omega KSRF relation : mV=afpg2 2 2 Bando, Kugo, Yamawaki, Phys. Rep. (1988)

46. E/B without Omega

47. E/B with Omega

48. E/B

49. <s> & <c> without Omega

50. <s> & <c> with Omega