1. Half-Skyrmion Matter & Quarkionic Matter HIM-WCU workshop Hanyang U. Oct. 31, 2009 Byung-Yoon Park (Chungnam Nat’l Univ.)

2. Collaborators M. Rho(Saclay, Hanyang Univ.) V. Vento(Valencia Univ.) D.-P. Min(Seoul National Univ.) H.-J. Lee(Chungbuk National Univ.)

3. Contents 1.Skyrme Model ? 2. Dense Skyrmion Matter 3. Dense & Hot Skyrmion Matter 4. Summary

4. 1. Skyrme Model?

5. Skyrmion Model 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 ?

6. protonneutron 1919 Rutherford 1932 Chadwick pion protonneutron 1935 Yukawa Hadronic World (Skyrmionist’s Viewpoint) pion 1960 Skyrme

7. SU(2) Collective Coord. Quantization N,  SU(3) collective Coordinate Quatization  ,  * 

8.  ,  *  Hedgehog Soliton SU(2) collective Coordinate Quatization bound kaon

9.  c  ,  *  *  c Hedgehog Soliton SU(2) collective Coordinate Quatization bound D,D* c c

10. Multi-Skyrmion system B=2 Torus B=3 Tetrahedron B=4 Cube B=5 with D d2 sym B=6 with D d4 sym B=7 Dodecahedron

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

12. 2. Dense Skyrmion Matter

13. 2. Dense Skyrmion matter

14. Two skyrmions in the most attractive configuration. 2. Dense Skyrmion matter

15. 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 2. Dense Skyrmion matter

16. Half-Skyrmion Crystal U(x+L C,y,z) =  y U(x,y,z)  y 1987, A. S. Goldhaber & N. S. Manton + additional Symmetry w.r.t.   -  (E/B) min =1.076 at L C =5.56 y zx X LCLC  =-1  =+1 (L b /2 above) 0 2. Dense Skyrmion matter

17. U = exp(i  F(r)  r ) ^. Half-skyrmion? F (r )F (r ) r  U =-1 2. Dense Skyrmion matter

18. U =-1 U =+1 2. Dense Skyrmion matter

19. U =-1 U =+1 2. Dense Skyrmion matter

20. B=4 skyrmion 2. Dense Skyrmion matter

21. 1989, L. Castellejo et al. & M. Kulger 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 2. Dense Skyrmion matter

22. 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 2. Dense Skyrmion matter

23. E/B vs. L F 2. Dense Skyrmion matter

24. = Chiral symmetry restoration in dense matter? 2. Dense Skyrmion matter

25. static soliton config. fluctuating pions Pion in the dense baryonic matter? classical dense matter config. 2. Dense Skyrmion matter

26. Skyrme Model ( m  =0 ) \ Pion fluctuation in  B =0 space Vacuum : U=1 2. Dense Skyrmion matter

27.  dynamics (  =0) \ +  - skyrmion matter interactions Skyrmion matter Pion fluctuations on top of the skyrmion matter 2. Dense Skyrmion matter

28.  dynamics (  =0) \ 2. Dense Skyrmion matter

29.  dynamics (  =0) \ 2. Dense Skyrmion matter

30.  dynamics (  =0) \ In-Medium pion decay constant ? In-Medium pion mass ? 2. Dense Skyrmion matter

31. pion effective mass H.-J. Lee, B.-Y. Park, D.-P. Min, M. Rho, V. Vento, Nucl. Phys. A (2003) ! 2. Dense Skyrmion matter

32. ff   Pseudogap? Zarembo, hep-ph/0104305 U still remains on the Chiral Circle But =0 Chiral Symmetry Restoration 2. Dense Skyrmion matter

33. Skyrme Lagrangian Trace Anomaly of QCD 2. Dense Skyrmion matter

34. Skyrme Lagrangian Ellis & Lanik, PLB(1985) Brown-Rho scaling, PRL(1992) m  ~ 720 MeV, f  ~240 MeV 2. Dense Skyrmion matter

35. ff  V  Vacuum (  =0) U=1  =f  ff   <><> U  U 2. Dense Skyrmion matter

36. Naive Estimation E/B=M 2 (L)  2 +M 4 (L) +M m (L)  3 +V(  )L 3 2. Dense Skyrmion matter

37. Naive Estimation 2. Dense Skyrmion matter

38. E/B =0 phase Chiral phase transition =0 phase / 2. Dense Skyrmion matter

39.  & <><> <><> Pseudogap Phase?  S Phase  SB Phase m  =0 2. Dense Skyrmion matter

40.  Pseudogap still remains? ff  ff   * *  SB Phase Pseudogap Phase  S Phase   2. Dense Skyrmion matter

41. 3. Hot & Dense Skyrmion Matter

42. ? 2. Hot & Dense Skyrmion matter

43. Skyrmion Soup Condiments : dilaton vector mesons Heat Main ingredients : pions B.-Y. Park, H.-J. Lee, V. Vento, Phys. Rev. D80 (2009) 2. Hot & Dense Skyrme matter

44. Skyrmion from Instanton 1989, M. F. Atiyah & N. S. Manton time component of SU(2) gauge potential for the instanton field of charge N time-ordering constant matrix to make U approaches 1 at infinity constant rotation matrix 2. Hot & Dense Skyrmion matter

45. E/B vs. L F 2. Hot & Dense Skyrmion matter

46. B.-Y. Park, D.-P. Min, V. Vento & M. Rho, Nucl. Phys. A707(2002) 381 2. Hot & Dense Skyrmion matter

47. B.-Y. Park, D.-P. Min, V. Vento & M. Rho, Nucl. Phys. A707(2002) 381 2. Hot & Dense Skyrmion matter

49. Pion Gas! P = T 4  2 30 E/B = 3PV E/B=(M 2 (  )+3PV)  2 +M 4 (  ) +V(  )/  1/3 2. Hot & Dense Skyrmion matter

50. Conclusion 2. Hot & Dense Skyrmion matter

51. Summary Skyrme Model can be applied to study (1) dense hadronic matter (2) hadron properties in dense matter 4. Summary

52. Thank You!