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Half- Skyrmion Matter & Quarkionic Matter

HIM-WCU workshop Hanyang U. Oct. 31 , 2009. Half- Skyrmion Matter & Quarkionic Matter. Byung -Yoon Park ( Chungnam Nat’l Univ.). Collaborators. M. Rho( Saclay , Hanyang Univ.) V. Vento(Valencia Univ.) D.-P. Min(Seoul National Univ.) H.-J. Lee( Chungbuk National Univ.). Contents.

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Half- Skyrmion Matter & Quarkionic Matter

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  1. HIM-WCU workshop HanyangU. Oct. 31, 2009 Half-Skyrmion Matter&Quarkionic Matter 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 • Skyrme Model ? • 2. Dense Skyrmion Matter • 3. Dense & Hot Skyrmion Matter • 4. Summary

  4. 1. Skyrme Model?

  5. Skyrmion Model topological soliton U(x) : mapping fromR3-{ }=S3toSU(2)=S3 8 BARYON ? 1960, T. H. R. Skyrme R ~ 1 f m M ~ 1.5 GeV

  6. 1935 Yukawa 1919 Rutherford1932 Chadwick 1960 Skyrme pion proton neutron pion proton neutron HadronicWorld(Skyrmionist’s Viewpoint)

  7. SU(2) Collective Coord. Quantization N, D SU(3) collective Coordinate Quatization N, S, X, D, S*, X*,W

  8. bound kaon Hedgehog Soliton N, S, X, D, S*, X*,W SU(2) collective Coordinate Quatization

  9. bound D,D* Hedgehog Soliton N, S, Xc, D, S*, X*,Wc c c SU(2) collective Coordinate Quatization

  10. Multi-Skyrmion system B=2 Torus B=3 Tetrahedron B=4 Cube B=5 with Dd2 sym B=6 with Dd4 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. 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 2. Dense Skyrmion matter

  16. Half-Skyrmion Crystal z x LC y X 0 s=-1 s=+1 (Lb/2 above) 1987, A. S. Goldhaber & N. S. Manton U(x+LC,y,z) =tyU(x,y,z)ty + additional Symmetry w.r.t. s -s (E/B)min=1.076 at LC=5.56 2. Dense Skyrmion matter

  17. Half-skyrmion? . ^ U = exp(iF(r)t r ) U =-1 p F(r) r 2. Dense Skyrmion matter

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

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

  20. B=4 skyrmion 2. Dense Skyrmion matter

  21. 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. Castellejo et al. & M. Kulger et al. Y 2. Dense Skyrmion matter

  22. 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 2. Dense Skyrmion matter

  23. E/B vs. LF 2. Dense Skyrmion matter

  24. <U>=<s> Chiral symmetry restoration in dense matter? 2. Dense Skyrmion matter

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

  26. Skyrme Model(mp=0) \ Pion fluctuation in rB=0 space Vacuum : U=1 2. Dense Skyrmion matter

  27. pdynamics(r=0) \ Skyrmion matter Pion fluctuations on top of the skyrmion matter + p-skyrmion matter interactions 2. Dense Skyrmion matter

  28. pdynamics(r=0) \ 2. Dense Skyrmion matter

  29. pdynamics(r=0) \ 2. Dense Skyrmion matter

  30. pdynamics(r=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. Pseudogap? Chiral Symmetry Restoration p fp s U still remains on the Chiral Circle But <U>=0 Zarembo, hep-ph/0104305 2. Dense Skyrmion matter

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

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

  35. p V(c) fp s c fc <c> U cU <U> Vacuum (r=0) U=1 c=fc 2. Dense Skyrmion matter

  36. Naive Estimation E/B=M2(L)c2+M4(L) +Mm(L)c3+V(c)L3 2. Dense Skyrmion matter

  37. Naive Estimation 2. Dense Skyrmion matter

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

  39. <c>& <U> mp=0 <c> <s> cSB Phase Pseudogap Phase? cS Phase 2. Dense Skyrmion matter

  40. Pseudogapstill remains? p Pseudogap Phase * fp p * fp s cS Phase p s cSB Phase s 2. Dense Skyrmion matter

  41. 3. Hot & Dense Skyrmion Matter

  42. ? 2. Hot & Dense Skyrmion matter

  43. Skyrmion Soup Main ingredients : pions Condiments : dilaton vector mesons Heat 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. LF 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

  48. 2. Hot & Dense Skyrmion matter

  49. Pion Gas! P = T4 E/B = 3PV p2 30 E/B=(M2(r)+3PV)c2+M4(r) +V(c)/r 1/3 2. Hot & Dense Skyrmion matter

  50. Conclusion 2. Hot & Dense Skyrmion matter

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