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Topological Structure of Dense Hadronic Matter

May 2006 Trieste. Topological Structure of Dense Hadronic Matter. V. Vento Universitat de València. Colaborators: Heejung Lee (APCTP), Byung-Yung Park (Chungnam Nat’l Univ.), Dong-Pil Min (Seoul Nat’l Univ.) and Mannque Rho(Saclay). Introduction A theory for Nuclear Structure

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Topological Structure of Dense Hadronic Matter

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  1. May 2006 Trieste Topological StructureofDense Hadronic Matter V. Vento Universitat de València Colaborators: Heejung Lee (APCTP),Byung-Yung Park (Chungnam Nat’l Univ.), Dong-Pil Min (Seoul Nat’l Univ.) and Mannque Rho(Saclay)

  2. Introduction • A theory for Nuclear Structure • 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. 2. A theory for Nuclear Structure

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

  9. Skyrme’s Old Idea topological soliton U(x) : mapping fromR3-{ }=S3toSU(2)=S3 8 R ~ 1 f m M ~ 1.5 GeV 1960, T. H. R. Skyrme BARYON 1983 Adkins,Nappi,Witten,….

  10. Two Skyrmions Product Ansatz 1984 Orsay group, VV,..

  11. Toroidal B=2 Skyrmion 1988, Braaten,Carson,…. Manton and collaborators

  12. Multi-Skyrmion Systems (surface of constant baryon number density)

  13. Quantization is progressing Manton (B=2), Carson (B=3), Walhout (B=4), Irwin (B=4 to 9), Krusch (general formalism!)

  14. 3. Dense Skyrmion Matter B.-Y. Park, D.-P. Min, M. Rho, V. Vento,

  15. Skyrmion Crystal y y o o o o o o o o z z x x 1985, CC, I. Klebanov, 1987, Half-Skyrmion BCC, A. S. Goldhaber & N. S. Manton 1989, FCC & Half-Skyrmion CC, L. Castillejo et al., M. Kugler et al. z 2LFCC

  16. E/B vs. LF

  17. <tr(U)> Chiral symmetry restoration in dense matter?

  18. 3. Pions in Dense Skyrmion MatterB.-Y. Park, H.-J. Lee, M. Rho, V. Vento

  19. Skyrme Model(mp=0) \

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

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

  22. Chiral Symmetry Restoration p-Nsigma term nuclear matter density pion properties in dense medium?

  23. Chiral symmetry restoration GellMann-Oakes-Renner Relation

  24. pion condensation? GellMann-Oakes-Renner Relation

  25. Pseudogap phase? Pion effective mass

  26. Pion velocity in medium

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

  28. Zarembo, hep-ph/0104305

  29. 4. Sliding VacuuaB.-Y. Park, H.-J. Lee, M. Rho, V. Vento

  30. Skyrme Lagrangian Trace Anomaly of QCD Ellis & Lanik, PLB(1985) mc ~ 720 MeV, fc~240 MeV

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

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

  33. E/B

  34. In-medium quantities

  35. 5. Vector Mesons

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

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

  38. E/B

  39. <s> & <c> without Omega

  40. <s> & <c> with Omega

  41. 6. Ongoing work

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

  43. 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

  44. E/B vs. LF

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