1. 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)

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?
Theory
Effective
Relevant degrees of freedom?
Dynamics?

5. QCD
Effective
Theory
Observation

6. Quantum Chromo-Dynamics
Effective Theory
at zero
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. U(x) : mapping from R3-{ }=S3 to SU(2)=S3
Skyrme’s Old Idea
1960, T. H. R. Skyrme
U(x) : mapping from R3-{ }=S3 to SU(2)=S3 8
topological soliton
R ~ 1 f m
M ~ 1.5 GeV
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. B.-Y. Park, D.-P. Min, M. Rho, V. Vento,
3. Dense Skyrmion Matter
B.-Y. Park, D.-P. Min, M. Rho, V. Vento,

15. Skyrmion Crystal x y z z o 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. o z x y z
2LFCC

17. E/B vs. LF

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

19. 3. Pions in Dense Skyrmion Matter B. -Y. Park, H. -J. Lee, M. Rho, V
3. Pions in Dense Skyrmion Matter B.-Y. Park, H.-J. Lee, M. Rho, V. Vento

20. Skyrme Model(mp=0) \

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

24. Wavefunction renormalization constant Z-1
p dynamics(r=0) \
Wavefunction renormalization constant Z-1

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

26. GellMann-Oakes-Renner Relation
Chiral symmetry
restoration

27. GellMann-Oakes-Renner Relation
pion condensation?

28. Pion effective mass
Pseudogap phase?

29. Pion velocity in medium

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

31. Zarembo, hep-ph/

32. 4. Sliding Vacuua B.-Y. Park, H.-J. Lee, M. Rho, V. Vento

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

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

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

36. E/B

38. In-medium quantities

39. 5. Vector Mesons

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

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

42. E/B

43. <s> & <c> without Omega

44. <s> & <c> with Omega

45. 6. Ongoing work

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

47. 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

48. E/B vs. LF

51. 7. Concluding remarks

52. The skyrmion role in dense matter

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

54. 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