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Topological Structure of Dense Hadronic Matter May 2006 Trieste V. Vento Universitat de València Colaborators: Heejung Lee (APCTP), Byung-Yung Park (Chungnam.

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Presentation on theme: "Topological Structure of Dense Hadronic Matter May 2006 Trieste V. Vento Universitat de València Colaborators: Heejung Lee (APCTP), Byung-Yung Park (Chungnam."— Presentation transcript:

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

2 1.Introduction 2.A theory for Nuclear Structure 3.Dense Skyrmion Matter 4.Pions in Dense Skyrmion Matter 5.Sliding Vaccua 6.Vector Mesons 7.Ongoing work 8.Concluding remarks

3 1. Introduction

4 Theory Effective Relevant degrees of freedom? Dynamics?

5 Effective Theory QCD 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 Skyrmes Old Idea 1960, T. H. R. Skyrme

9 Skyrmes Old Idea 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 1983 Adkins,Nappi,Witten,….

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

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

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 z Skyrmion Crystal 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 o o o o o o z z x y x o y 2L FCC

16

17 E/B vs. L F

18 Chiral symmetry restoration in dense matter?

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

20 Skyrme Model ( m =0 ) \

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

22

23

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

25 nuclear matter density -N sigma term Chiral Symmetry Restoration 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 f Pseudogap? Zarembo, hep-ph/ U still remains on the Chiral Circle But =0 Chiral Symmetry Restoration

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 m ~ 720 MeV, f ~240 MeV Ellis & Lanik, PLB(1985)

34 f V Vacuum ( =0) U=1 =f

35 Naive Estimate E/B=M 2 (L) 2 +M 4 (L) +M m (L) 3 +V( )

36 E/B

37

38 In-medium quantities

39 5. Vector Mesons

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

41 KSRF relation : m V =af g 2 22 Bando, Kugo, Yamawaki, Phys. Rep. (1988) pions, chi, rho and omega

42 E/B

43 & without Omega

44 & with Omega

45 6. Ongoing work

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

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. L F

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50

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


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