Presentation is loading. Please wait.

Presentation is loading. Please wait.

Topological Structure of Dense Hadronic Matter

Similar presentations


Presentation on theme: "Topological Structure of Dense Hadronic Matter"— Presentation transcript:

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

16

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

22

23

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

37

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

49

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


Download ppt "Topological Structure of Dense Hadronic Matter"

Similar presentations


Ads by Google