Topological Structure of Dense Hadronic Matter October, 2004 Seoul V. Vento Universitat de València Colaborators: Heejung Lee (Universitat de València), Byung-Yung Park (Chungnam Nat’l Univ.), Dong-Pil Min (Seoul Nat’l Univ.) and Mannque Rho(Saclay & Hanyang)

1.Introduction 2.Dense Skyrmion Matter 3.Pions in Dense Skyrmion Matter 4.Sliding Vaccua 5.Vector Mesons 6.Ongoing work 7.Concluding remarks

1. Introduction

Theory Effective Relevant degrees of freedom? Dynamics?

Effective Theory QCD Observation

Quantum Chromo-Dynamics Effective Theory at zero Temp./Density Effective Theory at finite Temp./Density

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

Skyrme’s 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

2. Dense Skyrmion Matter B.-Y. Park, D.-P. Min, M. Rho, V. Vento, Nucl. Phys. A707 (2002) 381

Two Skyrmions Product Ansatz 1960, T. H. R. Skyrme

1988, Braaten & Carson, 1995, Leese, Manton & Schroers Toroidal B=2 Skyrmion

Multi-Skyrmion System

1985, I. Klebanov (E/B) min =1.078 at L C =5.56 Simple Cubic Skyrmion Crystal U(x+L C,y,z) =  y U(x,y,z)  y y Y z xz x x x X y LCLC o

Half-Skyrmion Crystal U(x+L C,y,z) =  y U(x,y,z)  y 1987, A. S. Goldhaber & N. S. Manton y zx X LCLC  =-1  =+1 (L c /2 above) + additional symmetry (E/B) min =1.076 at L C =5.56

1989, L. Castillejo et al. & M. Kugler et al. y Y x x X y z=L F /2 plane Y o z z z X z LFLF z=0 plane FCC Skyrmion Crystal

Y X (E/B) min =1.038 at L f =4.72 o z Y z z X z LFLF y x x y Half-Skyrmion CC

E/B vs. L F

Chiral symmetry restoration in dense matter?

3. Pions in Dense Skyrmion Matter H.-J. Lee, B.-Y. Park, D.-P. Min, M. Rho, V. Vento, Nucl. Phys. A723 (2003) 427; Nucl. Phys. A741 (2004) 161

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

GellMann-Oakes-Renner Relation Chiral symmetry restoration

GellMann-Oakes-Renner Relation pion condensation?

Brown-Rho scaling ?

Deeply Bound Pionic States Yamazaki et al., 1998

Skyrme Model ( m  =0 ) \

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

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

Pion effective mass Pseudogap phase?

Pion velocity in medium

ff   Pseudogap? Zarembo, hep-ph/ U still remains on the Chiral Circle But =0 Chiral Symmetry Restoration

Zarembo, hep-ph/

4. Sliding Vacuua H.-J. Lee, B.-Y. Park, M. Rho, V. Vento, Nucl. Phys. A723 (2003) 427

Skyrme Lagrangian Trace Anomaly of QCD m  ~ 720 MeV, f  ~240 MeV Ellis & Lanik, PLB(1985) Brown-Rho scaling, PRL(1992)

ff  V  Vacuum (  =0) U=1  =f 

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

E/B

In-medium quantities

Without 

In-medium pion velocity

5. Vector Mesons B.-Y. Park, M. Rho, V. Vento, Nucl. Phys. A736 (2004) 129

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

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

E/B without Omega

E/B with Omega

E/B

& without Omega

& with Omega

6. Ongoing work

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

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

E/B vs. L F

7. Concluding remarks

The skyrmions role in dense matter

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

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