Topological Structureof

Dense Hadronic Matter

October, 2004Seoul

V. VentoUniversitat 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. Introduction2.Dense Skyrmion Matter3.Pions in Dense Skyrmion Matter4.Sliding Vaccua5.Vector Mesons6.Ongoing work7.Concluding remarks

1. Introduction

TheoryEffectiveRelevant degrees of freedom?

Dynamics?

Effective Theory

QCD

Observation

Quantum Chromo-Dynamics

Effective Theoryat zero

Temp./Density

Effective Theoryat finite

Temp./Density

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

Skyrme’s Old Idea

U(x) : mapping from R3-{ }=S3 to SU(2)=S38

topological soliton

1960, T. H. R. Skyrme

R ~ 1 f m M ~ 1.5 GeV

BARYON

2. Dense Skyrmion MatterB.-Y. Park, D.-P. Min, M. Rho, V. Vento,

Nucl. Phys. A707 (2002) 381

Two Skyrmions

Product Ansatz1960, T. H. R. Skyrme

1988, Braaten & Carson, 1995, Leese, Manton & Schroers

Toroidal B=2 Skyrmion

Multi-Skyrmion System

http://www.damtp.cam.ac.uk/user/hep/research.html#solitons

1985, I. Klebanov

(E/B)min=1.078 at LC=5.56

Simple Cubic Skyrmion Crystal

U(x+LC,y,z) =y U(x,y,z) y

y

Y

z

x z

xx

x

Xy

LC

o

Half-Skyrmion Crystal

U(x+LC,y,z) =yU(x,y,z)y

1987, A. S. Goldhaber & N. S. Manton

y

z x

X

LC

=-1=+1(Lc/2 above)

+ additional symmetry

(E/B)min=1.076 at LC=5.56

1989, L. Castillejo et al. & M. Kugler et al.

y

Y

x

x

Xy

z=LF/2 plane

Y

o

z

z z

X

z

LF

z=0 plane

FCC Skyrmion Crystal

Y

X

(E/B)min=1.038 at Lf=4.72

o

z

Y

z z

X

z

LF y

x

x

y

Half-Skyrmion CC

E/B vs. LF

<tr(U)>

Chiral symmetryrestoration

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 matterinteractions

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

Pseudogap?

Zarembo, hep-ph/0104305

U still remains on the Chiral Circle

But <U>=0Chiral Symmetry

Restoration

Zarembo, hep-ph/0104305

4. Sliding VacuuaH.-J. Lee, B.-Y. Park,

M. Rho, V. Vento, Nucl. Phys. A723 (2003) 427

Skyrme Lagrangian

Trace Anomalyof QCD

m ~ 720 MeV, f~240 MeV

Ellis & Lanik, PLB(1985)

Brown-Rho scaling, PRL(1992)

f

V

Vacuum (=0)U=1=f

Naive Estimate

E/B=M2(L)2+M4(L) +Mm(L) 3+V()

E/B

In-medium quantities

Without

In-medium pion velocity

5. Vector MesonsB.-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 : mV=afg222

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 mechanicsStatistical mechanicsQuantum mechanics

Skyrmion from Instanton1989, M. F. Atiyah & N. S.Manton

time component of SU(2) gauge potential for the instanton field of charge N

time-orderingconstant matrix to make U approach 1 at infinity

constant rotation matrix

E/B vs. LF

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 hadronsin 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