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

orientationsize

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