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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)
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1. Introduction2.Dense Skyrmion Matter3.Pions in Dense Skyrmion Matter4.Sliding Vaccua5.Vector Mesons6.Ongoing work7.Concluding remarks
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1. Introduction
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TheoryEffectiveRelevant degrees of freedom?
Dynamics?
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Effective Theory
QCD
Observation
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Quantum Chromo-Dynamics
Effective Theoryat zero
Temp./Density
Effective Theoryat finite
Temp./Density
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Skyrme’s Old Idea 1960, T. H. R. Skyrme
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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
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2. Dense Skyrmion MatterB.-Y. Park, D.-P. Min, M. Rho, V. Vento,
Nucl. Phys. A707 (2002) 381
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Two Skyrmions
Product Ansatz1960, T. H. R. Skyrme
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1988, Braaten & Carson, 1995, Leese, Manton & Schroers
Toroidal B=2 Skyrmion
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Multi-Skyrmion System
http://www.damtp.cam.ac.uk/user/hep/research.html#solitons
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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
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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
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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
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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
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E/B vs. LF
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<tr(U)>
Chiral symmetryrestoration
in dense matter?
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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
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nuclear matter density
-N sigma term
Chiral Symmetry Restoration
pion properties in dense medium?
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GellMann-Oakes-Renner Relation
Chiral symmetry restoration
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GellMann-Oakes-Renner Relation
pion condensation?
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Brown-Rho scaling
?
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Deeply Bound Pionic States
Yamazaki et al., 1998
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Skyrme Model(m=0)\
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dynamics(=0)\
+ -skyrmion matterinteractions
Skyrmion matter
Pion fluctuations on top of the
skyrmion matter
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dynamics(=0)\
Wavefunction renormalization constant Z-1
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Pion effective mass
Pseudogap phase?
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Pion velocity in medium
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f
Pseudogap?
Zarembo, hep-ph/0104305
U still remains on the Chiral Circle
But <U>=0Chiral Symmetry
Restoration
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Zarembo, hep-ph/0104305
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4. Sliding VacuuaH.-J. Lee, B.-Y. Park,
M. Rho, V. Vento, Nucl. Phys. A723 (2003) 427
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Skyrme Lagrangian
Trace Anomalyof QCD
m ~ 720 MeV, f~240 MeV
Ellis & Lanik, PLB(1985)
Brown-Rho scaling, PRL(1992)
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f
V
Vacuum (=0)U=1=f
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Naive Estimate
E/B=M2(L)2+M4(L) +Mm(L) 3+V()
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E/B
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In-medium quantities
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Without
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In-medium pion velocity
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5. Vector MesonsB.-Y. Park, M. Rho, V. Vento, Nucl. Phys. A736 (2004) 129
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Hidden Local Gauge Symmetry
dilaton
Trace Anomaly
rho & omega vector mesons
HLG
+ Vector Meson Dominance
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KSRF relation : mV=afg222
Bando, Kugo, Yamawaki, Phys. Rep. (1988)
pions, chi, rho and omega
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E/B without Omega
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E/B with Omega
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E/B
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<> & <> without Omega
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<> & <> with Omega
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6. Ongoing work
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position
orientation
size
Introduce variables describing the single skyrmion dynamics
Classical mechanicsStatistical mechanicsQuantum mechanics
Skyrmion from Instanton1989, M. F. Atiyah & N. S.Manton
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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
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E/B vs. LF
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7. Concluding remarks
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The skyrmions role in dense matter
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1. Construct dense skyrmion matter 2. Fluctuations
on top of this skyrmion matter.
Properties and Dynamics of hadronsin dense medium.
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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