Topological Structure of Dense Hadronic Matter
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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)
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
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