Page 1
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)
Page 2
1. Introduction2.Dense Skyrmion Matter3.Pions in Dense Skyrmion Matter4.Sliding Vaccua5.Vector Mesons6.Ongoing work7.Concluding remarks
Page 4
TheoryEffectiveRelevant degrees of freedom?
Dynamics?
Page 5
Effective Theory
QCD
Observation
Page 6
Quantum Chromo-Dynamics
Effective Theoryat zero
Temp./Density
Effective Theoryat finite
Temp./Density
Page 7
Skyrme’s Old Idea 1960, T. H. R. Skyrme
Page 8
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
Page 9
2. Dense Skyrmion MatterB.-Y. Park, D.-P. Min, M. Rho, V. Vento,
Nucl. Phys. A707 (2002) 381
Page 10
Two Skyrmions
Product Ansatz1960, T. H. R. Skyrme
Page 11
1988, Braaten & Carson, 1995, Leese, Manton & Schroers
Toroidal B=2 Skyrmion
Page 12
Multi-Skyrmion System
http://www.damtp.cam.ac.uk/user/hep/research.html#solitons
Page 13
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
Page 14
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
Page 15
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
Page 16
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
Page 18
<tr(U)>
Chiral symmetryrestoration
in dense matter?
Page 19
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
Page 20
nuclear matter density
-N sigma term
Chiral Symmetry Restoration
pion properties in dense medium?
Page 21
GellMann-Oakes-Renner Relation
Chiral symmetry restoration
Page 22
GellMann-Oakes-Renner Relation
pion condensation?
Page 23
Brown-Rho scaling
?
Page 24
Deeply Bound Pionic States
Yamazaki et al., 1998
Page 25
Skyrme Model(m=0)\
Page 26
dynamics(=0)\
+ -skyrmion matterinteractions
Skyrmion matter
Pion fluctuations on top of the
skyrmion matter
Page 29
dynamics(=0)\
Wavefunction renormalization constant Z-1
Page 30
Pion effective mass
Pseudogap phase?
Page 31
Pion velocity in medium
Page 32
f
Pseudogap?
Zarembo, hep-ph/0104305
U still remains on the Chiral Circle
But <U>=0Chiral Symmetry
Restoration
Page 33
Zarembo, hep-ph/0104305
Page 34
4. Sliding VacuuaH.-J. Lee, B.-Y. Park,
M. Rho, V. Vento, Nucl. Phys. A723 (2003) 427
Page 35
Skyrme Lagrangian
Trace Anomalyof QCD
m ~ 720 MeV, f~240 MeV
Ellis & Lanik, PLB(1985)
Brown-Rho scaling, PRL(1992)
Page 36
f
V
Vacuum (=0)U=1=f
Page 37
Naive Estimate
E/B=M2(L)2+M4(L) +Mm(L) 3+V()
Page 40
In-medium quantities
Page 42
In-medium pion velocity
Page 43
5. Vector MesonsB.-Y. Park, M. Rho, V. Vento, Nucl. Phys. A736 (2004) 129
Page 44
Hidden Local Gauge Symmetry
dilaton
Trace Anomaly
rho & omega vector mesons
HLG
+ Vector Meson Dominance
Page 45
KSRF relation : mV=afg222
Bando, Kugo, Yamawaki, Phys. Rep. (1988)
pions, chi, rho and omega
Page 46
E/B without Omega
Page 49
<> & <> without Omega
Page 50
<> & <> with Omega
Page 52
position
orientation
size
Introduce variables describing the single skyrmion dynamics
Classical mechanicsStatistical mechanicsQuantum mechanics
Skyrmion from Instanton1989, M. F. Atiyah & N. S.Manton
Page 53
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
Page 57
7. Concluding remarks
Page 58
The skyrmions role in dense matter
Page 59
1. Construct dense skyrmion matter 2. Fluctuations
on top of this skyrmion matter.
Properties and Dynamics of hadronsin dense medium.
Page 60
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