Topological Structure of Dense Hadronic Matter October, 2004 Seoul V. Vento Universitat de Valncia...
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Transcript of Topological Structure of Dense Hadronic Matter October, 2004 Seoul V. Vento Universitat de Valncia...
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