Topological Structure of Dense Hadronic Matter

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Topological StructureofDense Hadronic Matter
October, 2004 Seoul
V. Vento Universitat de València
Colaborators Heejung Lee (Universitat de
València), Byung-Yung Park (Chungnam Natl
Univ.), Dong-Pil Min (Seoul Natl Univ.)
and Mannque Rho(Saclay Hanyang)
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• Introduction
• Dense Skyrmion Matter
• Pions in Dense Skyrmion Matter
• Sliding Vaccua
• Vector Mesons
• Ongoing work
• Concluding remarks

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1. Introduction
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QCD
Effective Theory
Observation
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Quantum Chromo-Dynamics
Effective Theory at zero Temp./Density
Effective Theory at finite Temp./Density
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Skyrmes Old Idea
1960, T. H. R. Skyrme
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Skyrmes Old Idea
1960, T. H. R. Skyrme
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2. Dense Skyrmion Matter
B.-Y. Park, D.-P. Min, M. Rho, V. Vento, Nucl.
Phys. A707 (2002) 381
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Two Skyrmions
1960, T. H. R. Skyrme
Product Ansatz
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Toroidal B2 Skyrmion
1988, Braaten Carson, 1995, Leese,
Manton Schroers
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Multi-Skyrmion System
http//www.damtp.cam.ac.uk/user/hep/research.html
solitons
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Simple Cubic Skyrmion Crystal
1985, I. Klebanov
U(xLC,y,z) ty U(x,y,z) ty
(E/B)min1.078 at LC5.56
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Half-Skyrmion Crystal
1987, A. S. Goldhaber N. S. Manton
U(xLC,y,z) tyU(x,y,z)ty
additional symmetry
(E/B)min1.076 at LC5.56
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FCC Skyrmion Crystal
1989, L. Castillejo et al. M. Kugler et al.
Y
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Half-Skyrmion CC
Y
Y
z
x
z
y
o
y
LF
X
X
z
z
x
(E/B)min1.038 at Lf4.72
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E/B vs. LF
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lttr(U)gt
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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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Chiral Symmetry Restoration
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GellMann-Oakes-Renner Relation
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GellMann-Oakes-Renner Relation
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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(mp0)
\
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p dynamics(r0)
\
p-skyrmion matter interactions
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p dynamics(r0)
\
Wavefunction renormalization constant Z-1
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Pion effective mass
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Pion velocity in medium
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Pseudogap?
p
fp
s
U still remains on the Chiral Circle But ltUgt0
Zarembo, hep-ph/0104305
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Zarembo, hep-ph/0104305
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4. Sliding Vacuua
H.-J. Lee, B.-Y. Park, M. Rho, V. Vento, Nucl.
Phys. A723 (2003) 427
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Skyrme Lagrangian
Ellis Lanik, PLB(1985) Brown-Rho scaling,
PRL(1992)
mc 720 MeV, fc240 MeV
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Vacuum (r0) U1 cfc
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Naive Estimate
E/BM2(L)C2M4(L) Mm(L) C3V(C)
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E/B
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In-medium quantities
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Without c
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In-medium pion velocity
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5. Vector Mesons
B.-Y. Park, M. Rho, V. Vento, Nucl. Phys. A736
(2004) 129
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Hidden Local Gauge Symmetry
Vector Meson Dominance
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pions, chi, rho and omega
Bando, Kugo, Yamawaki, Phys. Rep. (1988)
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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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ltsgt ltcgt without Omega
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ltsgt ltcgt with Omega
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6. Ongoing work
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Skyrmion from Instanton
1989, M. F. Atiyah N. S.Manton
Introduce variables describing the single
skyrmion dynamics
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time component of SU(2) gauge potential for the
instanton field of charge N
time-ordering
constant 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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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