Topological Structure of Dense Hadronic Matter

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Topological StructureofDense Hadronic Matter
May 2006 Trieste
V. Vento Universitat de València
Colaborators Heejung Lee (APCTP), Byung-Yung
Park (Chungnam Natl Univ.), Dong-Pil Min (Seoul
Natl Univ.) and Mannque Rho(Saclay)
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1. Introduction
2. A theory for Nuclear Structure
3. Dense Skyrmion Matter
4. Pions in Dense Skyrmion Matter
5. Sliding Vaccua
6. Vector Mesons
7. Ongoing work
8. 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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2. A theory for Nuclear Structure
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Skyrmes Old Idea
1960, T. H. R. Skyrme
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Skyrmes Old Idea
1960, T. H. R. Skyrme
BARYON
1983 Adkins,Nappi,Witten,.
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Two Skyrmions
Product Ansatz
1984 Orsay group, VV,..
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Toroidal B2 Skyrmion
1988, Braaten,Carson,. Manton and collaborators

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Multi-Skyrmion Systems (surface of constant
baryon number density)
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Quantization is progressing Manton (B2), Carson
(B3), Walhout (B4), Irwin (B4 to 9), Krusch
(general formalism!)
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3. Dense Skyrmion Matter
B.-Y. Park, D.-P. Min, M. Rho, V. Vento,
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Skyrmion Crystal
1985, CC, I. Klebanov, 1987,
Half-Skyrmion BCC, A. S. Goldhaber
N. S. Manton 1989, FCC Half-Skyrmion CC,
L. Castillejo et al., M. Kugler et
al.
z
2LFCC
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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 B.-Y.
Park, H.-J. Lee, M. Rho, V. Vento
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Skyrme Model(mp0)
\
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p dynamics(r0)
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p-skyrmion matter interactions
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p dynamics(r0)
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Wavefunction renormalization constant Z-1
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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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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 B.-Y. Park, H.-J. Lee, M.
Rho, V. Vento
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Skyrme Lagrangian
Ellis Lanik, PLB(1985)
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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5. Vector Mesons
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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
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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 skyrmion 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